extfieldsofstudy: Sociology Medicine

text:
Effects of amusing memes on concern for unappealing species

There is limited knowledge of the mechanisms that can inspire people's concern and engagement in the protection of unpopular and unappealing species. We analyzed Polish people's interest in themed internet memes featuring the proboscis monkey (Nasalis larvatus) and the consequences of this interest for conservation marketing. We examined Google Trends data, used Google Search, and searched popular media materials to estimate interest in the proboscis monkey in Poland. Photos of the proboscis monkey when presented with humor in internet memes attracted as much interest as usually more popular species (e.g., koala, panda, and orangutan) used in marketing by nongovernmental organizations. Amusing internet memes spread by social media positively correlated with increasing interest in the unappealing species, such as proboscis monkey. Interest in amusing internet memes positively correlated with individuals’ decisions to donate to 6 crowdfunding actions. Thus, conservation marketing that includes amusing memes and social media may provide a worthwhile complement to traditional campaigns and are likely to influence individuals who are unaffected by the usual means.

Abstract: There is limited knowledge of the mechanisms that can inspire people's concern and engagement in the protection of unpopular and unappealing species. We analyzed Polish people's interest in themed internet memes featuring the proboscis monkey (Nasalis larvatus) and the consequences of this interest for conservation marketing. We examined Google Trends data, used Google Search, and searched popular media materials to estimate interest in the proboscis monkey in Poland. Photos of the proboscis monkey when presented with humor in internet memes attracted as much interest as usually more popular species (e.g., koala, panda, and orangutan) used in marketing by nongovernmental organizations. Amusing internet memes spread by social media positively correlated with increasing interest in the unappealing species, such as proboscis monkey. Interest in amusing internet memes positively correlated with individuals' decisions to donate to 6 crowdfunding actions. Thus, conservation marketing that includes amusing memes and social media may provide a worthwhile complement to traditional campaigns and are likely to influence individuals who are unaffected by the usual means.

Introduction
The continued existence of threatened species often depends on conservation programs (Stokes 2006;Colleony et al. 2017). Support for such programs depends on the available information and may be influenced by individual decision-making, emotions, or biases (e.g., in visual perception) (Fleming & Bateman 2016;Colleony et al. 2017;Verissimo et al. 2018). For example, people often show positive attitude toward species that look similar to human infants, in particular, those with a big head in relation to the rest of the body, large eyes, and a small nose (Estren 2012;de Pinho et al. 2014). Conservation organizations take advantage of such preferences (e.g., World Wildlife Fund [WWF]) in their promotional materials aimed at encouraging support for conservation (Verissimo et al. 2017(Verissimo et al. , 2018. However, the majority of threatened species are unknown to the public or do not look infant like. Consequently, gaining the public's interest and financial support for the conservation of unappealing species, or those sometimes literally called ugly, is far more difficult (Estren 2012;Smith et al. 2012;Colleony et al. 2017). Conservation of such species may require nonstandard actions, and the efficiency of such actions may be enhanced with marketing strategies (Kidd et al. 2018). One possible way to promote unknown and unpopular species (Kidd et al. 2018) is by using humororiented marketing techniques in social media, which are known from business marketing (Eisend 2009). The role of satire in saving species and habitats has been suggested Ripple et al. 2018), and there have been a few attempts to apply humor to promote so-called ugly species, such as The Ugly Animal Preservation Society (O'Callaghan 2013, The Ugly Animal Preservation Society 2019). Nevertheless, evidence that humor in social media can be used to promote species and conservation is limited.
Social media (e.g., Facebook and Twitter) makes extensive use of visually oriented forms of communication; one of particular popularity is the meme. The term meme was coined by Dawkins (1976), who proposed an evolutionary model of cultural change and development grounded in the replication of ideas and knowledge through imitation and cultural transfer. The concept was later adopted by internet users, and it generally describes the rapid uptake and spread of particular ideas presented as written text, images, movies, or other media on the internet that go viral (Knobel & Lankshear 2007). Internet viral memes spread through replication in social networks, have certain longevity, and mutate over time (Knobel & Lankshear 2007). We applied a narrower definition of internet memes (used interchangeably with memes): digital images (often containing text) created for the purpose of communication.
We examined the possible role of amusing memes in generating interest in unappealing species and the differences in the perceived emotional context between amusing memes and traditional campaigns of conservation nongovernmental organizations (NGOs). In particular, we studied the possible dissemination of conservation-relevant information regarding threatened species via memes and the association of increased interest in amusing themed memes with individual decisions to support conservation-oriented crowdfunding actions.
We analyzed interest in the proboscis monkey in Poland and in amusing themed memes of this species (hereafter amusing memes) (Supporting Information). The proboscis monkey (Nasalis larvatus) was voted in the British Broadcasting Company's ranking as one of the ugliest animals in the world (Bates 2013;Marshall 2016). It is listed as endangered species on the International Union for Conservation of Nature Red List, and is endemic to the Southeast Asian island of Borneo. Its total population has decreased by more than 50% in the last 5 decades due to ongoing loss of habitat and hunting (Sha et al. 2008). The species was little known to the general audience of Poland prior to 2016 when the first amusing memes appeared (Fig. 1). We collected data from Google Search, Google Trends, Google Graphics, Facebook, and media articles to test the following hypotheses: increasing interest in the proboscis monkey in Poland correlates with the interest in the amusing memes (Hypothesis 1) (Supporting Information); interest in proboscis monkeys is relatively higher in Poland than in the species' range states when compared with a group of typically popular species (Hypothesis 2) (Supporting Information); interest in social media profiles with amusing memes involving proboscis monkeys is greater than that in NGO social media profiles devoted to nature conservation and the monkey (Supporting Information) (Hypothesis 3); perceived emotional context of amusing memes differs from the context of traditional campaigns of species conservation performed in social media by NGOs (Hypothesis 4) (Supporting Information); and interest in the amusing themed memes coincides with the occurrence of conservation crowdfunding actions (Hypothesis 5) (Supporting Information).

