Conclusion and Recommendation Introduction

51 management should communicate with their staff members to have a common view and goals to enhance their productivity, as shown in correlational analysis, management in both industries emphasize more on stress and job satisfaction; while non-management employees in food services and information and communication industries emphasize more on working arrangement and job content and information technology skills respectively. Other critical factors also important and correlated to enhance the productivity of employees, hence management would not ignored them. Management can learn from the case of LBA to adopt work-life balance and flexible working arrangement schemes to reduce the conflicts between employees’ family and work, and enhance the job motivation of employees Verespej 2000:25. Also, good matching of job contents and information technology skills could make better use of employees’ abilities, increasing job satisfaction and productivity in the long term Anderson 1989:171-186. Employees were important assets in an organization, and the management should make use of the findings to enhance productivity of employees. Learning from other organization and understand the needs of employees were essential for developing optimal schemes to enhancing job motivation and satisfaction, thereby benefit the competiveness of organization in the long run. References 1. Accel-Team 2011 ‘What is productivity?’ Productivity Improvement [online] available from http:www.accel-team.comproductivityproductivity_01_what.html [17 March 2011] 2. Akerlof, G. A. 1984 ‘Gift Exchange and Efficiency-Wage Theory: Four Views.’ The American Economic Review 74, 2 80-82 3. Albion, M. J. 2004 ‘A Measure of Attitudes Towards Flexible Work Options.’ Australian Journal of Management, 292, 285 4. Anderson, E. E. 1989 ‘The Implementation of Information Systems for Workers: A Structural Equation Model.’ Information Management 16, 4 171-186 5. Census and Statistics Department 2011 Checking Hong Kong Standard Industrial Classification Version 2.0 HSIC V2.0 - Detailed Structure. [online] available from http:www.censtatd.gov.hkproducts_and_servicesonline_serviceshsic_search_toolindex .jsp?page=full_hierarchy [17 March 2011] 6. Census and Statistics Department 2011 Employed persons by hours of work during the seven days before enumeration and sex. [online] available from http:www.censtatd.gov.hkhong_kong_statisticsstatistical_tablesindex.jsp?tableID=015 [17 March 2011] 7. Census and Statistics Department 2011 Median hours of work during the seven days before enumeration of employed persons by sex and industry of main employment. [online] available from http:www.censtatd.gov.hkhong_kong_statisticsstatistical_tablesindex.jsp?charsetID=1 tableID=016 [17 March 2011] 8. Census and Statistics Department 2011 Number of employed persons by industry and occupation. Census and Statistics Department, The Government of the Hong Kong Special Administrative Region 9. Census and Statistics Department 2011 Number of establishments, persons engaged and vacancies other than those in the Civil Service analysed by industry section. [online] 52 available from 10.http:www.censtatd.gov.hkhong_kong_statisticsstatistical_tablesindex.jsp?tableID=017 [17 March 2011] 11. Census and Statistics Department 2011 Quarterly Survey of Employment and Vacancies. Census and Statistics Department, The Government of the Hong Kong Special Administrative Region 12. Department of Psychology, University of Minnesota 1997 Minnesota satisfaction questionnaire. United States: Department of Psychology, University of Minnesota 13. Halkos, G. and Bousinakis, D. 2010‘The effect of stress and satisfaction on productivity.’ International Journal of Productivity and Performance Management 59, 5 415-431 14. Heneman, H. G., and Schwab, D.P. 1985 ‘Pay satisfaction: Its multidimensional nature and measurement.’ International Journal of Psychology 20, 2 136 15. Heuvel, S. G. V. D., Geuskens, G. A., Hooftman, W. E., Koppes, L. L. J. and Bossche, S. N. J. V. D. 2010 ‘Productivity Loss at Work; Health-Related and Work-Related Factors.’ Journal of Occupational Rehabilitation 20, 3 331-339 16. International Institute for Management development 2009 ‘Factor breakdown’ IMD WORLD COMPETITIVENESS YEARBOOK 2009 Switzerland: International Institute for Management development: 36-37 17. International Labour Office 2004 Working time and productivity Switzerland: International Labour Office, Information sheet No. WT-18 18. Legislative Council 2000 ‘The Council negatived a motion moved by Hon LAU Chin- shek urging the Administration to expeditiously legislate for regulating workers working hours’ Proposal for prescribing the maximum number of working hours in Hong Kong. Legislative Council, The Government of the Hong Kong Special Administrative Region 19. Legislative Council 2011 Proposal for prescribing the maximum number of working hours in Hong Kong [online] available from http:www.legco.gov.hkdatabaseenglishdata_mpmp-max-working-hour.htm [17 March 2011] 20. Lindbeck, A. and Snower, D. J. 1987 ‘Theories of Involuntary Unemployment: Efficiency Wages Versus Insiders and Outsiders.’ European Economic Review 31, 1,2 407-410 21. Mahambare, V. 2010 Getting the best out of our workers. New Delhi: Mint. 23 September 22. Schramm J. 2010 ‘Clockwork Productivity.’ HR Magazine 55, 9 136 23. South-Western 2011 Labour Productivity [online] available from http:www.swlearning.comfeaturesbefecon_datalabor_productivitylabor_productivity_ definition.html [17 March 2011] 24. Spector, P. E. 1985 ‘Measurement of human service staff satisfaction: Development of the Job Satisfaction Survey.’ American Journal of Community Psychology 13, 6 708-711 25. Trayner, J. 2008 ‘No Saturdays. No 55-Hour Requirement. Are You Sure This Is a CPA Firm?’ CPA Practice Management Forum 4, 6 5-9 26. Vernon, K. 2009 Work-Life Balance: The Guide Hong Kong: Community Business 27. Yellen, J. L. 1984 ‘Efficiency Wage Models of Unemployment.’ The American Economic Review 74, 2 200-205 53 ISBBME-1167 A Genetic Algorithm and a Largest-order-value Method for the Two-machine Flowshop Scheduling Problem to Minimize the Total Tardiness Wei-Chieh Liang a Department of Business Administration, Cheng Shiu University, Taiwan oh_jackhotmail.com Chih-Hou Wen Department of Statistics, Feng Chia University, Taiwan m0043379fcu.edu.tw Win-Chin Lin Department of Statistics, Feng Chia University, Taiwan linwcfcu.edu.tw Chin-Chia Wu Department of Statistics, Feng Chia University, Taiwan cchwufcu.edu.tw Cheng-Hsiung Shin Department of Business management, Cheng Shiu University, Taiwan alpincsu.edu.tw Shuenn-Ren Cheng Graduate Institute of Business Administration, Cheng Shiu University, Taiwan tommycsu.edu.tw Abstract The tardiness criterion is one of the most prominent measures in the scheduling area. To keep the tardiness in a lower level means to reduce the penalties incurred for late jobs. On the other hand, the precedence constraint exists in some real-life scheduling problems. For example, in the scheduling of patients from multiple waiting lines or different physicians, patients in the same waiting line for scarce resources such as organs, or with the same physician often need to be treated in the first-come-first serve sequence to avoid ethical or legal issues, and precedence constraints can restrict their treatment sequence. Motivated by these observations, we study a two-machine flowshop scheduling problem to minimize the total tardiness. To solve this problem, we use a genetic and a larger-order-value method for searching a near optimal solution and evaluate the yielded solution compared with an optimal solution obtained by full enumeration method. Finally, we conduct the experiments to test performances of all the proposed algorithms for the small and big numbers of jobs, respectively. Keywords: Scheduling; Two-machine flowshop; total tardiness 54

