ارایه یک مدل بهینه سیستم خدماتی رقابتی در حالت عدم قطعیت با استفاده از الگوریتم تکامل تفاضلی بهبود یافته
محورهای موضوعی : آمار
محمد فلاح
1
,
رضا توکلی مقدم
2
,
علی پهلوانی
3
,
علی رضا سلامت بخش ورجوی
4
1 - گروه مهندسی صنایع، واحد تهران مرکزی، دانشگاه آزاد اسلامی، تهران، ایران
2 - دانشکده مهندسی صنایع، پردیس دانشکده‌های فنی، دانشگاه تهران، تهران، ایران
3 - دانشکده مهندسی صنایع، دانشگاه علم و صنعت ایران، تهران، ایران
4 - گروه مهندسی صنایع، واحد علوم و تحقیقات، دانشگاه آزاد اسلامی، تهران، ایران
کلید واژه: Competition, Differential Evolution, Congestion, Location allocation,
چکیده مقاله :
در این مقاله، ارائه یک مدل بهینه‌سازی همزمان جایابی و تخصیص سرور برای شرکت تازه وارد در یک بازار رقابتی مورد توجه قرار گرفته است. هدف بیشینه‌سازی سود شرکت است. مشتریان بهصورت احتمالی و بر اساس معیارهای قیمت، زمان سفر و زمان انتظار در صف، تسهیلات مورد نظر را انتخاب می‌کنند. همچنین فرض می‌شود میزان آگاهی مشتریان از سطوح زمان‌های انتظار در مراکز به صورت مرحله‌ای و طی استفاده‌های متوالی از شبکه افزایش می‌یابد. تقاضا به صورت کششدار و تابعی از مطلوبیت مشتریان از طراحی کل شبکه و هزینه ارائه یک واحد خدمات در یک مرکز به صورت تابعی از تقاضای جذب شده آن تعریف می‌شود. برای حل مدل یک الگوریتم تکامل تفاضلی بهبود یافته توسعه داده شده و مسائل نمونه برای نمایش کارایی آن حل شده است. نتایج با روش‌های معرفی شده در تحقیقات پیشین مقایسه گردیدند. نتایج عددی حاکی از آن است که رویکرد پیشنهادی قادر است نسبت به روش‌های پیشین نتایج بهتری ارایه نماید و می‌تواند در حل مسائل کاربردی مورد استفاده قرار بگیرد.
This paper presents a simultaneous optimization model of location and server allocation for a company that enters into a competitive market. The goal is company's profit maximization. Customers are likely to select the facility based on price, travel time and queue time. Furthermore, as a contribution to the literature, it is assumed that customer awareness of the levels of waiting times in the facilities will increase in stages and over the successive uses of the facilities network. Demand is defined elastic and as a function of the customer's desirability of network’s design and the cost of delivering service at a facility is defined as a function of its demand attraction. An improved differential evolution algorithm has been developed to solve the model and sample problems to demonstrate its efficiency have been solved.
[1] Ahn, H. K., Siu-wing,ch., Otfried, ch., Mordecai,G. and Renevan, O., ”Competitive facility location: The Voronoi game”, Theoretical Computer Science, 2004, Vol. 310, pp. 457-467.
[2] C. F. Saidani N., Chen H, “Competitive facility location and design with reactions of competitors already in the market,” European Journal of Operational Research, 2012, Vol. 219, No. 1, pp. 9-17.
[3] Drezner, T. “Competitive location strategies for two facilities”. Regional Science and Urban Economics, 1982, Vol. 12, pp. 485-493.
[4] Drezner, T. “Locating a single new facility among existing unequally attractive facilities”. Journal of Regional Science, 2006, Vol. 34. pp. 237-252
[5] Plastria, F. and L. Vanhaverbeke,” Discrete models for competitive location with foresight”. Computers and Operations Research, 2008, Vol.35, pp. 683-700.
