Determining optimal reorder intervals in capacitated production- distribution systems. (English) Zbl 0661.90041

Jackson, Peter L.; Maxwell, William L.; Muckstadt, John A.

Manage. Sci. 34, No. 8, 938-958 (1988).

The problem of determining consistent and realistic reorder intervals in complex production-distribution environments was formulated as a large scale, nonlinear, integer programming problem by the second and third author [Oper. Res. 33, 1316-1341 (1985; Zbl 0579.90048)]. They show how the special structure of the problem permits its solution by a standard network flow algorithm. In this paper, we review this model, provide necessary and sufficient conditions that characterize the solution, and show that the optimal partition of nodes in the production-distribution network is invariant to an arbitrary scaling of the set-up and holding cost parameters. We consider two capacitated versions of the model: one with a single constrained work center, and the other with multiple constrained work centers. For single constraint problems, the invariance corollary provides a simple closed-form solution. For the multiple work center problem, the invariance corollary is exploited in the development of a Lagrange multiplier method of solution. The technique is illustrated by means of a small example problem and a problem taken from a real industrial setting.

MSC:

90B30	Production models
90B05	Inventory, storage, reservoirs
90C10	Integer programming
90C30	Nonlinear programming
90C90	Applications of mathematical programming

Keywords:

logistics; optimal reorder intervals; complex production-distribution environments; large scale, nonlinear, integer programming; production- distribution network; capacitated versions; single constrained work center; multiple constrained work centers; Lagrange multiplier method

Citations:

Zbl 0579.90048