A model for optimizing multi-product inventory systems with multiple constraints

Abstract “How much to order” and “when to order” are the two fundamental issues managers have to resolve in an inventory system. Making these decisions in inventory systems with multiple products is a challenging task for managers because these decisions are often subject to several constraints due to limited resources such as budget, space, and the maximum weight of goods that can be stored. Most approaches in the literature for optimizing decisions in such an environment consider only a single budgetary constraint. This paper presents a mixed-integer programming model to optimize the two fundamental decisions of inventory management for ordering multiple inventory items subject to multiple resource constraints. It also determines whether a fixed cycle for all products or an independent cycle for each should be used for a lower total cost. The solution of the model does not seem to require excessive central processing unit (cpu) time as indicated by the computational experience reported in this paper; solution of the largest test problem, with 30 products and five resource constraints, required less than 20 cpu seconds on a personal computer.

[1]  R. Roundy.  98%-Effective Integer-Ratio Lot-Sizing for One-Warehouse Multi-Retailer Systems , 1985 .

[2]  Faruk Güder,et al.  Ordering policies for multi-item inventory systems subject to multiple resource constraints , 1999, Comput. Oper. Res..

[3]  Bala Shetty,et al.  A Model for Resource Constrained Production and Inventory Management , 1994 .

[4]  C. C. Holt,et al.  Planning Production, Inventories, and Work Force. , 1962 .

[5]  Steven Nahmias,et al.  Production and operations analysis , 1992 .

[6]  L. C. Thomas,et al.  The Deterministic, Two-Product, Inventory System with Capacity Constraint , 1982 .

[7]  Meir J. Rosenblatt,et al.  On the Single Resource Capacity Problem for Multi-Item Inventory Systems , 1990, Oper. Res..

[8]  Ernest Koenigsberg,et al.  Scientific Inventory Management , 1963 .

[9]  Faruk Güder,et al.  Non-Stationary Ordering Policies for Multi-Item Inventory Systems Subject to a Single Resource Constraint , 1995 .

[10]  Rasoul Haji,et al.  Optimum common cycle for scheduling a single-machine multiproduct system with a budgetary constraint , 1995 .

[11]  P. Jackson,et al.  The warehouse scheduling problem: formulation and algorithms , 1996 .

[12]  Moncer Hariga.  The Warehouse Scheduling Problem , 1989 .

[13]  S. K. Goyal,et al.  A Note on “Multi-Product Inventory Situations with One Restriction” , 1978 .

[14]  Cerry M. Klein,et al.  Constrained multi-item inventory systems: An implicit approach , 1993, Comput. Oper. Res..

[15]  K. Jo Min,et al.  A multi-product EOQ model with pricing consideration—T. C. E. Cheng's model revisited , 1994 .

[16]  Won J. Lee.  Optimal order quantities and prices with storage space and inventory investment limitations , 1994 .

[17]  Hans Ziegler,et al.  Solving certain singly constrained convex optimization problems in production planning , 1982, Oper. Res. Lett..

[18]  Roger Hartley,et al.  An Algorithm for Limited Capacity Inventory Problem with Staggering , 1983 .

[19]  R. Paul,et al.  Multi-Product Inventory Situations with One Restriction , 1976 .

[20]  L. Zurich,et al.  Operations Research in Production Planning, Scheduling, and Inventory Control , 1974 .

[21]  Arthur F. Veinott,et al.  Analysis of Inventory Systems , 1963 .

[22]  K. Zoller.  Deterministic Multi-Item Inventory Systems with Limited Capacity , 1977 .

[23]  M. J. Rosenblatt.  Multi-item inventory system with budgetary constraint: a comparison between the Lagrangian and the fixed cycle approach , 1981 .

[24]  David Simchi-Levi,et al.  Single Resource Multi-Item Inventory Systems , 1996, Oper. Res..

[25]  S. Goyal.  Determination of Economic Packaging Frequency for Items Jointly Replenished , 1973 .

[26]  E. Silver.  A Simple Method of Determining Order Quantities in Joint Replenishments Under Deterministic Demand , 1976 .

[27]  Meir J. Rosenblatt,et al.  An Improvement of Silver's Algorithm for the Joint Replenishment Problem , 1983 .

[28]  Nicholas G. Hall.  A multi-item EOQ model with inventory cycle balancing , 1988 .