Owner’s Risk Management System

Currently, with the development of digital management in companies, negative trends are increasing due to the lack of new tools to identify critical deviations that reduce business efficiency. Overcoming this negative trend in practice is carried out by creating an effective risk management system. The example of owner’s risk management shows their place in the process of creating value, defined the role of participants in this activity, On the example of financial risks, a system of measures to minimize risks for a manufacturing company is described. The key focus of the study is the assessment of the relationships between the financial component of owner’s risks, places of their occurrence, risk factors and the degree of influence on potential losses of the company owner.

Therefore, the owner must correctly assess the degree of risk and be able to manage risk in order to achieve more effective results in the market. This is only possible if there is a certain risk management system that is an integral part of ownership management.
There are a significant number of studies on risk management systems. Most of them cover the tools inherent in managers. A number of researchers focused on analyzing fundamental approaches to Risk assessment and management. An example is T.Aven's publication [1]. In this paper, investigated principles and methods, which developed for how to conceptualize, assess and manage risk linked to both the theoretical platform and practical models and procedures.
Another approach is to evaluate management decisions by Risk-Informed Decision-Making (RIDM) methodology [2]. Decision-making considered under the influence by various factors (strategic, technical/technological, economic, organizational, regulatory, safety, markets, etc.). Sound decisionmaking in AM ought to take into account relevant factors in order to balance risks, opportunities, performance, costs and benefits.
At the company level, Enterprise Risk Management (ERM) accepted as a tool that allows the management to strengthen the positive influence from the drivers and overcome the challenges posed by the significant hindrances. Companies in various countries and fields of activity focus this aspect of risk management on research. For example, Chinese construction firms in Singapore [3], Croatian Companies [4], Malaysian companies [5], petrochemical industry companies [6], French firms [7], Australia, Germany and the USA companies [8], Spanish companies [9].
Analysis of studies revealed that RIDM and ERM goals are to increase the likelihood that an organization will achieve its objectives, meaning that ERM should be created and implemented with the aim to protect and create shareholder value. For example, research of Croatian Companies revealed that the level or risk management system development is dependent only on the size of the company and value of the growth options. At the same time, this does not answer the question of creating a system for managing ownership risks, which require special tools different from those used by managers.

II. EXPLORE IMPORTANCE OF THE PROBLEM
Risk management is the processes associated with identification, risk analysis and decision-making, which include maximizing the positive and minimizing the negative consequences of risk events.
Risk management includes risk management strategy and tactics. Risk analysis allows owners to evaluate decisions and minimize possible losses. A prerequisite for an effective owners' risk management system is the availability of relevant information for making timely management decisions and optimally aligned business processes in all aspects of its activities.
The key elements of an owner's risk management system (ORMS) are: The object of an ORMS is a significant owner's risk, which to the arising in the process of creating value for the consumer and is a combination of the probability of an event and its consequences. Then the owner's work with the risk object is to analyze the types of risks of the company, their classification and regulation of the rules for exposure to risks.
The subject of an ORMS is a unit or individual employee who is specially trained to respond to risks and participate in various stages of owner's risk management (Table 1).

Source: prepared by Authors
The methodology for building a risk management system is based on the fact that the participation of a business owner in managing an organization is to solve two problems:1) define a business model (strategic goals and mechanisms for their achievement) and 2) to formulate its participation in the current (operational activity) of the company.
A business model is an idea of how a company makes (or intends to make) money. The business model describes the value that the company offers to various customers, reflects the organization's abilities, the list of partners required to create, promote and deliver this value to customers, necessary to obtain sustainable revenue streams.
The business model also defines the interaction of elements of the organization as a system -material and intangible resources, equipment, products, technologies, personnel, customers, partners, etc.

III. MATERIALS AND METHODS
The owner's risk in the business model are the possibility of achieving strategic goals with a certain period and reasonable costs. In this case, the development and subsequent operation of the owner's risk management system can reduce the time and cost of achieving the strategic goals of the organization, as well as increase the investment attractiveness of projects.
An effective owner's risk management system allows you to get investment in the business on favorable terms. Thus, it becomes possible to accelerate the development processes of the organization, to reduce the time to achieve strategic goals (Fig  1).
When defining a business model, a set of unique features can be quite wide. At the same time, the key elements of the business model of any company that determine its content are: • he values for customers that the company offers on the basis of its products and services; • value creation system, including suppliers and target customers, as well as value chains; • the assets that the company uses to create value; • he financial model of the company, which determines both the structure of its costs and the ways of making profit.
Another significant aspect of the definition of a business model is related to the fact that a business model is often confused with a strategy, replacing one concept with another, or including strategy as one of the components in the business model. Sometimes companies go bankrupt, despite the presence of a well-developed model, it happens and vice versa: the company prospers, although its business model is quite "loose". Nevertheless, the business model can provide significant benefits to both the entrepreneur himself and other interested parties (his employees, banks, business partners, consultants).
The business model is not something rigid and unchanged until the end of the life of the company -together with the company it lives, develops, adapts to changing environmental conditions. On the contrary, often in conditions of increasing competition or, conversely, seizing clear leadership, companies try to make the transition to more efficient or profitable business models.
In order to create an effective business model, the owner needs to create a quality value chain. When analyzing the value chain, the processes included in them are considered enlarged, for example, the production process, the storage process, the delivery process, etc.
The most important indicator of each link in the chain is the part of value it creates. The risks of a business model are realized with a process approach, the use of which can reorganize the value chain in order to: • eliminating stages that do not add value; • elimination of problems at the junction of stages; • increase the efficiency of individual stages of the chain; • adding new links or combining existing links with suppliers and consumers to jointly carry out individual processes in the chain.
Analysis and subsequent reorganization of the value chain in terms of ownership risks allow: • find out the optimality of the business model of the company as a whole, including highlighting those processes that increase or decrease its added value; • get benefits by reorganizing the chain (selling part of the business that is part of the chain, or outsourcing part of its processes, purchasing another company to gain control over a critical part of the chain, creating strategic partnerships with suppliers to reduce costs in a certain part of the chain or reduce risks, etc.); • effectively implement the organization's strategy from the standpoint of using resources for the development of

IV. RESULTS
For a business owner, the risks consist in the inefficient use of available financial resources, which is manifested in the discrepancy between the directions of their use and the sources of financing.
In order to identify possible risks, the owner receives from each stage of the value chain information on the directions of using the company's own working capital invested in settlements with suppliers and customers, stocks of raw materials, materials, finished products, work in progress.
Next comes the moment of assessing the risk factors. They may be decisions of the owner of the company, for example, an incorrect assessment of a business model, lack of resources for funding sources, ineffective actions of managers, for example, poor financial planning and budgeting, or false reporting data.
Clarification of risk factors is a key point of the management system for the owner, as they determine the value of potential losses. There are several components of potential losses of the owner of the company (by significance): loss of company profit, decrease in business capitalization, etc. (Tables 2 and 3).  The role and importance of the owner's risks management system consists, ultimately, in the use of management tools that solve the tasks of risk management: risk prevention, minimizing the consequences of risks and risk insurance. Such tools are the following: selection of risk assessment indicators, assessment of indicator boundaries, and development of risk management measures and visualization of the risk state using the "traffic light" indicator values (red, yellow, and green).
Consider the assessment of owner's risks on the example of the financial component of the company. Take the risk «Inconsistency of sources for financing needs» (he answers to the question -"Where are the funds invested?").
For each range of indicator values ("red", "yellow", "green"), conditions are developed in advance under which the owner and the hired manager are included in risk management, for which typical activities are formed that they should take.
For example, risk «Inconsistency of sources for financing needs» may arise due to the growth of balances in the finished goods warehouse. The risk factor is insufficient sales. The risk probability will be 40% for the "Losses" indicator, and by its magnitude, the risk will lead to losses of 56 million rubles. ("Red" zone of the risk scale). At the same time, the decrease in the company's capitalization will amount to 8 million rubles. ("Green" zone of the risk scale). Thus, if there is a "green" zone of the risk scale, the owner should take radical steps to reduce the balance of finished products in the warehouse.
On this basis, in the future, relationships established between the manifestation of the financial component of ownership risks, places of their occurrence, risk factors (causes), and degree of influence on potential losses of the company owner Evaluation of these connections requires specific actions by the business owner and hired managers, for which it is necessary to have an action plan that is aimed at quickly responding to the deviations in the company's activities, potentially leading to losses.

V. CONCLUSION
The implementation of measures may not lead to a reduction in ownership risks due to various reasons, one of which is mainly the inconsistency of measures with risks. To understand the reasons for this situation, the business owner should analyze the relationship between the measures and the correct understanding of the place of occurrence of risks, factors and reasons for the appearance of risks, quantitative and qualitative assessment of the significance of risks, as well as calculations of potential losses due to risks.
Because of the analysis of the decision to change the ownership risk management system, it may concern changes in measures, clarification of the composition of experts who participate in assessing the likelihood of risks, nonperformance of staff and insufficient qualifications, etc.


extfieldsofstudy:
Computer Science
Mathematics

text:
Exact and heuristic solutions for the assembly line balancing problem with hierarchical worker assignment

This paper proposes new algorithms for the assembly line balancing problem with hierarchical worker assignment (ALBHW). The ALBHW appears in real industrial contexts where companies deal with a multi-skilled workforce. It considers task execution times that vary depending on the worker type to whom the task is assigned. Qualification levels among workers are ranked hierarchically, where a lower qualified worker costs less but requires larger execution times. The aim is to assign workers and tasks to the stations of an assembly line, in such a way that cycle time and precedence constraints are satisfied, and the total cost is minimized. In this paper, we first present a mathematical model and improve it with preprocessing techniques. Then, we propose a constructive heuristic and a variable neighborhood descent that are useful to solve large instances. Extensive computational experiments on benchmark instances prove the effectiveness of the algorithms.