Methods
We collected data from Google, Facebook, and media articles. In Poland and other studied countries, the Google family of services has very high coverage (estimated market share >95% [Supporting Information]). Facebook had 2.2 billion and 14 million monthly active users worldwide and in Poland, respectively, in 2017 (Facebook 2018). It is globally the most popular internet social media platform (Supporting Information).
The essential feature of memes is their ability to be replicated by user-induced mutations (Knobel & Lankshear 2007). Therefore, it is crucial to measure the inflow of new memes and meme propagation. For this purpose, we created an index based on the number of proboscis monkey images present in time-restricted search results of Google Search browser for the keyword nosacz (common name of proboscis monkey in Polish), and we restricted results to images. Based on the index, we constructed a time series (at a monthly frequency) representing the intensity of the meme-generating process. The index was based on classification of relevant images as memes, according to the definition of meme (classification method in Supporting Information). We refer to this index as the meme index.
We used Google Trends to measure how often a particular search item was entered into Google Search browser relative to the total search volume. Time series obtained from this tool are informative for determining the dynamics of society's demand for information (Vlastakis & Markellos 2012) about a species and may be a measurement of interest (e.g., Nghiem et al. 2016). We filtered the Google Trends index by turning the "animals" category on to avoid homonyms and restricted trends to a relevant country and language to avoid a geolocation effect in results obtained from Google Trends. The term nosacz has no alternative meaning in commonly used Polish vocabulary. We analyzed regional differences in the interest in proboscis monkey and compared interest in proboscis monkey with interest in related species. We compared interest in the proboscis monkey determined from Google Trends interest in Poland with the interest in the region where it is indigenous (all 3 countries on Borneo island: Malaysia, Indonesia, and Brunei) and with interest in English-speaking population of internet users. We checked how interest has changed with the publication of amusing monkey memes in Poland. We used the species' Polish name to check for interest in Poland. For Borneo we used the Indonesian and Malaysian ((bekantan) and Brunei (bangkatan) words for the species and restricted the region to the relevant country. We used the English proboscis monkey to estimate interest in the species globally. Using Google Trends, we also checked whether the appearance of amusing memes was associated with the interest in Poland in 2 other primates, uakari (Cacajao calvus) and Yunnan snub-nosed monkey (Rhinopithecus bieti), which sometimes appear in such memes.
We also checked how many times the proboscis monkey could be found in Google Search browser in Poland in Polish and worldwide in English. We compared the Google Search browser search results for proboscis monkey with 5 popular species used by WWF in crowdfunding: macaques, orangutans, gorillas, pandas, and koalas. The latter 2 are not primates, but they are 2 of the most popular species used for crowdfunding by WWF globally (Supporting Information). We used the same procedure for other animal names (Supporting Information). To collect the data from the Google Search browser, we used filters recommended by Google to get an accurate count for up to 1 million documents and to avoid duplications to improve data quality (procedure in Supporting Information). We also conducted a search with this set of species to see if there were differences in the interest over time among these species based on data from Google Trends in Poland and worldwide. To avoid geolocation effect in data from Google searches in global searches, we applied the "global search area" filter and collected data from 2 different computers in Poland and 2 different computers in Australia. For data collection from Google Search browser in Poland, we restricted the search area to Poland and performed the search with 2 different computers in Poland and 2 different computers in Australia.
We used Facebook to collect data on relative interest in the amusing proboscis monkey memes compared with the interest in the memes published on conservation NGO Facebook webpages.
The Facebook data allowed us to construct an alternative measure of interest in the species in social media based on the number of people who followed proboscis monkey profiles on Facebook, regardless of their purposes. There were 2 types of proboscis monkey profiles in Facebook: amusing proboscis monkey profiles and profiles dedicated to the protection of the species (referred to as official monkey profiles) developed by organizations, such as WWF Poland and Polish Greenpeace. The list of profiles with amusing proboscis monkey and official monkey profiles in English is in Supporting Information. Facebook allows members to share, publish, comment on, exchange content uploaded by people throughout the world, and express opinions by clicking like. Since mid-2016, users can also express other opinions toward posts or images with 5 other emoticons: love, haha, wow, sad, and angry. We used the number of followers and the number of people who clicked like for a single meme as a gauge of interest (Cristofaro et al. 2014) in published memes, that is, as a measure of the effectiveness in gaining users' attention. We used the number of likes as in Cristofaro et al. (2014) and because they have been used by Facebook users since 2004. Emoticons were relatively new in 2017, so there had not been sufficient time for people to become familiar with them.
We compared all 6 types of emoticons assigned by Facebook users with the memes of the cute species presented in the profiles of WWF Poland (https://www.facebook.com/WWFpl/) with the 6 types of emoticons assigned to the most well-known amusing profile of the proboscis monkey in Poland (Nosacze Polskosci). We refer to these WWF memes as cute WWF memes, and they pertain only to memes on WWF Poland's Facebook profile. In addition to the analyses of Google and Facebook data, we analyzed differences in the number of media releases involving information about the proboscis monkey in Poland (through various search engines) over time. We searched all content in traditional Polish media, such as newspapers, radio, and television, for information about proboscis monkeys released from 2004 to 2018. Since 2004, the largest traditional media sources in Poland publish their content online. We noted the dates of publication, names of the sources, and keywords in Polish that occurred in the text. The keywords were nosacz, nosacz sundajski (full name of the species in Polish), mem (meme), Borneo, and media URLs for identification. We also marked the cases where the species (or its images or memes) was explicitly referred to as funny or entertaining. The articles were analyzed to confirm relevance of the keywords.
Finally, we analyzed crowdfunding actions related to proboscis monkey conservation emerging from internet websites with amusing memes of the species. We recorded the date of publication and an organizer and whether amusing proboscis monkey profiles promoted donating to the conservation of the species. We also checked how many times Polish people shared information about the crowdfunding action in social media and the amount of collected money. All of the abovementioned data were publicly available on Facebook and did not include user names.
We used general additive model (GAM) to estimate the temporal changes in the species interest. The regression package segmented in R was used to estimate the breakpoint of the function slope change, corresponding to changes in the index of interest in the species (Muggeo 2008). Associations in Google Trends among different species were tested using nonparametric correlation analysis. Generalized linear mixed models (GLMMs) were used to compare the number of Google Search records for different species on the different computers used to perform the searches. Nonparametric correlations were used to compare temporal changes in relative interest among different species based on Google Trends in Poland, worldwide, and in the proboscis monkey's native countries. We used general linear modeling (GLM) to check the differences in the number of Facebook likes among 30 of the most recent photos or memes published on amusing monkey profiles (3), conservation of proboscis monkey official profiles (3), and conservation of animals in general (2 [WWF and Greenpeace]). We also controlled the time of a day (hour) when the post was published, and this variable was a covariate in the model. The GLM was used to compare the type and number of emoticons associated with memes published in the largest profiles associated with amusing monkey memes and the profile of the largest animal conservation agency, WWF Poland. Data on likes and emoticons collected from Facebook profiles were log transformed to minimize the influence of detached data points. These calculations were based on Facebook data and were performed with raw data and with data scaled by the number of Facebook users in a given Conservation Biology Volume 34, No. 5, 2020 country and by the number of followers of a Facebook profile (Supporting Information). Both procedures gave similar results; thus, we present analyses on raw data in the main text for simplicity. All calculations were performed in R (R Core Team 2017), and formulas for GLMs and GLMMs are in Supporting Information.

Hypothesis 1
The number of memes with proboscis monkeys published in Poland was negligible prior to 2016 and increased afterward (Fig. 1). The first proboscis monkeythemed entertaining internet content appeared in April 2016, and meme mutation and propagation behavior appeared in August 2016. The largest relative increase in the meme index was in January 2017. Google Trends index of interest in the proboscis monkey in Poland was negligible prior to 2016 and increased afterward (GAM parametric effects: F = 55.477, df = 1, p < 0.001; GAM nonlinear effects: F = 35.053, df = 5, p < 0.001, R 2 = 0.98; segmented regression breakpoint July-August 2016) (Fig. 1). The indices displayed strong cotrending (Kendal correlation coefficients, tau = 0.905, p < 0.001) (Fig. 1). The increase in the number of traditional press articles about proboscis monkeys followed the number of amusing memes with proboscis monkeys (tau = 0.874, p < 0.001) (Fig. 1). Two species (uakari and Yunnan snub-nosed monkey), often co-occurring with the proboscis monkey in memes, also gained interest in Poland, and these data from Google Trends correlated with data on the proboscis monkey (Kendall correlation coefficients between the proboscis monkey and uakari: tau = 0.396, p < 0.001; between the proboscis monkey and Yunnan snub-nosed monkey: tau = 0.239, p < 0.001 [Supporting Information]) but not with data on each other (tau = 0.022, p = 0.317).

