Establishing consistent and realistic reorder intervals in production- distribution systems. (English) Zbl 0579.90048

Maxwell, William L.; Muckstadt, John A.

Oper. Res. 33, 1316-1341 (1985).

Summary: The objective of this paper is to present a model and algorithm that can be used to find consistent and realistic reorder intervals for each item, in large-scale production-distribution systems. We assume such systems can be represented by directed acyclic graphs. Demand for each end item is assumed to occur at a constant and continuous rate. Production is instantaneous and no backorders are allowed. Both fixed setup costs and echelon holding costs are charged at each stage. We limit our attention to nested and stationary policies. Furthermore, we restrict the reorder interval for each stage to be a power of 2 times a base planning period. The model that results from these assumptions is an integer nonlinear programming problem. The optimal solution can be found using the proposed algorithm, which is a polynomial time algorithm. A real world example is given to illustrate the procedure.

MSC:

90B30	Production models
90B05	Inventory, storage, reservoirs
90C90	Applications of mathematical programming
90C30	Nonlinear programming
65K05	Numerical mathematical programming methods
90C10	Integer programming
68Q25	Analysis of algorithms and problem complexity

Keywords:

consistent and realistic reorder intervals; large-scale production- distribution systems; directed acyclic graphs; nested and stationary policies; integer nonlinear programming; polynomial time algorithm