Introduction
Assembly lines are essential parts of manufacturing systems for large scale production (see, e.g., Becker and Scholl 2006, Cortés, Onieva, and Guadix 2010, Otto and Otto 2014and Dolgui et al. 2019). An assembling process consists of a fixed set of tasks (indivisible elements), which need to be executed on stations while taking into account technological precedence relations. The simple assembly line balancing problem (SALBP) is the basic problem encountered when optimizing assembly systems. It considers straight assembly lines and aims at assigning tasks to stations in such a way that task precedence constraints are satisfied, and the total amount of time for each station does not exceed a maximum productive rate called cycle time. Two main SALBP variants have been considered in the literature: the SALBP-1 aims at minimizing the number of stations for given cycle time, whereas the SALBP-2 aims at minimizing the cycle time for a fixed number of stations. We refer the reader interested in the SALBP literature to Baybars (1986), Scholl and Becker (2006), Becker and Scholl (2006), Boysen, Fliedner, and Scholl (2007), and Battaïa and Dolgui (2013), among others.
In this paper, we study the assembly line balancing problem with hierarchical worker assignment (ALBHW). The problem has been introduced by Sungur and Yavuz (2015) and generalizes the SALBP-1. It considers task times that depend on the workers, and workers that are divided into hierarchical skill levels. Workers need to be assigned to a station that contains tasks that are compatible with their skills. A worker with higher qualifications incurs a higher cost but executes tasks taking shorter times. The goal is to find a minimum-cost assignment of tasks and workers to the stations of the line while satisfying maximum cycle time as well as precedence constraints. The problem is NP-hard in the strong sense. As stressed in Sungur and Yavuz (2015), applications of the ALBHW are numerous and can be found in contexts such as health-care, military, manufacturing, and maintenance systems. In addition, studying hierarchical worker assignment is of interest not only for the ALBHW but also because this characteristic might be found in many other types of assembling and disassembling problems (see, e.g., Özceylan et al. 2019), just to cite some.
Our contribution to the solution of the ALBHW is threefold. First, we propose a new formulation that strengthens the mathematical model by Sungur and Yavuz (2015). Second, we implement a station-based constructive heuristic that combines a number of task priority and worker priority selection rules. Third, we present a variable neighborhood descent (VND) algorithm (Mladenović and Hansen 1997) composed of two neighborhood procedures, both based on the use of mixed integer linear programs (MILP). The computational tests that we performed on the benchmark problem instances show that the new formulation improves the previous one for what concerns both the optimality gap and the execution time. The improvement is sometimes small but consistent on all attempted instances. Instances with up to 50 tasks can be solved to proven optimality in a matter of seconds, whereas for large-sized instances, involving 100 tasks, we need to content us with heuristic solutions. The VND produces solutions that are just 2% away, on average, from the best-known solution values, requiring short computing times.
The remainder of the paper is organized as follows. In Section 2, we present the formal definition of the ALBHW. Section 3 surveys the related literature, focusing on multi-skilled and heterogeneous worker assignments, and on labor-cost variants. Section 4 presents the mathematical model by Sungur and Yavuz (2015), as well as our improvements. The heuristic procedures that we implemented are provided in Section 5, and the computational experiments are discussed in Section 6. Final remarks and conclusions are given in Section 7.

Formal problem definition
We consider a single product straight assembly line. Let T = {1, 2, . . . , n} be the set of indivisible tasks to be allocated in the line, and S = {1, 2, . . . , m} be the set of stations, where m is an upper bound on the number of stations required to process all tasks (e.g., m = n). We use the notation i j to state that task i must be executed before task j in the line, i.e., the index of the station processing i should be lower than or equal to the index of the station processing j. The task precedence network is represented by a topological ordered graph G = (T, E), where E = {(i, j) : i j}. Figure 1 gives an example (extracted from a benchmark by Sungur and Yavuz 2015) of a precedence graph involving 13 tasks and 10 precedences.
Let K = H = {1, 2, . . . , l} be two coincident set denoting, respectively, the set of task types and that of workers types, where l stands for the number of qualification levels. We use index k to denote a task type, and index h to denote a worker type. In this notation, the workers of type 1 are the most qualified, while those of type l are the less qualified. Each task i ∈ T has a type k i ∈ K, and can only be executed by workers of type h satisfying h ≤ k i .
Each task i is also characterized by an execution time t ih that depends from the worker type h that executes i. We assume that the execution time of each task increases when lower-qualified workers are employed, that is, t i1 ≤ t i2 ≤ . . . ≤ t il . The right top part of Figure 1 gives an example of execution times. If a task requires a minimum qualification level higher than the one possessed by a worker, then the worker cannot execute such a task. In our notation, this is simply represented in the time matrix by a value +∞.
The cost of assigning a worker of type h to a station is defined by c h , for h ∈ H, and is proportional to its qualification level, so that c 1 ≤ c 2 ≤ . . . ≤ c l . Given a cycle time C, that is, a maximum total execution time allowed at each station, the ALBHW is to assign workers and tasks to stations in order to minimize the total cost, while satisfying constraints on qualifications levels, cycle time, and task precedences. In Figure 2, we present an optimal solution for the instance given in Figure 1. We use h(s) to denote the worker type assigned to station s, andC(s) to denote the total execution time computed according to the worker/task assignment in the station. In this example, we have C = 600, c 1 = 100, c 2 = 70, and c 3 = 49, and so the solution cost is 319.

Brief literature review
The interest of the scientific community in incorporating heterogeneity in assemblyline problems has increased over the years. Surveying the entire literature produced in the field is out of the scope of our work. Nevertheless, in this section, we provide the reader with a brief literature review that focuses on those aspects that are most relevant to the problem we tackle. In particular, we focus on articles that take into account (i) manufacturing systems with skilled level workers, (ii) heterogeneity over task execution times for each worker, and (iii) hierarchical labor-cost assembly lines. We refer the reader interested in the vast area of assembly line systems to the surveys by Becker and Scholl (2006), Cortés, Onieva, and Guadix (2010), Battaïa and Dolgui (2013), and Otto and Otto (2014). Generalizations of the SALBP involving different task precedence constraints can be found in Dell'Amico, Díaz Díaz, and Iori (2012) and Kramer, Dell'Amico, and Iori (2017), among others. These last works also gave inspiration to the improvement techniques that we present below in Sections 4.1 and 4.2. Mansoor (1968) introduced worker performance skills to define task execution times in assembly line systems. He also proposed a constructive heuristic based on positional weighting criteria. Bartholdi III and Eisenstein (1996) considered a case study at Toyota Sewn Products Management System, where workers were classified according to different speed levels. Their results show that sequencing workers from the slowest to the fastest can produce a reasonable line balance. Gel, Hopp, and Van Oyen (2002) considered the possibility of sharing tasks among workers whose task execution times differ by a multiplicative factor. Their study uses a Markov decision process to find good-quality solutions. This approach was later extended by Hopp, Tekin, and Van Oyen (2004), who included cross-training schemes during task assignments. Techawiboonwong, Yenradee, and Das (2006) presented a mathematical model that considers the presence of both permanent (skilled) and temporary (unskilled) workers, as well as specific constraints on the worker assignment on some stations. In the same context, Corominas, Pastor, and Plans (2008) applied a model to solve a rebalancing problem arising in motorcycle assembly lines. They considered given incompatibilities among groups of tasks and aimed at minimizing the number of temporary workers employed. In their experimental tests, optimal solutions were found for some realistic instances within a limited computational effort. Koltai, Tatay, and Kalló (2014) presented a similar approach, but focused, instead, on workforce skills in the context of bicycle assembly lines. We refer to De Bruecker et al. (2015) for a survey on workforce planning under different skills. Miralles et al. (2007) introduced the assembly line worker assignment and balancing problem (ALWABP), as a problem arising in the context of sheltered worker centers for disabled (SWD) in Valencia (Spain). In the ALWABP, task execution times vary according to the workers, not all workers can perform all tasks, and the aim is to minimize the required cycle time. The authors solved the problem by utilizing a mathematical model. Since the ALWABP is NP-hard, heuristic methods have been developed for its solutions. Among these, we mention clustering search by (Chaves, Miralles, and Lorena 2007), beam search by (Blum and Miralles 2011), tabu search by (Moreira and Costa 2009), genetic algorithms by (Moreira et al. 2012;Mutlu, Polat, and Supciller 2013;Moreira and Ritt 2019), and variable neighborhood search by (Polat et al. 2016). Concerning exact methods for the ALWABP, we highlight the branch-and-bound approaches proposed by Miralles et al. (2008), Borba and Ritt (2014), and Vila and Pereira (2014). The particular ALWABP case in which the heterogeneity derives from the presence of robots is known as robotic assembly line balancing problem (RALBP). Cost-oriented approaches, which minimize the robot selection and task allocation costs, have been proposed by Rubinovitz, Bukchin, and Lenz (1993), Bukchin and Tzur (2000), and Pereira, Ritt, and Vásquez (2018).
Hierarchical workforce scheduling (HWS) is a class of problems that has, as its basis, the objective to find the most economical mix of workers that satisfies given labor requirements and worker characteristics. Since the seminal work by Emmons and Burns (1991), several authors have attempted to solve HWS problems. Hung and Emmons (1993) proposed a mathematical model for an HWS variant with compressed workweek arrangements and multiple shifts (rotation and downward worker substitutability). Hung (1994) minimized the labor costs in an HSW problem through a heuristic method, considering the possibility of a single-shift off-day. Still taking a single-shift off-day in seven-day-a-week industries, Narasimhan (1997) implemented an algorithm that minimizes the labor costs subject to a pre-defined demand of workers and desired work characteristics. Seçkiner, Gökçen, and Kurt (2007) and Pastor and Corominas (2010) extended the approach by Billionnet (1999), who studied an HWS case with variable demand, by including compressed workdays and suitability of task assignments. More recently,Özgüven and Sungur (2013) proposed five mathematical models to solve an HWS variant with divisible and indivisible tasks, by minimizing total costs.
As far as we know, Sungur and Yavuz (2015) is the only work directly focused on the ALBHW. Apart from introducing the problem, they also presented a mathematical model and performed extensive tests on a set of instances adapted from Otto, Otto, and Scholl (2013). Using CPLEX 12.3, their formulation found optimal solutions for small-size instances with 20 tasks but could not prove optimality for a number of medium-sized instances involving 50 tasks. These results motivate our work on the development of improved models and new effective heuristics for the problem.

