Incorporating Return on Inventory Investment into Joint Lot-Sizing and Price Discriminating Decisions: A Fuzzy Chance Constraint Programming Model

Document Type : Research Paper


1 Clothing Engineering and Management Group, Department of Textile Engineering, Amirkabir University of Technology, Tehran, Iran

2 Department of Industrial Engineering, Amirkabir University of Technology, Tehran, Iran

3 Department of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran


Coordination of market decisions with other aspects of operations management such as production and inventory decisions has long been a meticulous research issue in supply chain management. Generally, changes to the original lot-sizing policy stimulated by market prices may impose remarkable deviation revenue throughout the supply and demand chain system. This paper examines how to set the channel prices and the lot-sizing quantities so that the potential maximal return on investment is gained under a differential pricing scenario involving a number of possibilistic constraints to deal with market-segmented price setting, marketing and lot-sizing decisions, concurrently. The model aims to maximize return on inventory investment (ROII). To solve the model, a fuzzy solution approach based on the novel credibility measure is developed. An efficient and tuned search procedure using particle swarm optimization is tailored to reach the solutions of the resultant non-linear crisp model. An illustrative example is also studied to demonstrate the practicability of the proposed mathematical model and its solution approach.


Main Subjects

Article Title [فارسی]

ادغام بازگشت سرمایه موجودی در تصمیمات توام قیمت‌گذاری متمایز و تعیین اندازه انباشته: یک رویکرد برنامه ریزی محدودیت شانسی فازی

Authors [فارسی]

  • رضا قاسمی یقین 1
  • سیدمحمدتقی فاطمی قمی 2
  • سیدعلی ترابی 3
1 گروه مهندسی پوشاک و مدیریت، دانشکده مهندسی نساجی، دانشگاه صنعتی امیرکبیر، تهران، ایران
2 دانشکده مهندسی صنایع، دانشگاه صنعتی امیرکبیر، تهران، ایران
3 دانشکده مهندسی صنایع، دانشگاه تهران، تهران، ایران
Abstract [فارسی]

هماهنگ­سازی تصمیمات بازاریابی با دیگر جنبه‌های مدیریت عملیات مانند تصمیمات تولید و موجودی، یکی از مهم­ترین چالش‌های مدیریت زنجیره عرضه بوده­است. در حالت کلی، تغییرات در اندازه انباشته با قیمت بازار برانگیخته می‌شود. در این مقاله، تصمیمات توام قیمت گذاری متمایز، مخارج بازاریابی و اندازه انباشته با هدف ماکزیمم سازی بازگشت سرمایه موجودی با در نظر گرفتن محدودیت‌های شانسی فازی مدل­سازی می‌شود. تابع هدف بازگشت سرمایه موجودی است که از حاصل نسبت سود به میانگین موجودی محاسبه می‌شود. به جهت حل مدل، یک رویکرد برنامه ریزی محدودیت شانسی مبتنی بر اندازه اعتبار توسعه داده می‌شود. از یک الگوریتم بهینه­سازی انباشته ذراتِ تنظیم شده، برای حصول به جواب استفاده می شود. در نهایت، کاربرد مدل و روش حل  این مقاله از طریق ارائه مثال عددی تحت مطالعه قرار می‌گیرد.

Keywords [فارسی]

