Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-18T00:17:19.576Z Has data issue: false hasContentIssue false
  • English
  • Français

COORDINATED PRICING AND INVENTORY CONTROL WITH BATCH PRODUCTION AND ERLANG LEADTIMES

Published online by Cambridge University Press:  27 June 2014

Zhan Pang  and
Frank Y. Chen
Zhan Pang
Affiliation:
Lancaster University Management School, Lancaster, LA1 4YX, UK E-mail: [email protected]
Frank Y. Chen
Affiliation:
Department of Management Science, The City University of Hong Kong, Hong Kong E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper addresses a joint pricing and inventory control problem for a batch production system with random leadtimes. Assume that demand arrives according to a Poisson process with a price-dependent arrival rate. Each replenishment order contains a single batch of a fixed lot size. The replenishment leadtime follows an Erlang distribution, with the number of completed phases recording the delivery state of outstanding orders. The objective is to determine an optimal inventory-pricing policy that maximizes total expected discounted profit or long-run average profit. We first show that when there is at most one order outstanding at any point in time and that excess demand is lost, the optimal reorder policy can be characterized by a critical stock level and the optimal pricing decision is decreasing in the inventory level and delivery state. We then extend the analysis to mixed-Erlang leadtime distribution which can be used to approximate any random leadtime to any degree of accuracy. We further extend the analysis to allowing three outstanding orders where the optimal reorder point becomes state-dependent: the closer an outstanding order is to its arrival or the more orders are outstanding, the lower selling price is charged and the lower reorder point is chosen. Finally, we address the backlog case and show that the monotone pricing structure may not be true when the optimal reorder point is negative.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 28 , Issue 4 , October 2014 , pp. 529 - 563
Copyright
Copyright © Cambridge University Press 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Archibald, B.C. (1981). Continuous review (s, S) policies with lost sales. Manag. Sci. 27(10): 1171–1177.CrossRefGoogle Scholar
2.Benjaafar, S. & ElHafsi, M. (2006). Production and inventory control of a single product assemble-to-order system with multiple customer classes. Manag. Sci. 52: 1896–1912.CrossRefGoogle Scholar
3.Buchanan, D.J. & Love, R.F. (1985). A (Q, R) inventory model with lost sales and Erlang-distributed lead times. Naval Res. Logist. Quart. 32(4): 605–611.Google Scholar
4.Chao, X.L. & Zhou, S.X. (2006). Joint inventory and pricing strategy for a stochastic continuous-review system. IIE Trans. 38(5): 401–408.Google Scholar
5.Chao, X.L., Xu, Y. & Yang, B.M. (2012). Optimal policy for a production-inventory system with setup cost and average cost criterion. Prob. Eng. Inf. Sci. 26(4): 457–481.Google Scholar
6.Chen, F. (2000). Optimal policies for multi-echelon inventory problems with batch ordering. Oper. Res. 48(3): 376–389.Google Scholar
7.Chen, X. & Simchi-Levi, D. (2004). Coordinating inventory control and pricing strategies with random demand and fixed ordering cost: the finite horizon case. Oper. Res. 52(6): 887–896.Google Scholar
8.Chen, X. & Simchi-Levi, D. (2006). Coordinating inventory control and pricing strategies: the continuous review model. Oper. Res. Lett. 34(3): 323–332.Google Scholar
9.Chen, X. & Simchi-Levi, D. (2010). Pricing and inventory management. To appear in Handbook of Pricing, eds. Philips, R. and Ozalp, O.. Oxford University Press, United Kingdom, pp. 784–822.Google Scholar
10.Chen, L., Chen, Y. & Pang, Z. (2011). Dynamic pricing and inventory control in a make-to-stock queue with information on the production status. IEEE Trans. Autom. Sci. Eng. 8(2): 361–373.Google Scholar
11.Chen, L., Feng, Y. & Ou, J. (2006). Joint management of finished goods inventory and demand process for a make-to-stock product: a computational approach. IEEE Trans. Autom. Control 51(2): 258–273.Google Scholar
12.Chen, L., Feng, Y. & Ou, J. (2009). Coordinating batch production and pricing of a make-to-stock product. IEEE Trans. Autom. Control 54(7): 1674–1680.Google Scholar