Mathematical models
We first introduce the MILP model by Sungur and Yavuz (2015) and then discuss our improvements. We follow the notation given in Section 2. In addition, we use P i ⊆ T to denote the set of direct predecessors of task i, i ∈ T , and F i ⊆ T to denoted the set of direct successors of task i, i ∈ T . We also compute the transitive closures of these sets, and use P * i and F * i to denote, respectively, all (direct and indirect) predecessors and all successors of a task i, i ∈ T . Consider for example Figure 1, where we have , 7, 8, 9, 11, 12, 13}. The MILP model that we developed is based on the four families of decision variables given in Table 1, three of which are binary and one integer. takes the value 1 iff station s ∈ S is opened; x ihs ∈ {0, 1} takes the value 1 iff a worker of type h performs task i in station s; y hs ∈ {0, 1} takes the value 1 iff a worker of type h is assigned to station s; z h ∈ Z + gives the total number of workers of type h assigned to the stations.
The model by Sungur and Yavuz (2015), called MSY for short, is as follows: subject to: h∈H,h≤ki s∈S The objective function (1) minimizes the total cost of the assembly line. Constraints (2) guarantee that each task is assigned to a station. Constraints (3) impose the assignment of exactly one worker to a station if such station is opened. Coupling constraints between x ihs and y hs variables are ensured by (4). Constraints (5) determine the total amount of workers of type h that are assigned to the stations. Constraints (6) establish the precedence relations between the pairs of tasks. Constraints (7) prevent the total workload of each opened station to exceed the cycle time. Inequalities (8) allow a station s + 1 to be opened only if the previous station s is also opened. Constraints (9)-(12) define the domains of the variables. This model has O(|T ||H||S|) variables and O(|T | 2 + |H||S|) constraints.

Preprocessing
We use two preprocessing techniques, both aimed at including additional information, in terms of new arcs and precedence weights on arcs, in the input precedence graph G = (T, E). Recall, indeed, that G does not have precedence weights, so, if (i, j) ∈ E, then i and j can be assigned to the same station. The inclusion of new arcs and precedence weights can be beneficial for creating stronger cuts and valid inequalities (to be described next in Section 4.2). Both our two preprocessing techniques share this scope, but the first technique builds upon the cycle time restriction, whereas the second uses the sequence of precedences. The first technique creates an auxiliary graph G ′ , starting from the original graph G, as follows.
In addition, let A ′ ij denote the subset of arcs that belong to all paths from N ′ ij . Let LB ij be a lower bound on the number of station required to process all tasks in G ′ ij . We compute LB ij = k∈N ′ ij t k1 /C − 1 as the continuous lower bound on the processing times of the tasks, by considering the case in which they are executed by the fastest worker (of type 1). We then associate each LB ij with its corresponding arc A ′ ij . These values are used to produce improved inequalities and are the starting point of the next preprocessing technique. Let Z vnd be the cost of the solution found by the VND procedure. We define m ub = ⌊Z vnd /c l ⌋, which is the upper bound of workstations.
In the second technique, we solve the longest path problem using the classical critical path method (CPM) to obtain the earliest and latest station index to which task i ∈ T can be assigned, denoted by e i and l i , respectively. We create a new auxiliary graph G = (N ,Ā), based on the LB ij values. The arc values of G ′ are first copied toḠ. LetN = N ′ ∪ {0, n + 1}, where 0 and n+1 are two dummy tasks that represent the beginning and the end of all activities, respectively. To create the new arcs in the graph, we first updateĀ = A ′ ∪ {(0, i)}, ∀i ∈ T having P i = ∅, thus imposing 0 as source vertex. We then updateĀ =Ā ∪ {(j, n + 1)}, ∀j ∈ T having F j = ∅, thus imposing n + 1 as sink. After this update, we have a graph in which all vertices are connected directly or indirectly with the source and the sink. With the first step of the CPM, we are able to define the earliest workstation e i in which any task i can be processed. With the second step, we compute the latest workstation l i in which i can be processed. In detail, the value of l i is obtained by first setting l n+1 = m ub . Then, we take the transpose graph of G, named G t , and compute the earliest station of its tasks,ẽ i , by the CPM. The output of the preprocessing procedure is an interval [e i , l i ] of workstations, ∀i ∈ T .

Improvements to the mathematical model
We developed some techniques for improving the linear relaxation of the MSY model and removing useless variables. First, we set the number of workstations in the model to m = m ub . Then, we apply two reformulations to Constraints (4) and (7). We start by strengthening n in Constraints (4) by a sufficient large constant M h ≤ n, thus obtaining: The value of M h is computed by considering the maximum number of tasks that can be assigned to a station, while satisfying the cycle time C without precedence constraints and considering an assignment of only h-type workers to the stations. Such value is obtained, for each h ∈ H, by solving the MILP problem: subject to: i∈T :h≤ki where α i is a binary variable that takes the value 1 if task i is selected in the subset of maximum cardinality, and 0 otherwise. Model (14)- (17) is a maximum cardinality knapsack problem with additional incompatibilities imposed by (16). The maximum cardinality knapsack problem is easy, but the addition of the incompatibilities makes it an NP-hard problem. Nevertheless, the above MILP model can be solved very quickly for instances of medium size, as the ones that we face in our tests.
We use a similar technique for Constraints (18), replacing the original t ih values with new ones, t ′ ih ≥ t ih , resulting in: Each new value is obtained, for i ∈ T and h ∈ H, by solving a subset sum problem (SSP): given a station of capacity C −t ih and a set of tasks T /{i}, determine the subset of tasks not exceeding the capacity but having largest total time. The SSP solution value, denoted by ∆ ih , is obtained by solving the following model: subject to: where again α j takes the value 1 if task j is selected, and 0 otherwise. The SSP is known to be NP-hard, but, model (19)-(22) too can be quickly solved for instances of medium size. Once the problem is solved, we set t ′ ih = C − ∆ ih .
We also modify precedence constraints (6) Furthermore, for each station s that has the index smaller than the earliest possible or greater than the latest possible, we include the following reduction: Let us consider the number z 1 of workers of type 1 (i.e., the highest qualified ones). We limit by below this value by considering those tasks that can only be executed by workers of type 1 (i.e., those for which k i = 1), and computing a continuos lower bound on their processing times. We consequently add to the model the constraint: The resulting MILP model, called MCIM in the following, is to minimize (1) subject to (2), (3), (5), (8)-(13), (18) and (23)-(25).

Heuristic algorithms
In this section, we present a constructive heuristic based on the use of different priority rules, and then improve it employing a VND algorithm.