  • قیمت‌گذاری متمایز
  • اندازه انباشته تولید
  • مدیریت درآمد
  • بهینه سازی فازی
  • اندازه اعتبار
Abad, P. L. (1988). Determining optimal selling price and the lot size when the supplier offers all-unit quantity discounts. Decision Sciences, 3(19), 622-634.
Bera ,U. K., Maiti, M. K., & Maiti, M. (2012). Inventory model with fuzzy lead-time and dynamic demand over finite time horizon using a multi-objective genetic algorithm. Computers and Mathematics with Applications, 64(6), 1822-1838.
De-los-Cobos-Silva, S. G., Terceño-Gómez, A., Gutiérrez-Andrade, M. A., Rincón-García, E. A., Lara-Velázquez, P., Aguilar-Cornejo, M., & Aguilar-Cornejo, M. (2013). Particle swarm optimization: An alternative for parameter estimation in regression. Fuzzy Economic Review, 18(2), 19-32.
Driankov, D., Hellendoorn, H., & Reinfrank, M. (1996). An introduction to fuzzy control  (2nd ed.). London, UK: Springer-Verlag.
Dye, C., & Hsieh, T. (2010). A particle swarm optimization for solving joint pricing and lot-sizing problem with fluctuating demand and unit purchasing cost. Computers and Mathematics with Applications, 60(7), 1895-1907.
Eberhart, R. C., & Kennedy, J. (1995). A new optimizer using particle swarm theory. Proceedings of the 6th International Symposium on Micro Machine and Human Science, Nagoya, Japan, 39-43.
Esmaeili, M. (2009). Optimal selling price, marketing expenditure and lot size under general demand function. International Journal of Advanced Manufacturing Technology, 45(1),191-198.
Eynan, A., & Kropp, D. H. (2007). Effective and simple EOQ-like solutions for stochastic demand periodic review systems. European Journal of Operational Research, 180(3), 1135-1143.
Feng, L., Chan, Y., & Cárdenas-Barrón, L. E. (2017). Pricing and lot-sizing polices for perishable goods when the demand depends on selling price, displayed stocks, and expiration date. International Journal of Production Economics, 185, 11-20.
Ghasemy Yaghin, R., Fatemi Ghomi, S. M. T, Torabi, S. A. (2013). A possibilistic multiple objective pricing and lot-sizing model with multiple demand classes. Fuzzy Sets and Systems, 231(2013), 26-44.
Ghasemy Yaghin, R., & Fatemi Ghomi, S. M. T. (2012). A hybrid fuzzy multiple objective approach to lot-sizing, pricing, and marketing planning model. In A. Meier & L. Donzé (Eds.), Fuzzy methods for customer relationship management and marketing: applications and classifications. USA: IGI Global, 271-289.
Ghasemy Yaghin, R. (2018). Integrated multi-site aggregate production-pricing planning in a two-echelon supply chain with multiple demand classes. Applied Mathematical Modelling, 53, 276-295.
Ghasemy Yaghin, R., Fatemi Ghomi, S. M. T., Torabi, S. A. (2015). A hybrid credibility-based fuzzy multiple objective optimisation to differential pricing and inventory policies with arbitrage consideration. International Journal of Systems Science, 46(14), 2628-2639.
Huang, H., Xu, S., & Chiang, C. (2015). Optimal fuzzy controller design using an evolutionary strategy-based particle swarm optimization for redundant wheeled robots. International Journal of Fuzzy Systems, 17(3), 390-398.
Inuiguchi, M., & Ramik, J. (2000). Possibilistic linear programming: A brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem. Fuzzy Sets and Systems, 111, 3-28.
Kim, D., & Lee, W. J. (1998). Optimal joint pricing and lot sizing with fixed and variable capacity. European Journal of Operational Research, 109(1), 212-227.

Lee, W. J. (1993). Determining order quantity and selling price by geometric programming optimal solution, bounds, and sensitivity. Decision Sciences, 24(1),76-87.