13.Federgruen, A. & Heching, A. (1999). Combined pricing and inventory control under uncertainty. Oper. Res. 47(3): 454–475.Google Scholar
14.Feng, Y. & Chen, F.Y. (2005). Joint pricing and inventory control with setup costs and demand uncertainty. Working paper, Chinese University of Hong Kong.Google Scholar
15.Feng, Y. & Chen, F.Y. (2011). A computational approach for optimal joint inventory-pricing control in an infinite-horizon periodic-review system. Oper. Res. 59(5): 1297–1303.Google Scholar
16.Fleischmann, M., Hall, J.M. & Pyke, D.F. (2004). Smart pricing: linking pricing decisions with operational insights. Sloan Manag. Rev. 45(2): 9–13.Google Scholar
17.Gallego, G. & Toktay, L.B. (2004). All-or-nothing ordering under a capacity constraint. Oper. Res. 52(6): 1001–1002.Google Scholar
18.Green, H. (2003). The web smart 50: Northern Retail Group. Business Week, November 24, 94–96.Google Scholar
19.Ha, A.Y. (2000). Stock rationing in an M/E k/1 make-to-stock queue. Manag. Sci. 46(1): 77–87.CrossRefGoogle Scholar
20.Hill, R.M. (2007). Continuous-review, lost-sales inventory models with Poisson demand, a fixed leadtime and no fixed order cost. Eur. J. Oper. Res. 176(2): 956–963.Google Scholar
21.Hill, R.M. & Johansen, S.G. (2004). Optimal and near-optimal policies for lost sales inventory models with at most one replenishment order outstanding. Eur. J. Oper. Res. 169(1): 111–132.Google Scholar
22.Kapuscinski, R., Zhang, R., Carbonneau, P., Moore, R. & Reeves, B. (2004). Inventory decisions in Dell's supply chain. Interfaces 34(3): 191–205.CrossRefGoogle Scholar
23.Johansen, S.G. (2005). Base-stock policies for the lost sales inventory system with Poisson demand and Erlang lead times. Int. J. Prod. Econ. 93: 429–437.Google Scholar
24.Johansen, S.G. & Thorstenson, A. (1993). Optimal and approximate (Q, r) inventory policies with lost sales and gamma-distributed lead time. Int. J. Prod. Econ. 30–31: 179–194.CrossRefGoogle Scholar
25.Johansen, S.G. & Thorstenson, A. (1996). Optimal (r, Q) inventory policies with Poisson demands and lost sales: discounted and undiscounted cases. Int. J. Prod. Econ. 46–47: 359–371.CrossRefGoogle Scholar
26.Johansen, S.G. & Thorstenson, A. (2004). The (r, q) policy for the lost-sales inventory system when more than one order may be outstanding. Working Paper, University of Aarhus, Denmark.Google Scholar
27.Li, L. (1988). A stochastic theory of the firm. Math. Oper. Res. 13(3): 447–465.Google Scholar
28.Lippman, S. (1975). Applying a new device in the optimization of exponential queueing systems. Oper. Res. 23(4): 687–710.CrossRefGoogle Scholar
29.Nahmias, S. & Demmy, W.S. (1981). Operating characteristics of an inventory system with rationing. Manag. Sci. 27(11): 1236–1245.Google Scholar
30.Pang, Z. (2011). Optimal dynamic pricing and inventory control with stock deterioration and partial backordering. Oper. Res. Lett. 39(5): 357–379.Google Scholar
31.Pang, Z., Chen, F.Y. & Feng, Y. (2012). A note on the structure of joint inventory-pricing control with leadtimes. Oper. Res. 60(3): 581–587.Google Scholar
32.Porteus, E.L. (1982). Conditions for characterizing the structure of optimal strategies in infinite horizon dynamic programs. J. Optim. Theory Appl. 36(3): 419–432.Google Scholar
33.Puterman, M. (1994). Markov Decision Processes: Discrete Stochastic Dynamic Programming. New York: John Wiley & Sons.Google Scholar
34.Robinson, L.W., Bradley, J.R. & Thomas, L.J. (2001). Consequences of order crossover under order-up-to inventory policies. Manuf. Serv. Oper. Manag. 3(3): 175–188.Google Scholar
35.Tijms, H.C. (1994). Stochastic Models: An Algorithmic Approach. New York: John Wiley & Sons.Google Scholar
36.Veinott, A.F. (1965). Optimal policy in a dynamic, single product, nonstationary inventory model with several demand classes. Oper. Res. 13(5): 761–778.Google Scholar
37.Weber, R. & Stidham, S. (1987). Optimal control of service rate in networks of queues. Adv. Appl. Probab. 19: 202–218.Google Scholar
38.Xu, Y. & Chao, X. (2009). Dynamic pricing and inventory control for a production system with average profit criterion. Prob. Eng. Inf. Sci. 23: 489–513.Google Scholar
39.Zipkin, P. (1988). The use of phase-type distributions in inventory control models. Naval Res. Logist. Quart. 35(2): 247–257.Google Scholar
40.Zipkin, P. (2000). Foundations of Inventory Management. Boston: McGraw-Hill.Google Scholar