Constructive heuristic
The constructive heuristic that we built is inspired by Scholl and Voß (1997) and Moreira et al. (2012), and aims at filling one station at a time. For each station, and for each candidate worker type h ∈ H, the heuristic creates a set of tasks by using an input task priority rule while respecting precedence and cycle time constraints. Then, a worker type and the corresponding set of tasks just created are selected to be assigned to the station according to a given worker priority rule. The process is repeated until all tasks have been assigned. We implemented the following task priority rules: (t.1) max successors: select a task i having largest |F * i | value; (t.2) max direct successors: select a task i having largest |F i | value; (t.3) largest min processing time: select a task i with largest t i1 value; (t.4) largest max processing time: select a task i with largest t iki value; (t.5) largest min positional weight: select a task i with largest t i1 + j∈F * i t j1 value; (t.6) largest max positional weight: select a task i with largest t iki + j∈F * i t jki value; (t.7) largest positional weight: select a task i with largest t ih + j∈F * i t jh value; (t.8) shortest min processing time: select a task i with shortest t i1 value; (t.9) largest direct sucessors processing time: select a task i with largest |F i |/(t ih + j∈S * i t jh ) value; (t.10) largest successors processing time: select a task i with largest |F * i |/t ih value; (t.11) largest processing time: select a task i with largest t ih value; (t.12) largest worker-type processing time: select a task i with largest t iki , with k i = h; (t.13) shortest worker-type processing time: select a task i with shortest t iki , with k i = h; where for positional weight we simply mean the processing time of the job and of all its successors. Other techniques that we attempted did not produce improvements in the computational performance, and were thus disregarded. In addition, we implemented the following worker priority rules: (w.1) look ahead worker : select a worker of type h, by estimating the total cost in case h would not be chosen anymore. We divide the tasks not assigned yet by their larger worker type k i . Let λ h be the approximated solution cost in case no further worker of type h would be chosen and each remaining task i would be assigned to a larger worker type h ′ = h, h ′ ≤ k i . Let c curr be the cost of the partial solution under construction and recall c h is the cost of worker type h. We select the worker type h that produces the smallest {c curr + c h + λ h } value. (w.2) smallest cost per task assigned: select a worker type h that has the smallest c h /|T h | value; (w.3) smallest time per task assigned: select a worker type h that has the smallest c h /( i∈Th t ih ) value, where T h is the set of tasks assigned to worker type h; (w.4) largest time per workstation: select a worker type h that has the largest i∈Th t ih value.
The pseudocode of the constructive heuristic is given in Algorithm 1. It receives in input the set T of tasks, the worker priority rule, w rule, and the task priority rule, t rule. Starting from an empty station s, each step of the main loop operates as follows. Line 5 defines the setT , composed by candidate tasks that respect the precedence constraints at the current station. Line 7 creates a subset T h ⊆ T , for each worker type h, by respecting the cycle time restriction and using the rule t rule. If the worker of type h cannot execute a task chosen by t rule, then a new task is chosen with the largest time for the worker h, always considering the precedence or cycle time constraints. The worker priority rule is used at Line 9 to select the best worker according to its cost and its subset T h . Lines 10-13 perform the necessary updates on the data structures. The algorithm finally returns the number s of stations used, the set W of selected workers, and the task assignment S. return sol CH ={s, W, S} 16: end procedure

Improving heuristic solutions
We developed a VND procedure that makes use of two MILP-based neighborhood procedures. Throughout the procedure, the upper bound on the number of stations is set to the number of stations produced by the solution sol CH found by the constructive heuristic of Section 5.1. Algorithm 2 shows the pseudocode of the VND. The initial solution sol CH is copied into the incumbent sol best , which is then modified iteratively by means of k max = 2 neighborhood procedures N k . Such procedures are described in detail in the next two sections. return sol best 14: end procedure

Task relocations
The first local search procedure, called MILP-1, allows tasks to be reassigned to stations that are adjacent to the station in which they were assigned to in the input solution. Letm be the number of workstations in the input solution. Suppose task i was assigned to station s i , and let N i be the set of stations to which i can be reassigned. Formally, we set: Procedure MILP-1 finds the reallocations of tasks that is optimal with respect to these limited sets by solving the following model: subject to (3)-(12) and: h∈H,h≤ki s∈N (i) In practice, this is equivalent to the original model above in Section 4, but its size is consistently reduced by replacing constraints (2) by (27).

Worker and task reassignment
The second local search procedure, MILP-2, allows the tasks to be relocated in any position (while respecting the constraints), but requires that the number of workers for each type remain unchanged with respect to the input solution. To this aim, we create auxiliary binary variables β s , for s = {1, 2, . . . ,m}, taking the value 1 if and only if station s has no task assigned to it. We then let α s ∈ R, for s = {1, 2, . . . ,m} be the cost of the worker assigned to s when β s = 1. Letz h be the number of workers of type h selected in the input solution. We obtain the following model: subject to (3)-(11) and:m s=1 i∈T h∈H,h≤ki The objective function (28) maximizes the savings obtained by excluding a worker from the assembly line. Inequalities (30) and (31) are the coupling constraints between variables β and x, whereas (32) and (33) relate, respectively, α with y and with β.

Computational experiments
In our computational experiments, we evaluate the results obtained by the methods presented in this paper. The evaluation of the mathematical models is given in Section 6.2, and that of the heuristics in Section 6.3. The algorithms have been coded in C++, using Gurobi v9.0 as MILP solver. The tests have been executed on a PC Ubuntu 16.04.6 LTS 64-bit with Intel(R) Xeon(R) CPU E3-1245 v5 3.50GHz and 32GB RAM. The maximum execution time was set to 2 hours for the two models of Section 4, and to 15 seconds for each execution of the MILP-based neighborhoods of Section 5.2.
The tests were done using the small-size and medium-size instances by Sungur and Yavuz (2015), as well as new large-size instances that we created to obtain a better evaluation of our methods, as described in Section 6.1. In total, we solved 900 instances. Because of the large size of the testbed, we adopted, in this section, we only present aggregate results. All the instances that we used, together with the detailed computational results that we obtained on every single instance, have been made publicly available at https://github.com/NicolasCampana/ALBHW-Instances.

Benchmark set
To the best of our knowledge, the only benchmark instances for the ALBHW have been proposed by Sungur and Yavuz (2015). They chose 45 small-size (n = 20) and 45 medium-size (n = 50) instances among those created by Otto, Otto, and Scholl (2013) for the SALBP-1. For each such instance, they generated 5 ALBHW instances by attempting all combinations of two parameters, w 1 ∈ {1.10, 1.20} and w 2 ∈ {0.70, 0.85}, and including an additional instance in which both w 1 and w 2 were set to 1. In this way, they created 45 × 5 = 225 small-size and 225 medium-size instances. Parameter w 1 is the time factor that defines the time scaling from a worker type to the next, used in such a way that t i,h+1 = w 1 t ih . Parameter w 2 is used instead to determine the cost scaling among the worker types, in such a way that c h+1 = w 2 c h .
To obtain a better evaluation of our methods, we also created a new set of 225 large-size ALBHW instances having n = 100 tasks and 225 very large-size instances having n = 250. These have been obtained following the same procedure adopted by Sungur and Yavuz (2015). We thus adopted a random process to choose the SALBP-1 instances from Otto, Otto, and Scholl (2013) with mixed precedence graphs, balancing the amount of "extremely tricky", "very tricky", "less tricky" and "tricky" instances. Additional information about the instances can be found in Sungur and Yavuz (2015) and in our public repository. Table 2 presents the results obtained by the two models, MSY by Sungur and Yavuz (2015) and the newly proposed MCIM. For each model, we give the number of proven optimal solutions (#opt), the number of instances for which at least one feasible solution has been found (#feas), the percentage optimality gaps at the root node (%gap root ) and at the end of the execution (%gap), the number of explored nodes (#nodes) and the total computing time in seconds (time(s)). Each line in the table gives aggregate total (for #opt and #feas) or average (for all other columns) values for 45 instances sharing the same value of n, w 1 and w 2 . The lines called "average/total" give aggregate values for the 225 instances having the same value of n, and the last "overall" line presents aggregate results for the entire set of 900 instances. The best %gap values are highlighted in bold.

Evaluation of the mathematical models
Both models were very effective in solving the small-size instances with just 20 items. Some remarkable differences can be noticed, however, already for the cases with n = 50: MSY can only find 148 optima, with an average effort of 2821 seconds an average gap of 1.24%, whereas MCIM obtains 14 more optima, with just 2330 seconds of average effort and producing an optimality gap that is just 0.54%. The difference becomes more evident for the group having n = 100: MSY finds only 33 proven optima and 147 feasible solutions, with an average gap of about 44%, whereas MCIM obtains nine more optima, 24 more feasible solutions, and a smaller gap of just 28.89% on average. When n = 250, MCIM found less feasible solutions than MCY, but still more ones. It also obtained better gaps and larger numbers of explored nodes. In any case, it is evident from the results that heuristic algorithms should be developed to tackle the very large-size instances. Overall, MCIM is more accurate than MSY on all groups of instances. This is achieved at the expense of a slightly larger number of explored nodes, but with a reduction in the computing time. The good MCIM performance can also be imputed to the fact that it has a better root node gap than MSY, especially on the small-size and medium-size instances.
Overall, we can conclude that the two models are very effective in solving the smallsize instances, but show important drawbacks for the larger-size instances, for which it is important to invoke heuristic algorithms. We believe it is also important to notice the impact of the hierarchical worker assignment on the difficulty of the instances. This can be observed by comparing the instances having w 1 = 1.00 and w 2 = 1.00, which correspond to the pure SALBP-1 because all workers are equal one another both in terms of cost and of processing times, to the instances in the other groups, where indeed the hierarchical worker assignment has an impact. Such hierarchy increases the difficulty of the problem by increasing the %gap root values and the execution times consistently. This is particularly evident when n = 100, where %gap root increases from less than 10% to around 35% and 90% in the n = 250.