Hypothesis 2
The Google Trends index of interest in the proboscis monkey was constant among English-speaking global users (Kendal tau = 0.087, p = 0.242) of the internet and among Indonesia internet users (tau = -0.041, p = 0.581), but the index value increased among Malaysia users (tau = 0.360, p = 0.001), where the proboscis monkey is native (Supporting Information). In contrast, in Poland the interest in the proboscis monkey increased after 2016 (before 2016: tau = 0.398, p < 0.001; after 2016: tau = 0.909, p < 0.001) (Fig. 1 & Supporting  Information). In Poland interest in proboscis monkey was at least as high as interest in species typically used by WWF in crowdfunding (Fig. 2).

Figure 2. Relative changes in the Google Trends index of interest in the proboscis monkey (clear from key) and flagship species in (a) Poland and (b) the world.
In (a) data were derived from searches of species names in Polish in sources from Poland. In (b) data were derived from searches of species names in English in English-speaking countries, but no geographical restriction was set. In both cases, the search was restricted to the "animals" category.

Hypothesis 3
The Facebook profiles featuring the amusing monkey memes had fewer followers than the Facebook profiles of Conservation Biology Volume 34, No. 5, 2020

Hypothesis 4
Traditional media in Poland described the proboscis monkey memes as amusing (22 cases out of 38, none before 2016). When we compared the emoticons associated with 30 amusing monkey memes presented and 30 WWF memes with popular species, we found the former were more associated with emotions haha and like than with the latter (interaction terms between the emoticon Conservation Biology Volume 34, No. 5, 2020 type and webpage type in GLM: F = 141.745, df = 5, 348, p < 0.001, R 2 = 0.72) (Fig. 5). Overall, the number of recorded emoticons was larger for the amusing monkey memes published by the largest humoristic profile than any meme in the profile of WWF Poland (effect of webpage type in GLM: F = 50.449, df = 1, 290, p < 0.001, R 2 = 0.61; estimate [SE] for WWF Poland = -0.82 [0.09]).

Hypothesis 5
We found 38 media releases about the proboscis monkey in Poland, and the number of these publications increased following interest in the amusing memes (Fig. 1). The 5 articles published before 2016 were not related to amusing memes of the proboscis monkey. Thirty-two media releases after 2016 were linked to the amusing memes. Twenty-two media articles provided information about the biology, ecology, conservation status, and threats to the proboscis monkey. There were 6 crowdfunding actions organized relative to the amusing profiles of the proboscis monkey in Poland, all started in 2018. They raised funds for the species' conservation in Borneo (Table 1) and collected PLN2,318 (∼US$610) from 218 donors (Table 1).

Discussion
There has been a large debate about what kind of methods may work best to make conservation marketing more popular, although there is smtill not enough evidence (Sutherland et al. 2018). Multimedia campaigns using theatre, film, print media, and discussions may help primate conservation because they can increase societal awareness of endangered species (Sutherland et al. 2018). We found that the proboscis monkey's popularity increased in Poland and correlated with people's interest in amateur memes that appeared in social media. We suggest the memes could help gain widespread attention for proboscis monkey protection. The increasing interest in amusing memes with proboscis monkeys was also evident in the general search volume for the species' name. Our findings are consistent with those of Kidd et al. (2018), which suggests that increased presence of an unpopular species on social media may increase people's interest in protecting unpopular threatened species. We found that an increase in interest in amusing memes in Poland was correlated with a subsequent increase in traditional media reporting about the proboscis monkey (with a 1-year lag). This suggests that internet memes can generate interest in subjects that are later picked up in traditional media.
Similarly, the rise of such trends regarding uakari and the Yunnan snub-nosed monkey suggests they are benefitting from the increased interest in proboscis monkey. The powerful impact of memes on the worldwide interest in species (as measured with the Google Trends index) has also been noted in association with gorillas. This happened after a child fell into a gorilla's enclosure in a zoo (Judah 2017) and the gorilla was euthanized for safety reasons (Fig. 2).
Our study has revealed that in contrast to Poland interest in proboscis monkey has been relatively low and constant among English-speaking internet users and users in countries where the species is native, Indonesia and Malaysia. This is to some extent contradictory of the finding that people expect charitable donations to have more impact on nearby rather than faraway targets (Touré-Tillery & Fishbach 2017) and tend to donate to local causes (Schlegel & Rupf 2010). Our results are promising in that they show how a good marketing action may possibly break distance-related biases in the conservation propensities of people. Moreover, we have found that the interest in proboscis monkeys has increased so much in Poland that it currently exceeds interest in orangutans, gorillas, even koalas, and pandas, species typically used in marketing by the WWF.
The profiles of WWF and Greenpeace were of higher interest in social media than the amusing monkey profiles. However, interest in the amusing proboscis monkey memes were of similar interest to the cute WWF memes. The strength of the amusing social media profiles featuring the proboscis monkey is also striking when the number of its Facebook followers is compared with the interest in the official monkey profiles. One might think comparisons of the interest in amusing profiles to serious, official profiles are a mistake because the audience is different. However, regardless of their purpose, memes that gain more people's reactions increase interest in the featured species.
Amusing monkey memes gained similar or higher levels of positive emotional responses and more responses than the memes with cute species in the WWF Facebook profile. This suggests the positive emotions associated with the animal and the amusing way of showing the species may be effective in persuading people to be interested in the conservation of even very geographically distant species. Cavanaugh et al. (2015) found that positive emoticons, such as love, increase donations from people who would otherwise be geographically distant and unconnected because such emotions generated a feeling of connection, regardless of geography. According to a study by Dyck and Coldewin (1992), a positive picture of a child leads to higher than average donation than a negative picture of a child.
The increasing popularity of the proboscis monkey in Poland can be explained not only by the humor, but also by face-ism, the Zajonc effect, and humoristic identification with the species due to storytelling. In the Zajonc effect, frequent exposure to an image of an ugly species in media can decrease the subjective mental impression of its ugliness and can induce sympathy toward the species (Zajonc 1968). Proboscis monkeys in Polish amusing memes are also usually shown with a high face-to-body ratio, which is characteristic for face-ism but is rarely used in nature photography. This may generate more positive attitudes and ratings with regard to intelligence and physical appearance than photos with lower face prominence (Archer et al. 1983). Using many pictures of the species, mostly taken in native habitats, in different poses, of different sexes and ages, and performing different types of behaviors and texts creates a kind of continued story of a typical Pole's life, where the proboscis monkey has become a kind of character. This is not usual for memes and could be a good example of how storytelling can further conservation (Dahlstrom & Scheufele 2018).
Moreover, the increasing interest in amusing memes of the species inspired the establishment of some amateur donating actions that were advertised on Facebook by profiles featuring the amusing memes. The number of donations has been growing since November 2017, and according to the declarations of the owner of the leading amusing proboscis monkey profile, the money is being transferred to Orangutan Foundation International, a nonprofit organization dedicated to the conservation of wild orangutans, other primates, and their rainforest habitat (https://orangutan.org/). The amount of money collected (US$610) does not seem impressive, but relative to the minimum salary in Indonesia in 2017 (3.35 mln Indonesian Rupiah which is US$246) and considering that it was an unprofessional effort organized by unknown people without established Conservation Biology Volume 34, No. 5, 2020 public trust, it is substantial. This is a typical situation in crowdfunding actions (Gallo-Cajiao et al. 2018). However, the described crowdfunding actions were spontaneous and conducted by amateurs. Future crowdfunding should include professional planning and implementation (Gallo-Cajiao et al. 2018).
Our results present a different point of view to the hypothesis presented by Courchamp et al. (2018), that the frequent presence of a species in media may result in people having less knowledge about the species' extinction and habitat loss and that there is a reduced probability that people will search for information about its ecology. The media releases about amusing memes with proboscis monkeys usually included information on species ecology. Moreover, searches could result in unintentional finds of ecological and conservationrelevant information.