1. Introduction

In many manufacturing and assembly facilities each job has to undergo a series of operations. Often these operations have to be done on all jobs in the same order implying that the jobs have to follow the same routine. The machines are then assumed to be set up in series and the environment is referred to as a flow shop see Pinedo 2008. Panwalker and Iskander 1977 claimed that flow time and tardiness are the most prominent measures. Essentially, minimizing the flow time keeps the work-in-process inventory at a low level while minimizing the tardiness reduces the penalties incurred for late jobs. The former represents internal efficiency while the latter represents external efficiency. Yeung et al. 2004 emphasized that flowshop scheduling problems exist naturally in many real-world situations since there are many practical as well as important applications for a job to be processed series with more than one stage in industry. As for the literature on the flowshop problems with tardiness measures, Sen et al. 1989, Kim 1993, and Schaller 2005 propose branch and bound BB algorithms with the objective of minimizing total tardiness, whereas Kim 1995 and Chung et al. 2006 develop BB algorithms to minimize total tardiness in m-machine flowshops problems. On the other hand, Gelders and Sambandam 1978 present heuristics that are based on priority rules for minimizing the sum of weighted tardiness, and Ow 1985 develops a heuristic for a case in which processing times of the jobs on the machines depend on characteristics of the jobs such as orderprocessing quantities of the jobs. Furthermore, some meta-heuristics have been devised for flowshop problems with tardiness measures. For example, Parthasarathy and Rajendran 1997 propose a simulated annealing algorithm to minimize the weighted sum of tardiness and Armentano and Ronconi 1999 present a tabu search method, while Onwubolu and Mutingi 1999 and Gen and Lin 2012 develop genetic algorithms. A review on various heuristics developed for m-machine flowshop problems is given in Vallada et al. 2008. Note that the flowshop scheduling problem with the objective of minimizing total tardiness is shown to be NP- hard even for the two-machine case by Koulmas 1994. However, the precedence constraint has not been considered in the two-machine flowshp setting. Moreover, application can be seen in surgery scheduling, there are two types of patients, elective and nonelective. For the elective patients, surgeries can be planned in advance, whereas for nonelective patients, surgeries are unexpected and need to be performed urgently see Chandra et al. 2014. In light of the above observations, we discuss a set of n jobs to be processed no preemptively on a two-machine flowshop that can be processed at most one job at a time. The remainder of this paper is organized as follows: In Section 2 we introduce some notation and formulate the problem. In Section 3 we develop two heuristics combined with three local search methods to find near-optimal solutions for the problem. In Section 4 we present extensive computational results to determine the performance of all the proposed methods. We conclude the paper and suggest topics for future research in the last section.

2. Problem Definition

The problem formulation is formally defined as follows. Consider a job set N={ J 1 , …, J n } to be processed on machines M 1 and M 2 . The processing times for each job J i on M 1 and M 2 are all constant and fixed numbers, say 1 i p and 2 i p , respectively. All jobs have the same processing order through the flowshop machines and are available at zero. Assume that there are no set-up times and jobs are processed without interruption or preemption. Each job can be processed on 55 one machine only. Specifically, we consider there are no precedence constraints among operations of different jobs but J u and J v has a precedent constraint only. That is, J u should be processed before J v , and it is also assumed that the period between J u and J v can be processed other jobs on machines. For a given sequence  , the completion time of a job scheduled in the ith position on machines M 1 and M 2 are defined C 1[k]  and C 2[k]  , where square brackets [ ] are used to signify the position of jobs in a sequence. Then, the completion times for the kth job in  on machines M 1 and M 2 , respectively is given by. 1[ ] 1[ ] 1 k k l l C p     2[ ] 1[ ] 2[ 1] 2[ ] max{ , } k k k k C C C p       and its tardiness is given by [ ] 2[ ] [ ] max{0, } k k k T C d     . The objective of this article is to find a schedule that minimizes total tardiness of n given jobs or min{ , } i T     , which is a widely considered performance measure in literature.

3. Heuristics Methods

In this study, we first apply a largest-order-value combined with a pairwise improvement scheme that is one of the differential evolution algorithms, and then use a genetic algorithm GA for the proposed problem. A brief of the steps of these algorithms are introduced as follows: Storn and Price 1997 proposed a differential evolution approach for minimizing possibly nonlinear and non-differentiable continuous space functions. By means of an extensive test bed it is demonstrated that the method converges faster and with more certainty than many other acclaimed global optimization methods. The major advantage is that this method requires few control variables, is robust, easy to use, and lends itself very well to parallel computation. In order to apply the differential evolution method to solve discrete optimization problem, Bean 1994 adopted the largest-order-value method lov to decode a set of N initial populations, which are chosen completely at random, to be used in the discrete optimization problems. The most important implementation details lov of the algorithm are summarized as follows: Step 1: N initial sequences were randomly generated and each is decoded by the largest-order- value method, Say, X 1 , X 2 , …, X N . We set N to 30 in this study. Step 2: For each X i , we use the pairwise interchange to improve X i . Step 3: Compare the temporary solution with the current best sequence and keep the best one that has the smaller objective function until N is reached. Step 4: The process is ended at 30 iterations based on our pretests. On the other hand, literature shows that the genetic algorithm GA has been widely and successfully used in many combinational problems see Bean 1964, Reeves 1995, Chen et al. 1995, Etiler et al. 2004, Wu et al. 2011. In view of these successful cases, we also adopt the GA algorithm for this problem. The key steps of the GA are discussed in the following.