Lenscold, J. D. (2003). Marketing ROI: The path to campaign, customer, and, corporate profitability. USA: McGraw-Hill.
Li, J., Min, K. J.,  Otake,  T., & Voorhis, T. M. (2008). Inventory and investment in setup and quality operations under return on investment maximization. European Journal of     Operational Research, 185(2), 593–605.
Liu, B., & Iwamura, K. B. (1998). Chance constraint programming with fuzzy parameters. Fuzzy Sets and Systems, 94(2), 27-237.
Liu, B., & Liu, Y. K. (2002). Expected value of fuzzy variable and fuzzy expected value models. IEEE Transactions on Fuzzy Systems, 10(4), 445-450.
Lopez, J., Lanzarini, L., & Bariviera, F. A. (2012). Variable population MOPSO applied to medical visits. Fuzzy Economic Review, 17(1), 3-14.
Maity, K. (2011). Possibility and necessity representations of fuzzy inequality and its application to two warehouse production-inventory problem. Applied Mathematical Modelling, 35(3), 1252-1263.
Mandal, S., Maity, A. K., Maity, K., Mondal, S., & Maiti, M. (2011). Multi-item multi-period optimal production problem with variable preparation time in fuzzy stochastic environment. Applied Mathematical Modelling, 35(9), 4341-4353.
Montgomery, D. C. (2001). Design and analysis of experiments (5th ed.). New York, NY: John Wiley and Sons.
Mula, J., Peidro, D., & Poler, R. (2010). The effectiveness of a fuzzy mathematical programming approach for supply chain production planning with fuzzy demand. International Journal of Production Economics, 128(1), 136-143.
Otake, T., & Min, K. J. (2001). Inventory and investment in quality improvement under return on investment maximization. Computers and Operations Research. 28(10), 113-124.
Otake, T., Min, K. J., & Chen, C. (1999). Inventory and investment in setup operations under return on investment maximization. Computers and Operations Research, 26, 883-899.
Phillips, R. L. (2005). Pricing and revenue optimization. Stanford, US: Stanford University Press.
Poli, R., Kennedy, J., & Blackwell, T. (2007). Particle swarm optimization: An overview. Swarm Intelligence, 1(1), 33-57.
Porn R, Harjunkoski, I., & Westerlund T. (1999). Convexification of different classes of non-convex MINLP problems. Computer and Chemical Engineering, 23(3), 439-448.
Rosenberg, D. (1991). Optimal price-inventory decisions profit vs ROII. IIE Transactions, 23(1), 17-22.
Sadjadi, S. J., Ghazanfari, M., & Yousefli, A. (2010). Fuzzy pricing and marketing planning model: A possibilistic geometric programming approach. Expert Systems with Applications, 37(4), 3392-3397.
Schroeder, R. G., & Krishnan, R. (1976). Return on investment as a criterion for inventory model. Decision Sciences, 7(4), 697-704.
Sen, A. and Zhang, A. (1999). The newsboy problem with multiple demand classes. IIE Transactions, 31(5), 431-444.
 Tersine, R. J. (1994). Principles of inventory and materials management (4th ed.). NJ, USA: Prentice Hall PTR.
Torabi, S. A., & Hassini, E. (2008). An interactive possibilistic programming approach for multiple objective supply chain master planning. Fuzzy Sets and Systems, 159(2), 193-214.
Wang, C., Huang, R., & Wei, Q. (2015). Integrated pricing and lot-sizing decision in a two-echelon supply chain with a finite production rate. International Journal of Production Economics, 161, 44-53.
Wang, J., Hsieh, S., & Hsu, P. (2012).  Advanced sales and operations planning framework in a company supply chain. International Journal of Computer Integrated Manufacturing, 25(3), 248-262.
Wee, H., Lo, C., & Hsu, P. (2009). A multi-objective joint replenishment inventory model of deteriorated items in a fuzzy environment. European Journal of Operational Research, 197(2), 620-631.
Zhang, M., & Bell, P. C. (2007). The effect of market segmentation with demand leakage between market segments on a firm’s price and inventory decisions. European Journal of Operational Research, 182(2), 738-754.
Zhang, M., Bell, P., Cai, G., & Chen, X. (2010). Optimal fences and joint price and inventory decisions in distinct markets with demand leakage. European Journal of Operational Research, 204(3), 589-596.
Zhao, J., Tang, W., Zhao, R., & Wei, J. (2012). Pricing decisions for substitutable products with a common retailer in fuzzy environments. European Journal of Operational Research, 216(2), 409-419.
Zhou, C., Zhao, R., & Tang, W. (2008). Two-echelon supply chain games in a fuzzy environment. Computers & Industrial Engineering, 55(2), 390-405.
Zimmermann, H. J. (1978). Fuzzy programming and linear programming with several objective functions. Fuzzy Sets and Systems, 1(1), 45-55.