Study Limitations
We attach certain reservations to our findings. First, our analyses encompassed the fields of social media, internet marketing, and conservation policy, and there are currently no generally accepted, unambiguous, and common theoretical frameworks or terminology among these fields. Moreover, there are big semantic problems because different authors use terms differently, for example, popularity, familiarity, charisma, and interest. This is why we used terminology consistently in this article (e.g., interest). Google Search browser and Google Trends data may provide inaccurate numbers due to geolocation, homonyms, and duplication, counting multiple occurrences of records on the same page. However, they avoid biases in classic psychological questionnaires and experiments (Kemmelmeier 2016) and thus may accurately indicate fluctuations in public interest in various subjects. To increase accuracy of our data, we applied search filters in Google Trends to avoid geolocation and homonyms. Also, we used filters officially advised by Google to request an accurate result count for up to 1 million search returns and to avoid duplications in Google search engines. Of course, experiments are always the best, but not always possible especially in social sciences at a large spatial extent.
In our internet trend and search volume data exact numbers may not be accurate, but relative trends reflect reality. People searching for names or items are honest because most of them feel anonymous and do not think anyone will collect data on their activity; thus, there is no investigator effect (Golder et al. 2017). The extent to which our findings can be generalized is unclear. However, our main results regarding temporal trends and from comparisons among species seem resistant to change because for data collected through Google Trends, Google Search browser, and Google Graphics results were the same, even for different parts of the world (Poland and Australia).

Recommendations
We formulated 3 practical recommendations. First, easy access to meme-friendly visual content related to endangered species (good quality pictures, animations, etc.) should be provided because the interest in memes may correlate with an increased interest in species as indicated by our results from the meme index and Google Trends data. Second, conservation NGOs should monitor worldwide interest in social media images of endangered species (perhaps using automated algorithms) because we found that a local interest boom associated with proboscis monkey in Poland could result in gains in terms of spontaneous small donations. Third, conservation NGOs should provide trusted connections between donors and beneficiaries of conservation actions even in distant parts of the world, and social media may be appropriate solution to achieve this goal.


CORPORATE COMPLIANCE WITH INTERNATIONAL FINANCIAL REPORTING STANDARDS: A CASE STUDY OF SELECTED SMALL AND MEDIUM-SIZED ENTERPRISES (SMES) IN THE CAPE COAST METROPOLIS

The purpose of the study was to explore the extent to which Small and Medium Enterprises (SMEs) in the Cape Coast Metropolis (CCM) comply with International Financial Reporting Standards (IFRSs). The study further looked at firm attributes (size, profitability, audit type, internationality, type of SME, and leverage) that influence the level of SMEs’ compliance with IFRSs. The descriptive design was adopted for this study. The study sampled 89 SMEs within the metropolis, however, data from 67 medium scale enterprises were used. A self-constructed compliance index (CINDEX) checklist was the instrument used. Both descriptive and inferential statistics were used in analysing the data. The findings revealed that medium scale enterprises average level of compliance of IFRSs is 77.9%. Also, enterprise’s attributes such as types, profitability, and audit type are able to influence 70.6% of the variance in the level of enterprise’s compliance with IFRSs disclosure requirements. The study recommended that the National Board for Small Scale Industries (NBSSI) and the owner/managers of the various SMEs in the metropolis should liaise with Institute of chartered Accountant Ghana (ICAG) to organise regular training programmes, for accountants within the sector, intended to provide practical guide for compliance with the International Accounting Standard Board (IASB).

Introduction
The ever-increasing role and focus on financial accounting among Small and Medium-Sized Enterprises (SMEs) cannot be over emphasised because of its vital end products. Most SMEs performances are usually assessed using their financial statements. Through financial accounting, SMEs are able to identify, measure, classify, and communicate their financial information to owners and other stakeholders which permit users to make informed judgment and decisions (Wood & Sangster, 2008). Investors who have funds to invest or lend may decide where to place resources based on the financial reports.
As the forces of globalisation increase momentum, more and more countries are now opening their doors to foreign investment and as business themselves expand across borders, both the public and private sectors are increasingly recognising the benefits of having a uniform financial reporting framework supported by strong globally accepted accounting standards (Zorklui & Barbie, 2003). Attempt towards harmonisation led to the establishment of International Accounting Standards Committee (IASC) in 1973 which released a series of standards called International Accounting Standards (IAS) in a numerical sequence that began with IAS One (1) and ended with IAS 41 between the years 1973 to 2000 which was published in December, 2000 (Institute of Charted Accountants England and Wales, 2010).
From April 2001, the International Accounting Standard Board (IASB) assumed accounting standard setting responsibilities from its predecessor body IASC with the authority of making the standards mandatory among all it members (Addo, 2010). The IASB adopted the body of standard issued by IASC which will continue to be designated 'IAS' but any new standards would be published in series called International Financial Reporting Standards (IFRS). The long awaited globally accepted accounting standard has become a success with the development of IFRS by IASB with over 120 countries synchronising their standards to IFRS including Ghana.

Statement of the Problem
Ghana in its quest to promote accelerated growth of the economy through private sector-led growth converge its out-dated Ghana Accounting Standards (GAS) to IFRS effective 1 st January, 2007 (Addo, 2010;Antwi, 2010). The council of the ICAG, resolved to migrate from using the GAS as the financial reporting framework to the IFRS. The adoption formally launched on 23 rd January, 2007 required all enterprises including SMEs, to comply with the IFRS as at 31 st December, 2007 and other entities were given an additional transition period of two years to comply. At present Ghana is among 15 countries in Africa to have adopted IFRS (Zori, 2011). However, anecdotal study by Chatham (2008) revealed that SMEs within the financial sector have frequently noted in annual reports that they are in full compliance with IFRS, when in fact there are material deviations from IFRS. Similarly, the International Federation of Accountants (IFAC) has observed auditors asserting that financial statements comply with IASs when the accounting policies and notes indicate otherwise (Holt, 2010). Given these findings, the activity and effectiveness of enforcement bodies that are responsible for promoting compliance with IFRSs among SMEs in most developing countries such as Ghana has been questioned.
Previous research focus mainly on SMEs domiciled in developed countries and also large scale enterprises. Developing countries and SMEs have been somewhat neglected. Eleven years after IFRS adoption in Ghana, few studies have been carried out in the area of IFRS compliance among SMEs. It is this gap that the study seeks to narrow by inquiring the extent of compliance with IFRS by some selected SMEs in the Cape Coast Metropolis (CCM). [3]

Objectives of the Study
The general objective of the study was to explore the extent to which SMEs in CCM comply with IFRSs. The specific objectives of the study were to: 1) Examine the extent and level of compliance with IFRSs by SMEs in CCM? 2) Find out whether certain firm attributes influence the level of SMEs compliance with IFRSs?

