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A CAPACITATED REPLENISHMENT-LIQUIDATION MODEL UNDER CONTRACTUAL AND SPOT MARKETS WITH STOCHASTIC DEMAND

Published online by Cambridge University Press:  21 January 2014

Abhilasha Prakash Katariya ,
Eylem Tekin  and
Sila Çetinkaya
Abhilasha Prakash Katariya
Affiliation:
Department of Industrial and Systems Engineering, Texas A&M University, College Station, TX 77843-3131, USA
Eylem Tekin
Affiliation:
Department of Industrial Engineering, University of Houston, Houston, TX 77204-4008, USA
Sila Çetinkaya
Affiliation:
Department of Industrial and Systems Engineering, Texas A&M University, College Station, TX 77843-3131, USA E-mail: sila@tamu.edu
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Abstract

Various large-scale suppliers frequently use web-based spot markets, along with discount stores and foreign distributors, for inventory liquidation. Recognizing the potential benefits of such practices, we consider a multi-period, integrated replenishment, and liquidation problem for a capacitated supplier facing stochastic demand from a spot market along with its primary market (with higher priority contractual customers). In each period, the supplier must decide: (i) how much to produce, and (ii) if there are excess units left after sales to the primary market, how many of these to liquidate. We show that the optimal policy is characterized by two quantities: the critical produce-up-to level and the critical retain-up-to level. We establish bounds for these two quantities. We identify two practical benchmark policies and establish thresholds on the unit revenue earned from the spot market such that one of the two benchmark policies is optimal. We provide closed form expressions to determine these thresholds for the infinite horizon problem under specific conditions on the available production capacity. In general, it is difficult, if not impossible, to theoretically determine these thresholds in closed form for the finite horizon problem. Hence, we report results of a computational study to gain insights regarding the behavior of the optimal policy with respect to the spot market revenue. Our computational results also quantify the benefits of the optimal policy relative to the benchmark policies and examine the effects of demand correlation.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 28 , Issue 2 , April 2014 , pp. 223 - 269
Copyright
Copyright © Cambridge University Press 2014 

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References

REFERENCES

1.Araman, V.F. & Özer, Ö (2005). Capacity and inventory management in the presence of a long-term channel and spot market, Working Paper, New York University, New York.Google Scholar
2.Aviv, Y., & Federgruen, A. (1997). Stochastic inventory models with limited production capacity and periodically varying parameters. Probability in Engineering and Informational Sciences 11: 107–135.CrossRefGoogle Scholar
3.Çetinkaya, S., & Parlar, M. (2010). A one-time excess inventory disposal decision under a stationary base-stock policy. Stochastic Analysis and Applications 28(3): 540–557.Google Scholar
4.Chen, S., Xu, J., & Feng, Y. (2010). A partial characterization of the optimal ordering/rationing policy for a periodic review system with two demand classes and backordering. Naval Research Logistics 57(4): 330–341.Google Scholar
5.de Vericourt, F., Karaesmen, F. & Dallery, Y. (2002). Optimal stock allocation for a capacitated supply system. Management Science 48: 1486–1501.Google Scholar
6.Duran, S., Liu, T., Simchi-Levi, D., & Swann, J. (2007). Optimal production and inventory policies of priority and price-differentiated customers. IIE Transactions 39(9): 845–861.Google Scholar
7.Duran, S., Liu, T., Simchi-Levi, D., & Swann, J. (2008). Policies utilizing tactical inventory for service-differentiated customers. Operations Research Letters 36: 259–264.Google Scholar
8.Etzion, H., & Pinker, E.J. (2008). Asymmetric competition in B2B spot markets. Production and Operations Management 17(2): 150–161.Google Scholar
9.Federgruen, A., & Zipkin, P. (1986). An inventory model with limited production capacity and uncertain demands: The average-cost criterion. Mathematics of Operations Research 11: 193–207.Google Scholar
10.Federgruen, A., & Zipkin, P. (1986). An inventory model with limited production capacity and uncertain demands: The discounted-cost criterion. Mathematics of Operations Research 11: 208–215.Google Scholar
11.Feinberg, E.A. & Lewis, M.E. (2005). Optimality of four-threshold policies in inventory systems with customer returns and borrowing/storage options. Probability in the Engineering and Informational Sciences, 19(1): 45–71.Google Scholar
12.Frank, K.C., Zhang, R. Q., & Duenyas, I. (2003). Optimal policies for inventory systems with priority demand classes. Operations Research 51(6): 993–1002.Google Scholar
13.Fukuda, Y. (1961). Optimal disposal policies. Naval Research Logistics Quarterly 8: 221–227.Google Scholar
14.Haksoz, C. & Seshadri, S. (2007). Supply chain operations in the presence of a spot market: a review with discussion. Journal of the Operational Research Society 58(11): 1412–1429.Google Scholar
15.Hart, A. (1973). Determination of excess stock quantities. Management Science 19: 1444–1451.CrossRefGoogle Scholar
16.Kleijn, M.J., & Dekker, R. (1999). An overview of inventory systems with several demand classes. Lecture Notes in Economics and Mathematical Systems 480: 253–265.Google Scholar
17.Martinez-de-Albeniz, V. & Simchi-Levi, D. (2005). A portfolio approach to procurement contracts. Production and Operations Management 14(1): 90–114.Google Scholar
18.Petruzzi, N.C., & Monahan, G.E. (2003). Managing fashion goods inventories: dynamic recourse for retailers with outlet stores. IIE Transactions 35: 1033–1047.Google Scholar
19.Puterman, M.L. (1994). Markov Decision Processes: Discrete Stochastic Dynamic Programming. John Wiley and Sons, New York, NY.Google Scholar
20.Rosenfield, D.B. (1989). Disposal of excess inventory. Operations Research 37: 404–409.Google Scholar
21.Scarf, H.E. (2005). Optimal inventory policies when sales are discretionary. International Journal of Production Economics 93–4: 111–119.Google Scholar
22.Simpson, J. (1955). A formula for decisions on retention or disposal of excess stock. Naval Research Logistics Quarterly 2: 145–155.Google Scholar
23.Sobel, M.J. & Zhang, R.Q. (2001). Inventory policies for systems with stochastic and deterministic demand. Operations Research 49(1): 157–162.CrossRefGoogle Scholar
24.Topkis, D.M. (1968). Optimal ordering and rationing policies in a nonstationary dynamic inventory model with n demand classes. Management Science 48: 160–176.Google Scholar
25.Veinott, A.F. (1965). Optimal policy in a dynamic single product nonstationary inventory model with several demand classes. Operations Research 13: 761–778.CrossRefGoogle Scholar
26.Zhou, Y., & Zhao, X. (2010). A two-demand-class inventory system with lost-sales and backorders. Operations Research Letters 38: 261–266.CrossRefGoogle Scholar