This research focuses on the effect of setup time on lot sizing. The setting is the Capacitated Lot Sizing Problem (the single-machine lot sizing problem) with nonstationary costs, demands, and setup times. A Lagrangian relaxation of the capacity constraints of CLSP allows it to be decomposed...

Monahan (Monahan, J. P. 1984. A quantity discount pricing model to increase vendor profits. Management Sci. (June) 720--726.) adapted the quantity discount model of inventory theory to the problem of determining an optimal quantity discount schedule from a vendor's point of view, and opened up...

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.

In this paper, the joint problem of ordering and offering price discount by a supplier to his sole/major buyer is analyzed. The objective is to induce the buyer to alter his order schedule and size so that the supplier can benefit from lower set up, ordering, and inventory holding costs. We...

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...

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...

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...

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...