Research Question and Hypothesis
In order to address the specific objectives of the study, the following research question and hypothesis were formulated to help guide the study. 1) What is the extent and level of compliance with IFRSs by SMEs in CCM? H0: Firm attributes have no statistically significant influence on the level of SMEs compliance with IFRSs.

Significance of the Study
The study will contribute immensely to literature in the area of accounting standards and IFRS compliance in Ghana. The study will further provide information on the extent to which SMEs comply with IFRSs and factors accounting for differences in compliance. The study will also provide appropriate basis to conduct future research in the area of IFRS compliance in Ghana.

Delimitation
The population of interest to the study was some selected SMEs in CCM. Due to the numerous numbers of IFRs the study was restrict to a number of standards that in the researchers view are more relevant and applicable to SMEs in Ghana and for that matter Cape Coast, thus: IAS I -Presentation of Financial Statements, IAS 7 -Statement of Cash Flows, IAS 12 -Income Tax, IAS 16 -Property Plant and Equipment, IAS 18 -Revenues, and IAS 19 -Employee Benefit. Furthermore, the study was delimited to certain attributes of SMEs such as size, profits, multinational affiliations, and leverage. Only registered, recognised and active SMEs in the metropolis were considered.

Literature Review
Generally, the use of IAS compliance as a variable in studies has evolved considerably in the past years (Chatham, 2008). Chatham emphasize that, earlier research on IAS compliance now IFRS, assumed that an enterprise attestations regarding its use of IAS in the financial statement were sufficient to presume that the firms were fully complying with IASC standards, making IAS compliance a dichotomous measure. Some of these authors warn of tenuous nature of firm's degree of compliance, while others do not. These examinations often apply an event-study methodology to assess the effects of or reasons for initially adopting IAS.
Chatham (2008) measured degree of IAS compliance in SMEs domiciled in France, Sweden, and Switzerland. Two percentage compliance score were computed by Chatham (2008). The first score equally weights each of the forty six check list he developed. The second compliance score weights each question based on its perceived important to users of financial statement. Chatham discovered that, IAS compliance range from 70.25% to 95.31% compliance. Switzerland firms had the highest average percentage IAS compliance score of 85.3%, while the firms from Sweden had the lowest average compliance rate of 75.8%. Chatham also viewed the audit opinion on financial reports of firms as crucial in determining whether firms compliance or non-compliance with IAS are being affirmed by auditors in their blessings to the financial reports. The study revealed that out of the ninety one firms studied which claim compliance with IAS; only forty eight representing 52.7% had auditor confirmation of compliance.
Al-Shammari (2011) extends the study of IFRS compliance by investigating the extent to which 168 SMEs listed on KSE comply with the disclosure requirements of IFRSs. The annual reports of 2008 were examined using a self-constructed checklist based on 21 selected standards. Each disclosure item on the checklist was assigned the value of one if it was disclosed and zero if the item obviously applied but was not disclosed while items obviously not applicable to the report were coded as not applicable (NA). Disclosure index which was consistent with prior research was computed by dividing the total number of disclosure provided in SME's annual reports by the total applicable score. The study of Al-Shammari (2011) revealed that size, auditor type, liquidity, industry type, and internationality influenced the level of compliance among firms. Al-Shammari reported an adjusted R 2 of 0.407.

Materials and Methods
Descriptive research design was used for the study since the study sought to describe the extent of corporate compliance with IFRSs. The population of the study consisted of eight strata of registered SMEs grouped into various associations recognised by the National Board for Small Scale Industries (NBSS) in CCM (NBSS, 2017). The accessible population for this study was all medium scale enterprises in the metropolis. Emphasis was on medium scale enterprises because small scale enterprises usually do not lay much interest in IFRS disclosure or compliance. According to the NBSS (2017), there are 719 registered and active SMEs in CCM.

Sample and Sampling Procedure
A sample size of 89 was used for the study. The sample size was picked based on the recommendations of Ary, Jacobs, Razavieh and Sorensen (2006) who posit that a sample of 5 -10 percent of the population is appropriate for a descriptive survey study. This forms 12.4 percent of the population. Snowball sampling technique was used to select 89 medium scale enterprises in the metropolis since it was difficult to locate the various enterprises.
The sampling procedure began in each community with the help of the assembly men or women, other unit committee members and leaders of the various strata of SMEs in the metropolis. These people served as informants. As informants, the leaders of the groups of SMEs were able to identify other medium scale enterprises within the metropolis and also within their respective communities who qualified to participate in this study. Those medium scale enterprises identified in turn identify other medium scale enterprises in the study area not yet captured. Table 1 shows the sample of the study.

Sources of Data
The study mainly made use of secondary data. The secondary data were gathered through the various financial statements and reports of the selected medium scale enterprises. Also, review of existing literature mainly financial management books, articles, journals, theses and dissertations (both published and unpublished), internet, official records of the NBSSI and Newspaper reports. However, some primary data were obtained using an interview guide. This data dealt with information that were collected directly from the director of NBSSI, head of ICAG, Cape Coast office; and managers or owners of the selected enterprises.

Data Collection Instruments
Self-developed compliance checklist was used to collect data for the study. The self-developed compliance checklist was designed for each of the six selected IFRSs. The self-developed checklist was developed with reference to IFRSs issued by the IASB, checklist used in prior research (Street & Gray, 2002) and disclosure and presentation checklist published by Deloitte (2011). The validity and comprehensiveness of the checklist was confirmed by two experienced chartered accountant.
For each item on the checklist there are three possibilities for scoring: (a) the information item is disclosed in the annual report, denoted by "Yes"; (b) the information item is not disclosed in the annual reports despite the fact that it is applicable to the particular medium scale enterprise and the enterprise could have disclosed it, denoted by "No"; and the information item is not disclosed in the annual reports or financial statements because it is not applicable to the particular enterprise, denoted by "Not Applicable" (NA).

Measurement of Dependent Variable
The dependant variable in this research was IFRS compliance. The level of IFRS compliance was measured by a self-constructed compliance index (CINDEX) consistent with prior compliance studies (Ballas & Tzovas, 2010;Chatham 2008;Street & Bryant, 2002). The compliance index is the ratio of what an enterprise presented and disclosed in its annual report or financial statement  [6] to what it is obliged to present and disclose for each category of standard. Thus for each medium scale enterprise and for each standard selected compliance ratio was calculated as well as overall compliance ratio for each enterprise. For this reason, the compliance ratio is computed by dividing the total of (Yes) over the total applicable presentation and disclosure requirements.