[6] Drezner, T. and Z. Drezner. “Finding the optimal solution to the Huff based competitive location model”. Computational Management Science, 2004, Vol. 1, pp. 193-208.
[7] Eiselt, H., Laporte, G., and Thisse, J., "Competitive location models: A framework and bibliography", Transportation Science, 1993, Vol. 27, pp. 44-54.
[8] Drezner T., "Competitive facility location in the plane", in: Z. Drezner (Ed.), Facility Location. A Survey of Applications and Methods, Springer, 1995, pp. 285-300.
[9] Garcia Pérez, M. D. and Pelegrín, B. ‘All Stackelberg location equilibria in the Hotelling’s duopoly model on a tree with parametric prices’, Annals of Operations Research, 2005, Vol. 122, pp. 177-192.
[10] Eiselt, H.A. and Laporte, G. (1996) ‘Equilibrium results in competitive location models’, Middle East Forum, 1996, Vol. l, pp. 63-92.
[11] Eiselt, H.A. and Laporte, G. ‘Sequential location problems’, European Journal of Operational Research, 1996, Vol. 96, pp. 217-231.
[12] Kohlberg, E., "Equilibrium Store locations when consumers minimize travel plus waiting time", Economics Letters, 1983, Vol. 11, pp. 211-216.
[13] Silva, F. and Serra, D., "Incorporating waiting time in competitive location models", Networks and Spatial Economics, 2007. Vol. 7, pp. 63-76.
[14] Zhang, L. and Rushton, G., "Optimizing the size and locations of facilities in competitive multi-site service systems", Computers and Operations Research, 2008, Vol. 35, pp. 327-338.
[15] Aboolian, R., Sun, Y., and Koehler, G.J., "A location–allocation problem for a web services provider in a competitive market", European Journal of Operational Research, 2009, Vol. 194, pp. 64-77.
[16] Drezner, Z. and Wesolowsky, G. O., "Allocation of demand when cost is demand-dependent", Computers and Operations Research, 1995, Vol. 26, pp. 1-15.
[17] Farhan, B. and Murray, A. T., "Distance decay and coverage in facility location planning", Annals of
Regional Sciences, 2006, Vol. 40, No. 2, pp. 279-295.
[18] Dasci A. and Laporte G., "Location and pricing decisions of a multistore monopoly in a spatial market", Journal of Regional Science, 2004, Vol. 44, pp. 489-515.
[19] Aboolian, R., Berman, O. and Krass, D., "Competitive facility location model with concave demand", European Journal of Operational Research, 2007,Vol. 181, No. 1, pp. 598–619.
[20] Berman, O. and Krass, D., "Locating multiple competitive facilities: Spatial interaction models with
variable expenditures", Annals of Operations Research, 2002, Vol. 111, pp. 197-225.
[21] Huff, D., "Defining and estimating a trading area", Journal of Marketing, 1964, Vol. 28, pp. 34-38.
[22] McFadden, D., "Conditional Logit Analysis of Qualitative Choice Behaviour", Zarembka P. (ed.), Frontiers in Econometrics, Academic Press, New York, 1974.
[23] Marianov, V., Rios, M. and Icaza, M. J., "Facility location for market capture when users rank facilities by shorter travel and waiting times", European Journal of Operational Research, 2008, Vol. 191, pp. 32-44.
[24] Hillier, F., Lieberman, G., "Introduction to Operations Research", Holden-Day, Oakland, CA, 1986.
[25] Price, K.V., Storn, R.M, and Lampinen, J.A. “Differential Evolution: A Practical Approach to Global Optimization.” Natural Computing Series, Springer, 2005.
[26] L´opez Cruz, I.L., L.G., Willigenburg, van, and van Straten, G. “Efficient differential evolution algorithms for multimodal optimal control problems.” Applied Soft Computing, 2005. Vol. 3, PP. 97-122.
[27] Cordeau, J.F., Gendreau, M, and Laporte, G. “A tabu search heuristic for periodic and multi-depot vehicle routing problems.” Networks, 1997, Vol 30. PP.105