Evaluation of the heuristic algorithms
In Table 3, we present an aggregate evaluation of our heuristic procedures. To facilitate comparison, for MCIM, we resume from Table 2 the number of feasible solutions found (#feas) and the average gap from the lower bound (%gap). For the constructive heuristic, called CH for short in the following, we provide the average solution value (UB) and again the average percentage gap from the lower bound. For the VND, we provide the same information given for CH, but we also report the average improvement with respect to CH, computed as %impr = (U B V N D − U B CH )/U B V N D * 100, and the average execution time in seconds (time(s)). The constructive heuristic is 2.62% away from the lower bound on the instances with 20 tasks, and 3.21% on those with 50 tasks. The VND can improve CH by about 1.41% when n = 20, achieving a gap equal to 1.42%, and by 1.35% when n = 50, achieving a gap equal to 2.48%. In these cases, MCIM appears to be a good solution choice. However, as previously noted, MCIM fails in finding feasible solutions for many instances with n = 100 (namely, 54 instances) and for almost all instances with n = 250 (namely, 202). For all such cases, both CH and VND quickly found feasible solutions. In addition, they could reduce the gap consistently from the lower bound, from the very high 28.89% obtained on average by MCIM, to just 8.15% on average for CH and 7.27% for VND. For the instances with n = 250, CH reduces the average gap from 90.43% to 14.49%, and VND reduces it even more, arriving at 14.24%. The good algorithmic behavior is also confirmed by the computational efforts, which are quite limited. Indeed, CH never requires more than 0.1 second (not reported in explicit in the table), and VND about 35 seconds on average and around 110 seconds for the most difficult group of instances (having n = 250, w1 = 1.20 and w2 = 0.70). In Table 4, we try to obtain some insight into the performance of all task and worker priority rules (see Section 5.1) used by CH. Worker rules are summarized as lines in the table, whereas task rules as columns. Differently from the previous tables, in this case we opted to aggregate instances in groups (w 1 , w 2 ) having the same values of parameters w 1 and w 2 , independently of the value taken by n. As previously noted, the first group (1.00, 1.00) corresponds to the SALBP-1 because all workers are equal to one another both in terms of cost and of processing times. For this group, all worker rules are equivalent, and we thus concentrate only on the task rules. For the other four groups, where hierarchical worker assignment has instead an impact, we show the results obtained by both task and worker priority rules. Each cell in the table gives the number of times in which a pair of rules led CH to find the best solution cost. Total values are provided for each task rule in the last line, and for each worker rule in the right-most column. The best values for each group are highlighted in bold. For group (1.00, 1.00), the best task rule is t.3, which consists of selecting the task with the largest processing time using the worker type 1, which is a relaxation to the SALBP-1. For group (1.10, 0.70), the best result is obtained by the combination of rules w.3 and t.12. This corresponds to selecting the tasks with the shortest processing times and the workers that have the shortest time per task assigned. Task rule t.12 is also very effective for the groups (1.1, 0.85) and (1.20, 0.70), both combined with w.3. Task rule t.3 is the best for the last group (1.20, 0.85), and is the one obtaining the highest total number of best results, 296 out of 900. Overall, all rules have a positive impact on the algorithm. For some of them, this is small (as for t.8 and t.11), but for others, it is quite remarkable (as for t.1, t.3, and t.12). There is no clear winner among the worker priority rules, as all of them have a balanced positive impact on the algorithm. In Figures 3 and 4, we provide a further analysis aiming at evaluating the impact of each heuristic component, selecting only those instances for which MCIM found a feasible solution. In Figure 3 we show the overall gap for each group (w1, w2). As the analyse by size is also interesting to show the effectiveness of the procedures, we used the Figure 4, organized by each size n its the overall gaps. We then computed the percentage gap of a certain heuristic configuration, say, H, from the upper bound of the model, as (U B H − U B M CIM )/U B H * 100. We tested CH, CH improved by MILP-1 (run once) and CH improved by the VND. We can notice a decrease in the gap that is consistent on all groups and all sizes.

Conclusions
We studied the assembly line balancing problem with hierarchical worker assignment (ALBHW), a problem that requires to assign tasks and workers to the stations of an assembly line, to minimize costs while satisfying precedence and cycle time constraints. Workers are divided into different qualification levels, and lower qualified workers cost less but also require larger execution times for the tasks. We proposed some improvements to an existing mathematical model, and then developed a constructive heuristic and a variable neighborhood descent algorithm. The improved mathematical model is quite efficient in solving instances with up to 50 tasks, but for larger instances it is convenient to adopt the heuristic algorithms. Several instances, now made publicly available on the Internet, remain unsolved to proven optimality, and future more powerful exact and heuristic algorithms are envisaged for solving the problem. The inclusion of the hierarchical worker assignment makes the problem much more difficult to solve. Mathematical models incur, indeed, in much larger root node optimality gaps and, consequently, in much larger execution times. Making use of a multi-skill workforce to its full extent may have a critical impact in several production activities, not only assembling ones, but also disassembling and scheduling in general. Interesting future research directions include thus the addition of hierarchical worker assignment characteristics to other classes of problems.


extfieldsofstudy:
Materials Science
Computer Science

text:
Active Reconfigurable Ultra-Wideband Antenna With Complementary Frequency Notched and Narrowband Response

An active reconfigurable ultra-wideband antenna exhibiting complementary frequency notched and narrowband responses is proposed in this paper. The frequency responses are achieved on a CPW fed single element printed monopole antenna loaded with a pair of split ring resonators (SRR) and PIN Diodes. The SRRs and PIN Diodes embedded on the Coplanar Waveguide (CPW) feed works as an inline filter, when activated, exhibits frequency reconfigurability by transforming a frequency notched wideband antenna into a narrowband antenna. Different biasing conditions (reverse and forward) on the loaded PIN diodes toggle between frequency-notched and narrow band response of the antenna. Prototypes are fabricated and the measured impedance and radiation characteristics are presented. This concept offers multi-antenna functionality using a single radiator without any modification or addition to the radiator geometry.

I. INTRODUCTION
Modern RF systems employ transceivers which comprise multiple antennas for different functions and applications. Reconfigurable printed antennas are desirable in such wireless systems which can alleviate the undesired co-housing of multiple antennas [1]. Reconfigurable antennas have been studied by numerous research groups over last few decades and a good account of the works are compiled in [2]. Reconfiguration techniques in a reconfigurable antenna, as indicated in Figure 1, can be broadly classified into four categories: i) electrical reconfiguration, ii) optical reconfiguration, iii) physical reconfiguration, iv) material based reconfiguration [2], [3]. One of the recent techniques of achieving antenna reconfigurability is cascading a reconfigurable filter section in the feed line of the printed antennas. By this technique, a single antenna can be operated to work in different bands or different operating frequencies [4]- [7]. Figure 2 shows a basic block diagram of such The associate editor coordinating the review of this manuscript and approving it for publication was Santi C. Pavone . reconfigurable filtered based antenna. One such integrated antenna-filter combination, where a reconfigurable bandpass filter is incorporated within the feeding line of a printed antenna, is referred to as a filtenna in [8]. A recent paper showing a compact broadband reconfigurable frequency tunable structure using single ring rectangular shaped SRRs coupled to a CPW line provides a stop-band in the transmission characteristic of the line [9]. The structure can also be reconfigured from band-stop to band-pass configuration by switching the loaded pair of p-i-n diodes across slots of the host CPW [9]. When an additional PIN diode is connected between the two rectangular rings placed beneath the respective slots of the CPW in a diagonal fashion, it effectively acts like a new S-shaped SRR with enhanced length and thereby provides a new resonance frequency as also shown in the paper [9]. Table-1 presents a comprehensive summary of various reconfigurable UWB antennas [8], [10]- [23] reported over last few years.
In this paper, a multi-functional and reconfigurable antenna is realized using the design concept presented in [9] and [24]. A pair of SRRs and PIN diode loaded in the CPW feed line constitute a dual state filter section, exhibiting frequencynotched/narrow band-pass response depending on the status (ON/OFF) of the PIN diode. This filter section can be integrated in the feed-section of any CPW fed antenna. The present antenna, due to this integrated dual state filter section, exhibits a unique frequency reconfiguration capability that transforms a frequency notched wideband antenna into a narrowband antenna where the narrowband frequency complements the notch frequency. A single printed monopole antenna loaded with SRRs and PIN diodes on the feed section provides the dual functionality. Here, unlike in [9], the SRRs used are square shaped and no additional PIN/varactors diodes are connected between them. The frequency notch in the wideband printed monopole antenna is caused by the SRRs which are magnetically coupled with feeding CPW line and inhibit signal propagation around the SRRs' resonance frequency [24]- [26]. With the loading of PIN diodes on CPW and appropriate biasing, the frequency notched wideband antenna can be reconfigured into a narrowband antenna operating at the SRR's resonance. The design is realized using a printed circular monopole antenna having a wide bandwidth. The printed monopole is fed by a CPW transmission line loaded with a pair of SRRs and PIN diodes.
It is further demonstrated that the notch frequency and the narrowband frequency can be tuned by changing the physical dimension of the SRR geometry as well as shape of the SRRs without perturbing the radiator dimension. The various shapes of SRRs that can be utilized are circular, square, hexagonal and triangular. Moreover, the inclusion of the SRRs and the PIN diodes on the feed section of the antenna do not have any adverse impact on the radiation performance of the antenna. Physical insight of the dual functionality is explained using the simulated contour Poynting vector plots. Potent application of such reconfigurable antennas are, i) MIMO systems used for high-data rate applications, ii) cognitive radio (CR) systems of Software Defined Radio (SDR) which demand wideband and narrowband antennas [27], iii) multiservice/multiband/multi-standard radio (MSR).
The paper is organized as follows: Sec. II describes the realization of the dual state filter. Section III deals with the design and development of the proposed dual complimentary response based CPW fed monopole antenna. Antenna configurations and corresponding simulated and measured results are reported in section IV. This section also presents some physically insightful plots obtained from [28] which sheds more light on the principle of operation of the proposed antenna and are in confirmation with the measured results. The paper is concluded in Sec. V.

