This paper deals with the classical dynamic lot size problem without backlogging and capacity limitation. We derive worst case performance bounds for a class of lot sizing heuristics. When the considered methods are applied a decision whether to have a set-up or not in a certain period is taken...

In this paper we present a mathematical programming model for the Kanban system in a deterministic multi-stage capacitated assembly-tree-structure production setting. We discuss solution procedures to the problem and address three special cases of practical interest.

This paper develops optimal order quantities for firms that are offered a one-time opportunity to delay payment for an order of a commodity. Such delayed payments result in a reduction of the effective purchase cost, which is a function of the return available on alternative investments, the...

The multi-item joint replenishment problem is generalized to allow ordering costs to be dependent on the specific items jointly supplied. A fixed cycle approach is examined in which all the items of a group are always jointly replenished. A dynamic programming algorithm is developed for...

We consider the situation of a single item having a deterministic, time-varying demand pattern. Production lot sizes, so as to minimize the total of setup and carrying costs, are to be determined subject to production capacity restrictions that can vary with time. Two important theorems...

In this paper, we analyze how a supplier can structure the terms of an optimal quantity discount schedule. The vendor's challenge is to adjust his present pricing schedule to entice his major customer to increase his present order size by a factor of "K." Optimal levels for "K" and the...

This note considers two single-machine multi-product scheduling problems with deterministic demand that have appeared in the management science literature: the economic lot scheduling problem and the joint replenishment problem. These problems are shown to be closely related. In addition, they...

In this paper we present a heuristic method, based on Lagrangian relaxation, for multilevel lot-sizing when there is a single bottleneck facility. A series of Lagrangian relaxations (one for each item in the product structure) is imbedded in a branch and bound procedure. The objective is to find...

This paper presents a dynamic programming algorithm for simultaneous determination of production batch sizes in an assembly network and distribution batch sizes in a conjoined distribution ("arborescent") network. The objective is to minimize average cost per period over an infinite horizon....

A class of production planning problems is considered in which known demands have to be satisfied over a finite horizon at minimum total costs. For each period, production and storage cost functions are specified. The production costs may include set-up costs and the production levels may he...