Inventory Control for a Joint Replenishment Problem with Stochastic Demand

Most papers model Joint Replenishment Problem (JRP) as a (kT,S) where kT is a multiple value for a common review period T,and S is a predefined order up to level. In general the (T,S) policy is characterized by a long out of control period which requires a large amount of safety stock compared to the (R,Q) policy. In this paper a probabilistic model is built where an item, call it item(i), with the shortest order time between interval (T)is modeled under (R,Q) policy and its inventory is continuously reviewed, while the rest of items (j) are periodically reviewed at a definite time corresponding to item

Authors:

• Bassem Roushdy
• Nahed Sobhy
• Abdelrhim Abdelhamid
• Ahmed Mahmoud

Keywords:

• Inventory management
• Joint replenishment
• policy evaluation
• stochastic process

References:

[1] Atkins, D., Iyogun, P., 1988. Periodic versus can order policies for
coordinated multi-item inventory system. Management Science 34 (6),
791-796.
[2] Axsater, S., 2004.Inetory Control, Kluwer Academic Publisher Group.
[3] Eryan, A., Kropp, D.H., 2007. Effective and simple EOQ-like solutions
for stochastic demand periodic review systems. Eur. J. Oper. Res. 180,
1135-1143.
[4] Eryan, A., Kropp, D.H., 1998. Periodic review and joint replenishment
in stochastic demand environment.IIE Transactions 30, 1025-1033.
[5] Fung, R., MA, X., 2001.Anew method for joint replenishment problems.
Journal of Operational Research Society52, 358-362.
[6] Forsberg, R., 1995. Optimization of order-up-to S policies for two-level
inventory systems with compound Poisson demand. European Journal of
Operational Research 81.
[7] Goyal, S.K., 1973. Determination of economic packaging frequency for
items jointly replenished. Management Science 20 (2), 232.
[8] Goyal, S.K., 1974. Determination of optimum packaging frequency of
items jointly replenished. Management Science 21 (4), 436-443.
[9] Hariga, M., 1994. Two new heuristic procedures for the joint
replenishment problem, Journal of the Operational Research Society 45
463-471.
[10] Johansen, S.G., Melchior P., 2003. Can-order policy for the periodicreview
joint replenishment problem, Journal of the Operational Research
Society 54 283-290.
[11] Larsen,C., 2008.The Q(s,S) control policy for the joint replenishment
problem extended to the case of correlation among item-demand.
Journal of Production Economics,doi:10.1016/j.ijpe.2008.08.025
[12] Olsen, A.L., 2005. An evolutionary algorithm to solve the joint
replenishment problem using direct grouping. Computers and Industrial
Engineering 48 (2), 223-235.
[13] Pantumsinchai, P., 1992. A comparison of three joint ordering inventory
policies. Decision Science 23, 111-127.
[14] Porras E. and Dekker R. 2005. An efficient optimal solution method for
the joint replenishment problem with minimum order quantities.
European Journal of Operational Research (forthcoming)
[15] Silver, E.A., 1976. A simple method of determining order quantities in
joint replenishments under deterministic demand. Management Science
22 (12), 1351-1361.
[16] Van Eijs, M.J.G., 1993. A note on the joint replenishment problem under
constant demand. Journal of Operational Research Society 44 (2), 185-
191.
[17] Viswanathan, S., 1996. A new optimal algorithm for the joint
replenishment problem. Journal of Operational Research Society 47 (7),
936-944.
[18] Viswanathan, S., 2002. On optimal algorithms for the joint
replenishment problem. Journal of Operational Research Society 53
(11), 1286-1290.
[19] Wildeman, R.E, Frenk, J.B.G., Dekker, R., 1997. An efficient optimal
solution for the joint replenishment problem. European Journal of
Operational Research 99, 433-444.
[20] Zheng, Y.S., Federgruen, A., 1991. Finding optimal sً; S قpolicies is
about as simple as evaluating a single policy. Operations Research 39
(4), 654-665.
[21] Zipkin, P., 2000. Foundations of Inventory Management. McGraw-Hill.