Measurement of Independent Variables
Size of an enterprise (SME): The book value of equity and that of total assets was used to measure the size of an enterprise. This has been used in some prior studies (Ballas & Tzovas, 2010). Profitability: Profitability was measured by ratio of return on equity (ROE), and accounting profit. This has been used in previous studies (Ballas & Tzovas, 2010; Al-Shammari, 2011). Auditor type: Auditor type was measured by a dummy variable coded one if the enterprise was audited by one of the big four audit firms (PricewaterhouseCoopers, Deloitte & Touche, Ernst & Young, and KPMG) and zero otherwise. This measure is consistent with that of Al-Shammari (2011). The auditor type is identified from the auditor's report. Internationality: Internationality was measured by a dummy variable coded one if the enterprise has affiliation as subsidiary of a parent firm in any of the developed countries. This measure is consistent with that of Chattham (2008). Industry type: Industry was measured by a set of dummy variables. This measure is consistent with that of Al-Shammari (2011). Leverage: Leverage was measured by debt to equity ratio. This is consistent with prior research (Mutawaa & Hewaidy, 2010).

Data Collection Procedures
In this study, data was gathered largely from secondary source. They were obtained from the 2017 annual financial reports of the selected SMEs in CCM. In all, 89 available annual financial reports for 2017 financial year were gathered from the SMEs visited. Some of the reports were obtained from the websites of the selected medium scale enterprises. During the process of examining the annual financial reports for compliance, it was discovered that some of the medium scale enterprises have not prepare their financial reports in accordance with IFRS but in accordance with U.S GAAP making them irrelevant for their inclusion in the study. In effect, 67 annual financial reports were successfully obtained for analysis.
The self-developed compliance checklist was applied to each annual report to check compliance. Prior to checking compliance, each annual report was thoroughly read and consolidated by logical reasoning to determine applicability of each of the checklist items. For scoring, each disclosure item ticked under category "a" (Yes) on the checklist was given a score of one and a zero score for category "b" (No) and "C" (NA). This approach is consistent with prior research by Ballas and Tzovas (2010), and Al-Shammari (2011).

Data Processing and Analysis
The data collected were analysed both qualitatively and quantitatively. Descriptive and inferential statistics were used to analyse quantitative data while qualitative data were analysed interpretatively and patterns were identified after using the axial coding method. In line with the framework of analysis used by many researchers (Al-Shammari, 2011; Street & Bryant, 2002), compliance scores was categorised into four levels. High compliance, if the presentation and disclosure index is 80% or more, intermediate compliance between 60% and 79%, low compliance between 40% and 59%, and below 40% which reflects a substantial gap between an enterprise disclosure and present action practices and the IFRSs requirements.

Results and Discussions
This section deals with the descriptive statistics for the independent variables. The information on all the variables were obtained from the 2017 annual financial statements of 67 randomly selected medium scale enterprises in CCM. The results are presented in Table 2.  Table 2 shows a brief statistical description of the explanatory variables. The data was derived from 67 SMEs in CCM 2017 annual reports. The SMEs' size was measured by book value of equity and total assets. Company size measured by book value of equity ranged from -0.66725 to 27023 thousand Ghana cedis with an average size of 967 thousand Ghana cedis. Company size measured by total assets ranged from 0.953588 to 62629 thousand Ghana cedis with an average of 2750 thousand Ghana cedis. The standard deviation of this variable is moderate either measured in terms of book value of equity or total assets. This means that, measures of enterprise size are moderately non-dispersed in a widely-spread distribution, and that the effects of size of an enterprise on compliance level of IFRSs disclosure requirements was an approximation to a normal distribution.
Profitability was measured by return on equity and return on total assets. Average percentage profitability was -3.253 (reflecting high negative return on equity) as measured by return on equity with a minimum of -80.700 and a maximum of 1.170. However, profitability as measured by return on total assets gave a more positive picture with an average of 0.025 and ranged from -0.597 to 0.342.

Level of compliance with IFRSs by SMEs in CCM
The rationale behind this objective was to examine the extent as well as the level to which SMEs in CCM complies with IFRS presentation and disclosure requirements. Table 3 shows the presentation and disclosure compliance rates of industries with regards to each selected IFRS. For the purpose of ethics in research, the extents of compliance by medium scale enterprises in the metropolis are presented on the basis of SME groupings. From Table 3, with the exception of other services such as hairdressing, barbering and so on (Mean = 0.590), IAS 18 represented the only standard with absolute compliance of 100% observed for all the other seven categorise of medium scale enterprises. This implies that out of the 67 medium scale enterprises captured for the study, 64 of them complied fully with the presentation and disclosure requirement of IAS 18. This is incongruent with Street and Bryant (2002) who found significant non-compliance with IAS 18. With the exception of IAS 18 there are meaningful differences in compliance within and among medium scale enterprises with regard to the selected IFRSs.
IAS 1 differs among SME with the two highest means of 89.9% and 86.1% by the boarding and accommodation establishment, and manufacturing respectively; and with a least mean of 71.4% for paper converters/IT. Surprisingly no enterprise complied fully with the presentation and disclosure requirement of IAS 1. The checklist reveals non-compliance with regards to IAS 1 was common for disclosure required for management's assessment of an entities assessment as a going concern and disclosure information required to evaluate an entity's objectives, policies and processes for managing capital.
IAS 7 is the standard next to IAS 18 which is highly complied by all medium scale enterprises though did not achieve an overall 100% mean but an overall mean of 98.6%. Three industries embodying pharmaceutical and beverages; manufacturing and trading; and metal, engineering and oil scored a mean compliance of 100% respectively. This implies that all medium scale enterprises belonging to these industries fully complied with presentation and disclosure requirement of IAS 7. Medium scale enterprises belonging to boarding and accommodation establishment, finance and insurance, paper converters and information technology, and agric and agro industries scored a mean compliance of 99.2%, 98.0%, 97.8%, and 97.2% respectively. These results suggest little or no difficulty by medium scale enterprises in meeting the presentation and disclosure requirement of IAS 7.
The two highest rates of compliance for IAS 16 with a mean of 98.8% and 98.2% were achieved by medium scale enterprises in the categories of boarding and accommodation establishment, and pharmaceutical and beverages respectively. The average compliance level with regard to IAS 16 was 85.9% which reveals little or no difficulty in meeting presentation and disclosure requirement of property, plant and equipment. Surprisingly while SMEs in the boarding and accommodation establishment, and pharmaceutical and beverages SME were having less difficulty in dealing with this standard, some SMEs in the services such as hairdressing, barbering and so on scored as low as 46.2% compliance with IAS 16 suggesting difficulty in compliance by SMEs in such category.
The least compliance rate was observed for IAS 19 among other standard as noted earlier in the preliminary analysis. Paper converters and information technology medium scale enterprises scored as low as 30% mean compliance. Finance and insurance medium scale enterprises also had a poor mean compliance of 55.2%; however manufacturing and trading medium scale enterprises differ significantly with a mean compliance of 91.7%. This suggests extreme difficulty by most medium scale enterprises in meeting the presentation and disclosure requirement of employee benefit. Data gathered reveals extreme difficulty by most medium scale enterprises in dealing with disclosure required under defined benefit plan which involves critical actuarial assumptions.
IAS 12 also varies among SMEs with regards to their rate of compliance. Medium scale enterprises in the manufacturing and trading complied most with IAS 12 with a mean compliance of 95.8%, followed by metal, engineering and oil (86.1%), pharmaceutical and beverages (85.4%), paper converters and information technology (83.3%), finance and insurance (81%), and the least compliance by agric and agro medium scale enterprises with a mean compliance of 67.9%. IAS 12 requires a numerical reconciliation between tax expense and the product of accounting profit multiplied by the applicable tax rate, disclosing also the basis on which the applicable tax rate is computed; or a numerical reconciliation between the average effective tax rate and applicable tax rate is computed. This requirement was problematic for a number of medium scale enterprises accounting for significant non-compliance with IAS 12. Table 3 clearly reveal variability in compliance within medium scale enterprises and among medium scale enterprises and congruent with Street and Bryant (2002) who concluded that the level of compliance by SMEs claiming to have adopted IASs is mixed and selective.