II. REALIZATION OF DUAL STATE FILTER SECTION
Proposed active reconfigurable antenna design achieves reconfiguration features due to the reconfigurable filter section integrated in the feed-line of the antenna. This makes the design of the filter-section and the radiator mutually independent which allows the proposed concept to be easily extended to any other printed antenna. In this section, a very brief description on the realization of the dual-state filter section is discussed. Section-III employs this filter section in a printed monopole antenna which effectively converts the antenna into a reconfigurable filtenna. The dual state filter section is realized by loading a pair of square-shaped SRRs beneath the slot lines of a 50 CPW line and a pair of PIN diodes connected between the signal lines and ground lines of the CPW. To ensure best possible excitation of the SRRs by the propagating magnetic field of the CPW line, SRRs are precisely located so that centre of the SRRs falls on the centre of the slots of the CPW. Figure 3 shows the fabricated prototypes of such a dual state filter. The SRRs having dimension of a ext = 2.5 mm, c = 0.35 mm, d = 0.7 mm and g 1 = g 2 = 0.4 mm (see fig. 6(c) for notations)are printed on RT-Duriod 5870 laminate with ε r = 2.33 and tanδ = 0.0009 with precise location. A pair of silicon PIN diodes with model no. SMP 1145 are placed on the opposite side of substrate. When the diodes are not biased, due to the resonance of the SRR, the SRR loaded CPW yield band-notched function. On the other hand, with suitable forward bias voltage, the combination of SRRs and PIN-diodes acting as 'ON' switch constitute a narrow BPF. Figure 4 shows the experimental set up for characterizing the S-parameters of the SRRs and PIN diode loaded filter section.As indicated in Fig. 4, PIN diodes are biased ON/OFF using a DC bias source applied through the in-built bias Tee of the VNA which also ensures isolation of DC and RF. Figure 5(a) and (b) shows the measured S-parameters of the realized CPW based reconfigurable filter for the PIN diode in OFF and ON state respectively. As indicated in Fig 5(a), with diodes in OFF state the prototype yields band-notched response. The same prototype, with the PIN diode in ON state exhibits a narrow pass-band response. Thus, the SRR and PIN diode loaded CPW can act as a dual state reconfigurable filter.   Figure 6 shows the schematic of the proposed active antenna loaded with SRRs and PIN diodes on the CPW feed section. A circular monopole having radius R is fed by a CPW  line consisting of ground planes having width W 1 and W 2 , length Ls and a signal line of width S and length Ls + t. VOLUME 8, 2020 The signal line and the ground planes are separated by a symmetric pair of slot gaps, s g . The antenna is printed on a substrate having thickness h and dielectric constant ε r . Two square shaped split ring resonators having dimension, a ext , which is half the dimension of the side-length of the SRR, conductor thickness c, separation between rings d and split gaps g 1 and g 2 as shown in Fig. 6(c), are printed on the other side of the substrate with their centers coinciding with the slot lines of the CPW feed. A pair of PIN diodes are placed on the slots of the CPW with their positions coinciding with the axes passing through the center of the SRRs.

III. ANTENNA CONFIGURATION
In the proposed configuration, the CPW is inductively coupled to a pair of SRRs, having narrow split gaps g 1 and g 2 , which are symmetrically placed on the backside of the substrate. The propagating electric field vector is polarized along the plane of the SRRs and the magnetic field vector is polarized along the SRRs' axes. The propagating signal excites the SRR, which prohibits transmission around its resonance frequency determined by the SRRs' dimensions and the constitutive parameters of the host substrate yielding in frequency notch [26]. The symmetric position of the SRRs to optimize efficient magnetic coupling has been shown to yield notch in the antenna impedance and radiation characteristic [26], [29], [30].The CPW transmission line also being loaded with PIN diodes which on different biasing conditions (reverse and forward) would effectively open and short the signal line with the ground planes. This, in turn provides frequency notched response and its complementary narrow band response.
The prototype was fabricated on Taconic substrate having ε r = 2.33, tan δ = 0.0009 and thickness h = 1.575mm. The circular monopole having radius R = 12.5mm and fed with a CPW having ground plane length L s = 22.5 mm, width W = 50mm, signal line width S = 6mm, slot gap S g = 0.3mm and feed gap t = 0.2mm was etched on one side of the substrate. The slot gaps and the signal line width were optimized to yield a line impedance close to 50 . A pair of SRRs having dimensions a ext = 2.5mm, c = 0.35 mm, d = 0.6 mm and split gaps g 1 = g 2 = 0.5 mm, were printed on the other side of the substrate with their axes coinciding with the slot line in the CPW as shown in Fig. 7. A pair of silicon PIN diodes (SMP 1145) were placed on the slots between the ground planes and the signal line and aligned to the position of SRRs axes. As shown in Fig. 7(b), the required DC bias to the diodes are provided using a Mini circuits 15542 bias tee.

IV. MEASUREMENTS AND RESULTS
The proposed SRR and PIN diode loaded active antenna is simulated using a commercial electromagnetic simulator [28]. In this simulation two different configuration of the active antenna for ON and OFF state of the diodes are considered by replacing the diodes with the corresponding equivalent circuits as shown in Fig. 8. The lumped circuit parameters, obtained from the manufacturer's data sheet, in diode ON condition assigned in the simulation were  L s = 0.45nH and R s = 2 and in diode OFF condition were L s = 0.45nH and R p = 5M and C T = 0.14fF. The resultant HFSS model with lumped circuit parameters for both the cases are simulated. Figure 9 shows the simulated and measured S 11 plots of the proposed active antenna for OFF status of the diode. The plot indicates wideband characteristic from 2.5 GHz to 11 GHz with a sharp notch at 6.1 GHz and 6.01 GHz for simulated and measured data, respectively. This notch corresponds to the resonance frequency of the SRR and can be varied by scaling the physical dimension of the SRRs [26]. The variation between simulation and measurement post-resonance is due to the ohmic loss arising from the finite impedance of the PIN diodes in their OFF state. Figure 10 shows the simulated and measured S 11 of the prototype active antenna with the diode in ON condition. As revealed in the plot, with the diode in ON condition, the antenna yields a narrowband response centered at 6.12 GHz and 6.02 GHz for simulated and measured data and effectively complements the impedance behavior of the antenna in diode OFF condition. Figures 9 and 10 reveal the complementary nature of the antenna under diode OFF and ON conditions. The active antenna with diode ON condition provides a narrow band response due to the narrow band pass filter formed with the combination of SRRs and PIN diodes on the slots of the CPW. On the other hand, with diode in OFF condition, the band notch filtering of the SRRs contribute to  frequency notched UWB response of the antenna. The biasing of the diodes is conducted through 5V D.C. supply connected to the bias tee. The current flowing through the diodes in forward bias condition provides the DC-short between signal and ground planes of the CPW which in turn reconfigures the notched wideband antenna into a narrowband antenna. Figure 11 shows the measured maximum realized peak gain plotted against the frequency of the prototype active antenna in diode OFF and ON conditions. In diode OFF condition, the gain drops sharply at the notch frequency of 6.01 GHz prohibiting radiation whereas for the rest of the frequencies the gain remains above 0 dBi. A complementary gain profile is yielded when the diode is switched ON and the gain rises sharply at 6.02 GHz and drops off at either side of the radiating frequency. The measured gain value in FIGURE 11. Measured realized peak gain of the SRR coupled PIN diode loaded CPW fed printed circular monopole active antenna with diodes OFF and ON conditions. Parameters as in Fig. 9. diode ON condition at the narrowband frequency 6.02 GHz was obtained as 3.59 dBi.
The measured normalized radiation patterns in two principal planes, the x-y-plane (E-plane) and x-z-plane (H-plane), for the prototype in diodes OFF condition are shown in Fig. 12(a) and 12(b), respectively, for 3.8 GHz, 8 GHz and 9.4 GHz. The E-plane and H-plane at 6.02 GHz for diode ON condition are shown in Fig. 12(c) and 12(d). The radiation patterns indicate axial null along y-axis ensuring monopole type radiation for the x-y -plane with high cross polar discrimination. The H-plane radiation yields an omni-directional pattern for the x-z-plane. The simulated efficiency was obtained at 92% and 76% for diode OFF and diode ON conditions, respectively.
A more physical insight of the complementary nature of the antenna response can be arrived by observing the magnitude of the Poynting vector along the feed-line in diode ON and diode OFF conditions as illustrated in Fig. 13.The figure represents a 3D contour plot with x-axis being the distance from the connector to the radiator and y-axis representing the frequency and color coding represents the pointing vector, plotted using field calculator option of 3D EM solver [28]. As shown in Fig. 13(a), with the diode in OFF condition, the SRR prohibits propagation of electromagnetic energy at its resonance frequency yielding a notched UWB response. Before the SRR location electromagnetic energy of all frequencies propagating, after interaction with SRR one frequency is prohibited from reaching the radiator. With the diode in ON condition, a complementary nature of the propagation is triggered where electromagnetic energy over only a narrow frequency at approximately the SRRs resonance frequency band is propagated. The rest of the energy is reflected back to the input port as depicted in Fig. 13(b). Figure 14 shows the simulated reflection coefficient of the proposed antenna for different a ext dimensions in diode ON and diode OFF conditions. Three different a ext dimensions of 2.3mm, 2.5mm and 2.7mm yielded notch frequencies in diode OFF condition at 5.45 GHz, 6.1 GHz and 6.65 GHz while with diode in ON condition narrowband response centered at 5.5 GHz, 6.15 GHz and 6.7GHz is obtained. Figure 14 has an inset which shows the zoomed view of the notch and narrowband frequencies from 5GHz to 7GHz to increase the legibility. The wide variation of the notch and narrowband frequency using the proposed concept by  changing the SRR parameter and without altering the basic radiator dimension is evident from the figure. Similar variation can also be achieved by changing the other parameters of the SRRs like c, d and g. The corresponding simulated maximum realized gain as a function of frequency of SRRs with varying a ext is shown in Fig. 15. The dip and peak in gain parameters in diode OFF and ON conditions are evident from the plots.

