Several papers have been published which present simplified models for the aggregate planning problem which do not yield optimal schedules. They are typically supported with computations that suggest that the resulting schedules produce costs within a few percent of optimum. This note suggests...

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...

Monahan (Monahan, James P. 1984. A quantity discount pricing model to increase vendor profits. Management Sci. 30 (June) 720--726.) develops a model for establishing an optimal quantity discount schedule from a vendor's viewpoint. In this note we show that this model is limited to the case where...

Previous work dealt with the problems of nervousness in Material Requirements Planning (MRP) Systems when production schedules were modified to include setups which previously had not been scheduled. In this work we further examine nervousness and its cost. By modifying the setup costs used in...

Component lot-splitting considerations, in which the lot-size of a component item may cover only a fraction of its parent item's lot-size, have been ignored in the literature when determining lot-sizes of items in multi-stage manufacturing systems. In this paper, a multi-stage lot-sizing problem...

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.