Influence of firm attributes on the level of SMEs' compliance with IFRSs
The rationale behind the second research question was to determine which firm attributes account for differences among SMEs compliance rate with IFRSs presentation and disclosure requirement. This analysis is undertaken to better understand the individual contribution of the selected company attributes to the level of enterprise's compliance with IFRSs disclosure requirements. The summary of the result analysis is shown in Table 4.  Table 4 indicates that among the selected attributes of medium scale enterprises used for the study, profitability as measured by both return on equity and return on total assets, types of auditor, and types of SME were the only statistically significant attributes with regard to firm's level of compliance with IFRSs disclosure requirements. The attributes of medium scale enterprises that influence or predict enterprises level of compliance with IFRSs disclosure requirements in order of importance were types of SME ( = 0.538 (0.007), p < 0.01), profitability as measured by return on equity ( = 0.459 (0.002), p < 0.05), type of auditor ( = 0.406 (0.033), p < 0.05) and profitability as measured by return on total assets ( = -0.463 (0.078), p < 0.01). These findings are similar to that of Al-Shammari (2011) who found positive prediction for profitability as measured by return on equity ( = 0.118, p < 0.01); auditor type ( = 0.026, p < 0.01); and SME type ( = 0.084, p < 0.01). Table 4 indicates further that all the statistically significant attributes of medium scale enterprises influence firm's level of compliance with IFRSs disclosure requirements positively, except profitability as measured by return on total assets that contributes negatively to the dependent variable, though statistically significant.
It is however significant to observe that the proportional contribution (R 2 ) of all the attributes of the medium scale enterprises in the metropolis to the firm's compliance level with IFRSs disclosure requirements was 0.706 with an adjusted R 2 of 0.599 which is higher than that of Al-Shammari (2011) who reported an adjusted R 2 of 0.523. This means that the selected attributes of  [11] medium scale enterprises (independent variables) are able to influence, predict, or explain 70.6 percent of the variance in the level of enterprise's compliance with IFRSs disclosure requirements. It therefore, means that besides these selected attributes of medium scale enterprises identified; other variables that are not in the model have a chance of influencing, explaining or predicting about 29.4 percent to the level of medium scale enterprises' compliance with IFRSs disclosure requirements.
Company size as measured by book value of equity and total assets, internationality and leverage have no statistically significant influence or contribution to the medium scale enterprises level of compliance with IFRSs presentation and disclosure requirements. However, among the statistically significant contributing attributes, types of SME is the most statistically significant company attributes that influences or contributes to firm's level of compliance with IFRSs presentation and disclosure requirements in the metropolis.

Conclusions
Based on the findings from the study, it can be concluded that the extent of IFRSs compliance by SMEs in CCM is high with an overall mean compliance of 77.9% but far from full compliance. Also, no medium scale enterprise achieved full compliance score. Furthermore, medium scale enterprises who are audited by the international auditing firms comply more than companies audited by the local auditing firms. Firm attributes of profitability, internationality, auditor type, and SME type influence the extent of IFRSs compliance. However, SME type is the most influential among the attributes as well as the attribute with a strong link with IFRSs compliance level.


Single-Machine Parallel-Batch Scheduling with Nonidentical Job Sizes and Rejection

: We investigate the single-machine parallel-batch scheduling problem with nonidentical job sizes and rejection. In this problem, a set of jobs with different processing times and nonidentical sizes is given to be possibly processed on a parallel-batch processing machine. Each job is either accepted and then processed on the machine or rejected by paying its rejection penalty. Preemption is not allowed. Our task is to choose the accepted jobs and schedule them as batches on the machine to minimize the makespan of the accepted jobs plus the total rejection penalty of the rejected jobs. We provide an integer programming formulation to exactly solve our problem. Then, we propose three fast heuristic algorithms to solve the problem and evaluate their performances by using a small numerical example.

Introduction
In this paper, we investigate the single-machine parallel-batch scheduling problem with nonidentical job sizes and rejection. This problem can be addressed as follows. We are given a set of s ∈ , and a rejection penalty j e , 1, 2, , j n =  . A job j J is either accepted and then processed on the machine or rejected by paying a certain penalty j e , 1, 2, , j n =  . The machine can simultaneously process a number of jobs as a batch subject to the constraint that the total size of jobs in the batch is not larger than the capacity 1 of the machine. The processing time for a parallel batch is defined as the longest processing time of the jobs in the batch. Preemption is not allowed. Our task is to choose the accepted jobs and schedule them as batches on the single machine to minimize the makespan of the accepted jobs plus the total rejection penalty of the rejected jobs. Let A denote the accepted job subset and R J A = − denote the rejected job subset. Given the accepted job subset A and its corresponding schedule σ , let j C denote the completion time of job j J when job j J is accepted. Then, using the general three-field notation for scheduling problem [1], the problem can be denoted by cost. The first part max C represents the maximum completion time (i.e., makespan), which describes the cost for working time. The second part j j R e ∈  represents the total rejection penalty, which describes the cost for outsourcing and/or for loss in revenue and customer goodwill. The second part does not have to be scaled since we may always scale the individual rejection penalties. Our problem falls into the category of single-machine batch scheduling. Since Ikura and Gimple [2] initiated the work on the single-machine batch scheduling, single-machine batch scheduling has been investigated extensively in the past few decades. Brucker et al. [3] studied the single-machine batch processing scheduling problem with the goal to minimize regular scheduling criteria that are nondecreasing on the job completion times. Liu and Yu [4] considered the single-machine batch processing scheduling problem with jobs having release dates and the objective function is to minimize the makespan. Cheng et al. [5] investigated an unbounded batch processing machine scheduling problem with jobs having release dates and deadlines. Liu et al. [6] set the complexity of scheduling an unbounded batch machine. Zhang et al. [7] studied the single-machine batch processing scheduling problem with the goal to minimize the makespan. A survey on batch processing scheduling was given by Potts and Kovalyov [8].
In the above-mentioned studies, the assumption that all the jobs are required to be accepted with processing and no rejection is allowed is made. However, in some actual situations, due to the limited production capacity and tight delivery time requirement, the decision-maker may need to reject some jobs by paying the corresponding rejection penalties. In recent years, some researchers have started to focus on batch processing scheduling with job rejection. Lu et al. [9] studied an unbounded parallel-batch processing machine scheduling problem with release dates and rejection with the goal to minimize the makespan plus the total rejection penalty. They showed that the problem is weakly NP-hard and derived a fully polynomial time approximation scheme (FPTAS). Furthermore, for the bounded parallel-batch processing machine scheduling problem with release dates and rejection, Lu et al. [10] proved that it is strongly NP-hard and presented a two-approximation algorithm and a polynomial time approximation scheme (PTAS); Cao and Yang [11] also derived a PTAS. He et al. [12] considered two bi-criteria single parallel batch processing machine scheduling problems with job rejection being allowed; one is to minimize the makespan as long as the total rejection cost is not larger than a given threshold, and the other is to minimize the total rejection cost as long as the makespan is not larger than a given threshold.
Note that, if all jobs have identical processing time and the rejection penalty for each job is infinity, then the problem is just the classical one-dimensional bin packing problem, which is strongly NP-hard [13]. Naturally, our problem max 1| , , | j j j R p batch s rej C e ∈ − +  is strongly NP-hard.
Our problem extends the models proposed in Lu et al. [9] and Zhang et al. [7]. By setting each job has the identical size, the model proposed in Lu et al. [9] is our special case. When we set j e = +∞ , the model proposed in Zhang et al. [7] becomes our special case. The remainder of this paper is organized as follows. In Section 2, we give the integer programming formulation to exactly solve our problem. In Section 3, we proposed three fast heuristic algorithms to solve our problem followed by a numerical example to show the solution results by running these algorithms in Section 4. Finally, we conclude the paper in Section 5.