V. CONCLUSION
A novel active reconfigurable UWB antenna with real time switching yielding complementary responses of frequency notched wideband and narrowband is realized and validated in this paper. The multiple frequency reconfigurability is achieved by loading the CPW transmission line with a pair of SRRs and PIN diodes. The combination of the SRRs with different conditions of diode bias yield the two complementary characteristics. Prototype was fabricated to validate the simulated results with the measured impedance and radiation characteristics. Since the notch and narrow band frequency is determined by the SRRs geometry, several multi-dimensional SRRs can be used for multiple frequency notches. The antenna can be replaced with any other sensor which would yield the desired response using the proposed technique.


Exploring the Items for Measuring e-Procurement Usage Construct: An Exploratory Factor Analysis

The usage of Information system (IS) in any institution is vital and this human technology interaction is the heart of many world-changing endeavors. The aim of this research is to perform instrument validation through exploratory factor analysis (EFA) of using eprocurement. The questionnaire used in this study is adapted from two different studies: Venkatesh et al., (2012) and Norzaidi (2008). It consists of five sub-constructs; after the questionnaire was distributed, 115 responses were collected to do the EFA. EFA was done for each construct separately. The results show that all of the seven constructs have one component or dimension, the factor loading for every item in each construct is >0.6, Bartlett’s Test of Sphericity was <0.05 for all the constructs, which is Significant (P-value < 0.05). Kaiser-Meyer-Olkin Measure of Sampling Adequacy was higher than 0.6 for all the constructs, and this means that the sample size is adequate. Cronbach’s Alpha test was higher than 0.7 for the entire constructs’ items, which means that these items are all reliable. This study found a valid and reliable instrument for measuring the usage of e-procurement to Malaysian contractors’.

Introduction
E-procurement is the use of integrated information technology for part of or all the procurement functions, from the beginning to end, i.e. from searching, sourcing, negotiating, ordering, and receipt to post-purchase review (Croom & Jones., 2005;Trkman & McCormack, 2010). E-procurement has been recently receiving much attention from businesses, industries, and governments as it reportedly becomes a powerful tool to improve effectiveness and efficiencies as well as the service quality of its adopters.
Malaysian government procurement is perceived as a major function of government and a substantial amount of money is allocated annually for the procurement of goods and services (Thai, 2001;Maniam et al., 2009). The Malaysian government spends more than RM150 billion every year in procuring goods, works and services and this gives a sign of riskiness of public procurement being exposed to corruption (Ministry of Finance, 2011). AG Procurement automates the workflow of procurement/resource management processes, which reduces the cycle time of purchases, decreases stocking requirements, and lowers inventory management costs. Finally, e-Procurement applications enable enterprises to manage long-term relationships with suppliers. These relationships can be leveraged to create an enterprise-wide buying environment with the most favorable conditions.

Significance of the Study
Understanding factors as part of the cause of the system usage has become greater doubt in the field of Information System (IS). E-procurement is the use of integrated information technology for part of or all the procurement functions, from the beginning to end, i.e. from searching, sourcing, negotiating, ordering, and receipt to post-purchase review (Croom & Jones., 2005;Trkman & McCormack., 2010). E-Procurement is critical to construction because it involves a number of partners on each project who all have the need for inventory management in order not to delay the project or to tie space and money on excess inventory while also complying with specifications and other variables (Pheng & Meng, 1997). Beyond the obvious transaction cost savings and access to suppliers, e-Procurement can offer product standardization, quality assurance, inventory management and the opportunity to manage material flows down the value chain. The e-Procurement also automates the workflow of procurement/resource management processes, which reduces the cycle time of purchases, decreases stocking requirements, and lowers inventory management costs. Thus, there is a need to measure the usage of e-procurement in Malaysian construction, and its impact to contractors' performance, which represents the aim of this study to find a validated instrument measuring the usage and performance of the system.

Materials and Method
The data collection employed in this study is from a self-administered survey questionnaire. The questionnaire is adapted from two different studies: Vankatesh et al., (2012) and Norzaidi (2008). The questionnaire was adapted and customized to suit the field of this study and was distributed to the respondents who were responsible and in charge of the company's eprocurement that comprise of company officials -general manager, assistant general manager, project manager, site manager, engineer, and executive. The survey was composed from 5 constructs (after the demographical data concerning the respondents): The first four constructs were related to UTAUT model; first construct: Performance Expectancy (5 items using the scale of 7). Second construct: Effort Expectancy (5 items using the scale of 7). Third construct: Social Influence (5 items using the scale of 7). Fourth construct: Facilitating Condition (6 items using the scale of 7). Fifth construct: E-procurement usage (4 items using the scale of 7). Taherdoost (2019) in his study suggests the use of seven-point rating scale and if there is a need to have respondents to be directed on one side, then he claims that six-point scale is the most suitable. Accordingly, this study applied the interval scale of 7, in which the respondents selected a statement among several statements from 1-7 which is considered to reflect the perceived quality of the subject. Number 1 stands for strongly disagree, while, number 7 stands for strongly agree. According to Awang et al. (2010;2012;2014;2015) and Awang et al. (2018), the researcher should apply a Likert Scale without a label because this measure would give an interval type of data that is continuous and fit the data presumption for parametric analysis. As per Awang (2010;2012;2014;2015) and Hoque et al. (2017;, if the analyst adjusted instruments from past studies and altered accordingly, at that point the scientist needs to direct both pre-test and pilot-test for these "changed items" so as to approve them before it tends to be utilized in the final study. Content validity, face validity, and criterion validity were done as a pre-test for this questionnaire, content validity was done through content experts, and face validity was done through English language experts, criterion validity was done through a statistical expert, after these validation tests were completed, the researcher distributed the instrument to 3 respondents, in order to gather their comments, and check the consistency in their responses. After all the required changes according to pre-test results had been done, the researcher distributed the questionnaire to gather a minimum of 100 responses to be able to run the exploratory factor analysis (EFA) as according to many researchers for example: Awang (2010Awang ( , 2012Awang ( , 2014Awang ( , 2015, Hoque et al. (2017Hoque et al. ( , 2018, Noor et al. (2015), Awang et al. (2018) and Yahaya et al. (2018) claim that EFA should be done for each construct to explore changes in dimensionality of items from past studies due to changes in the characteristics of population from the past.

Results and Discussion
The EFA for the First Construct: Performance Expectancy Performance Expectancy construct was measured by using 5 items namely pe1 till pe5 (Table  1). Every statement of items was measured using Interval Scale ranging between 1 and 7, where 1 stands for strongly disagree and 7 stands for strongly agree. The mean score and standard deviation derived for every single item which measured the constructs are shown in Table 1. pe4 Using e-procurement increases my productivity 5.58 0.936 pe5 Overall, I would find e-procurement to be advantageous 5.45 1.011 EFA using Principal Component Analysis as an extraction method performed for these 5 items to measure performance expectancy of using e-procurement. The results in Table 2 shows Bartlett's Test of Sphericity which is Significant since it's <0.05. Kaiser-Meyer-Olkin Measure of Sampling Adequacy higher than 0.6 which is for the first construct 0.855, and this means that the sample size is adequate (Awang, 2010;2012;2014;2015;Hoque et al., 2017;and Noor et al., 2015). Accordingly, the current data are acceptable. 0.000 The scree plot in Figure 1 shows that only one component emerged from the EFA, accordingly all items in this construct will belong to one component. The results in Table 3 the components or dimension for each item is shown in this table, as it's clear all items are belonging to one component. The factor loading for every item should be >0.6 in order to be retained (Awang, 2010;2012;Awang et al. (2018) and Yahaya et al., 2018). Thus all items will be retained. The results in Table 4 show there are one dimension or component emerged from the EFA procedure based on the computed Eigenvalue >1.0. The total variance explained for measuring this construct is 78.183%. The total variance explained is acceptable since it exceeds the minimum 60% (Awang, 2010(Awang, , 20122014;2015;Noor et al., 2015;Hoque et al., 2017;and Yahaya et al., 2018).

The Internal Reliability for the Instrument Measuring Performance Expectancy
The last test that should be done is the internal reliability of each construct. As Table 5 shows that Cronbach's Alpha test is 0.929, higher than 0.7, which means that these items are reliable. The EFA for the Second Construct: Effort Expectancy This construct was measured using 5 items listed in Table 6 as ee1 to ee5, and each item was measured using Likert-scale of 7, where 1 stands for strongly disagree and 7 stands for strongly agree, the mean response, standard deviation and item statement, for each item, are listed in Table 6. EFA using principal component analysis as an extraction method performed for these 5 items to measure effort expectancy of using e-procurement. The results in Table 7 shows Bartlett's Test of Sphericity which is Significant since it's <0.05. Kaiser-Meyer-Olkin measure of sampling Adequacy higher than 0.6 which is for the 2nd construct 0.847, and this means that the sample size is adequate (Awang, 2010;2012;2014;2015;Hoque et al., 2017Hoque et al., , 2018Noor et al., 2015). Accordingly, the current data are acceptable. 0.000 The scree plot in Figure 2 shows that only one component is emerged from the EFA, accordingly all items in this construct will belong to one component. The results of the components or dimension for each item is shown in Table 8, as it's clear all items are belonging to one component. The factor loading for every item should be >0.6 in order to be retained (Awang, 2010;2012;2014;2015;Awang et al., 2018 andYahaya et al., 2018). Thus all items will be retained.  Table 9 show there are one dimension or component emerged from the EFA procedure based on the computed Eigenvalue >1.0. The total variance explained for measuring this construct is 73.217%. The total variance explained is acceptable since it exceeds the minimum 60% (Awang, 2010;2012;2014;2015;Noor et al., 2015;Hoque et al., 2017Hoque et al., , 2018and Yahaya et al., 2018).

The Internal Reliability for the Instrument Measuring Effort Expectancy
The last test that should be done is the internal reliability of each construct. As Table 10 shows that Cronbach's Alpha test is 0.898, higher than 0.7, which means that these items are reliable. The EFA for the Third Construct: Social Influence This construct was measured using 5 items listed in Table 11 as si1 to si5, and each item was measured using Likert-scale of 7, where 1 stands for strongly disagree and 7 stands for strongly agree, the mean response, standard deviation and item statement, for each item, are listed in Table 11. EFA using principal component analysis as an extraction method performed for these 5 items to measure social influence of using e-procurement. The results in Table 12 shows Bartlett's Test of Sphericity which is significant since it's <0.05. Kaiser-Meyer-Olkin measure of sampling Adequacy higher than 0.6 which is for the third construct 0.787, and this means that the sample size is adequate (Awang, 2010;2012;2014;2015;Hoque et al., 2017Hoque et al., , 2018Noor et al., 2015). Accordingly, the current data are acceptable. 0.000 The scree plot in Figure 3 shows that only one component is emerged from the EFA, accordingly all items in this construct will belong to one component. Figure 3: The Scree Plot for the third construct The results in Table 13, the components or dimension for each item is shown in this table, as it's clear all items are belonging to one component. The factor loading for every item should be >0.6 in order to be retained (Awang, 2010;2012;2014;2015;Awang et al., 2018 andYahaya et al., 2018). Thus all items will be retained. The results in Table 14 show there are one dimension or component emerged from the EFA procedure based on the computed Eigenvalue >1.0. The total variance explained for measuring this construct is 62.123%. The total variance explained is acceptable since it exceeds the minimum 60% (Awang, 2010;2012;2014;2015;Noor et al., 2015;Hoque et al., 2017Hoque et al., , 2018and Yahaya et al., 2018).

The Internal Reliability for the Instrument measuring Social Influence
The last test that should be done is the internal reliability of each construct. As Table 15 shows that Cronbach's Alpha test is 0.809, higher than 0.7, which means that these items are reliable. The EFA for the Fourth Construct: Facilitating Condition This construct was measured using 5 items listed in Table 16 as fc1 to fc5, and each item was measured using Likert-scale of 7, where 1 stands for strongly disagree and 7 stands for strongly agree, the mean response, standard deviation and item statement, for each item, are listed in Table 16. EFA using principal component analysis as an extraction method performed for these 5 items to measure facilitating condition of using e-procurement. The results in Table 17 shows Bartlett's Test of Sphericity which is Significant since it's <0.05. Kaiser-Meyer-Olkin measure of sampling Adequacy higher than 0.6 which is for the fourth construct 0.810, and this means that the sample size is adequate (Awang, 2010;2012;2014;2015;Hoque et al., 2017Hoque et al., , 2018Noor et al., 2015). Accordingly, the current data are acceptable. 0.000 The scree plot in Figure 4 shows that only one component is emerged from the EFA, accordingly all items in this construct will belong to one component. The results in Table 18 the components or dimension for each item is shown in this table, as it's clear all items are belonging to one component. The factor loading for every item should be >0.6 in order to be retained (Awang, 2010;2012;2014;2015;Awang et al., 2018 andYahaya et al., 2018). Thus, all items will be retained. The results in Table 19 show there are one dimension or component emerged from the EFA procedure based on the computed Eigenvalue >1.0. The total variance explained for measuring this construct is 67.955%. The total variance explained is acceptable since it exceeds the minimum 60% (Awang, 2010;2012;2014;2015;Noor et al., 2015;Hoque et al., 2017Hoque et al., , 2018and Yahaya et al., 2018).

The internal reliability for the instrument measuring Facilitating Condition
The last test that should be done is the internal reliability of each construct. As Table 20 shows that Cronbach's Alpha test is 0.880, higher than 0.7, which means that these items are reliable. The EFA for the Fifth Construct: e-procurement Usage This construct was measured using 4 items listed in Table 21 as pu1 to pu5, and each item was measured using Likert-scale of 7, where 1 stands for strongly disagree and 7 stands for strongly agree, the mean response, standard deviation and item statement, for each item, are listed in Table 21. EFA using principal component analysis as an extraction method performed for these 4 items to measure e-procurement usage of using e-procurement. The results in Table 22 shows Bartlett's Test of Sphericity which is Significant since it's <0.05. Kaiser-Meyer-Olkin measure of sampling Adequacy higher than 0.6 which is for the fifth construct 0.793, and this means that the sample size is adequate (Awang, 2010;2012;2014;2015;Hoque et al., 2017Hoque et al., , 2018Noor et al., 2015). Accordingly, the current data are acceptable. 0.000 The scree plot in Figure 5 shows that only one component is emerged from the EFA, accordingly all items in this construct will belong to one component. The results in Table 23 the components or dimension for each item is shown in this table, as it's clear all items are belonging to one component. The factor loading for every item should be >0.6 in order to be retained (Awang, 2010;2012;2014;2015;Awang et al., 2018 andYahaya et al., 2018). Thus all items will be retained. The results in Table 24 show there are one dimension or component emerged from the EFA procedure based on the computed Eigenvalue >1.0. The total variance explained for measuring this construct is 70.973%. The total variance explained is acceptable since it exceeds the minimum 60% (Awang, 2010;2012;2014;2015;Noor et al., 2015;Hoque et al., 2017Hoque et al., , 2018and Yahaya et al., 2018;Khalid, 2020).

The internal reliability for the instrument measuring e-procurement Usage
The last test that should be done is the internal reliability of each construct. As Table 20 shows that Cronbach's Alpha test is 0.880, higher than 0.7, which means that these items are reliable.

Conclusion
The current research adds a remarkable contribution to the measurement of the 5 constructs, mainly in the e-procurement context. The results show that every of the five constructs have one component or dimension, the factor loading for every item exceeds the minimum threshold of 0.6, with high Cronbach's Alpha value, meet Bartlet Test achievements (significant) for all the constructs, Kaiser-Meyer-Olkin Measure of Sampling Adequacy was higher than 0.6 for all the constructs, and factor loading exceeds the minimum threshold of 0.6. Hence, this study found a valid and reliable instrument for measuring the usage of eprocurement to Malaysian contractors'. Therefore, this instrument can be used to measure the usage of e-procurement in the targeted organizations in this study.
However, it is recommended during field study that some precautions need to be done to ensure that the data collection are free from response bias and common method variance and therefore, would generate significant findings.