Integer Programming Formulation
In this section, we derive an integer programming formulation for problem max 1| , , | , , 1,2, , ; ij i {0,1}, 1,2, , ; The objective function in Equation (1) tries to minimize the makespan (maximum completion time) of the accepted jobs plus the total rejection penalty of the rejected jobs. The constraint set in Equation (2) ensures that each job is either accepted to process in some batch or rejected. The constraint set in Equation (3) describes that the total size of the accepted jobs assigned into the same batch is not greater than the capacity size 1. The constraint set in Equation (4) states that there exists a job assigned into some batch if and only if this batch is opened. The constraint set in Equation (5) guarantees that the processing time of each job assigned into some batch is not greater than the longest processing time in this batch. The constraint set in Equation (6) gives the lower bound and upper bound for the longest processing time in some batch. Finally, the constraint sets in Equations (7)-(9) impose the binary restriction on ij Note that the problem includes the well-known strongly NP-hard problem Bin Packing [13] as its special case. Thus, exactly solving its IP Formulation is also strongly NP-hard [13]. It is impossible to solve it exactly in polynomial time according to the NPcompleteness theory [13]. Thus, we turn to design fast heuristic algorithms to obtain an approximate feasible solution. However, if one relaxes the binary variables ij x , i y , and j z , , 1,2, , to real variables, then we obtain its relaxed version for the IP Formulation, which can be exactly solved in polynomial time by using the well-known interior point method [14]. The optimal objective function value of the relaxed version is a lower bound for that of its IP Formulation.

Three Heuristics Algorithms
In this section, we focus on to design some fast heuristic algorithms to solve the approximate solution for problem max 1| , , | j j j R p batch s rej C e ∈ − +  . For the first two heuristic algorithms (Algorithms 1 and 2), the main idea is first to determine the rejected job subset and then construct batches for the accepted jobs to process them in an arbitrary order on the machine. For the third heuristic algorithm (Algorithm 3), the main idea is first to construct batches for the accepted jobs and then by checking each batch determine the rejected job subset. Our heuristic algorithms are listed as follows.

Algorithm 1
Step A π π π  is a permutation of the accepted jobs.
Step Step 4: From Step 5: Processing the opened batches 1 2 , , , k B B B  in an arbitrary order on the machine and output the solution Step 1. First sort all the jobs in J according to the non-increasing order of the job processing times, i.e., ( , , , ) n π π π  is a permutation of (1, 2, , ) n  .
Step 2. Construct a series of rejected job subsets i R as follows: Step 3: From 0 i = to n do the following: Step 3.1: For the accepted jobs in i A , first sequence them in non-increasing order of the job processing times, i.e.,  is a permutation of the accepted jobs in i A .
Step Step 3.4: Processing the opened batches 1 2 , , , in an arbitrary order on the machine. Step 1. First sort all the jobs in J according to the non-increasing order of the job processing times, i.e., ( , , , ) n π π π  is a permutation of (1, 2, , ) n  .
Step 2: Open the first batch 1 B . Initially, let 1 : Step 3: From 1 i = to n, do the following: Step 4: For all the constructed batches q B , , we remove batch q B and reject all the jobs in q B ; otherwise we reserve the batch q B .
Step 5: Processing the reserved batches in an arbitrary order on the machine. the reserved batches are subject to the batch capacity constraint, which implies the outputted solution is feasible. Hence, it is proven. □ The above three algorithms are combinatorial algorithms. Their running times are faster than some meta-heuristic approach proposed by Shojafar et al. [15] for cloud job scheduling problem and bio-inspired greedy or clustering algorithms proposed by Alizadeh et al. in [16] for batch scheduling problems and Amato et al. in [17] for multimedia stories' creation problem from online social networks.

A numerical Example
In this section, we present a small numerical example to show how Algorithms 1, 2 and 3 work and use the exact solution with solving the IP to evaluate the quality of solutions returned by the three heuristics algorithms.
Numerical example. Consider the following 10 n = jobs to be possible processed on a single batch processing machine. The capacity for the machine is 1. The corresponding processing times, sizes and reject penalties for the 10 jobs are shown in Table 1. Table 1. The processing times, sizes and reject penalties for the given 10 job. Solution results. The IP solver used was Lingo 11. Algorithms 1, 2 and 3 were implemented in MATLAB. All tests were run on an Intel Core i5-4200 PC with a 2.5 GHz dual core processor, 4 GB of RAM, and the Windows 10 operating system. The collected times are the actual run times for the program, in seconds.
We first solved the IP formulation for the numerical example with 10 jobs by using Lingo 11, which takes a very long time, about 14 h. We obtained the optimal values for * j Z , 1, 2, ,10 j =  , as shown in Table 2.
According to the values of An illustration chart for the makespan of the optimal solution is shown in Figure 1. Running Algorithms 1, 2 and 3 we obtained the solution results in 5 s. All solution results are shown in Table 3, where "OBJ" denotes the objective function value.

Algorithm
The Accepted Jobs and Its Batches The rejected jobs OBJ    In the actual application, we should run all the three proposed heuristic algorithms and choose the best solution.
Remarks. The above-proposed Algorithms 1, 2 and 3 cannot been applied to other objective functions. If one changes the objective function, then we should redesign the algorithms for the new objective function.

Concluding Remarks
In this paper, we investigate the single-machine parallel-batch scheduling problem with nonidentical job sizes and rejection. Our proposed problem generalizes many existing batch scheduling problems. Our proposed heuristic algorithms are combinatorial and run more quickly than some existing bio-inspired algorithms. It would be interesting to further explore other objective functions and design some fast algorithms with good performance ratio.