This paper considers the problem of finding a production schedule, in terms of how much to produce in each period, that minimizes the total cost of supplying known market requirements for a single product. The costs include a concave production cost, a concave inventory cost, and a piecewise...

Two dynamic economic lot size production systems are analyzed in this paper, the first being a single product model with backlogging and the second a multi-echelon model. In each model the objective is to find a production schedule that minimizes the total production and inventory costs. A key...

A deterministic multi-period production and inventory model that has concave production costs and piecewise concave [Zangwill, W. I. 1965. A dynamic multi-product, multi-facility production and inventory model. Technical Report 1, Program in Operations Research, Stanford University, Stanford,...

The literature is replete with analyses of minimum cost flows in networks for which the cost of shipping from node to node is a linear function. However, the linear cost assumption is often not realistic. Situations in which there is a set-up charge, discounting, or efficiencies of scale give...

Utilizing a cyclic queue system, this paper investigates the effect of variance on a multi-item production facility. The variance of setup time, service rate and arrival rate is shown to have a powerful and sometimes paradoxical influence. Reduction in setup time, for example, is usually...

This paper presents a method, called the convex simplex method, for minimizing a convex objective function subject to linear inequality constraints. The method is a true generalization of Dantzig's linear simplex method both in spirit and in the fact that the same tableau and variable selection...

An important function which is neither concave nor convex often arises in production and inventory models. This function is herein called piecewise concave and can be considered to be a generalization of the concave function. Essentially it is the maximum of a collection of concave functions....

Conditions which are necessary and sufficient for convergence of a nonlinear programming algorithm are stated. It is also shown that the convergence conditions can be easily applied to most programming algorithms. As examples, algorithms by Arrow, Hurwicz and Uzawa; Cauchy; Frank and Wolfe; and...

Zero Inventory (ZI) is a new and powerful concept to improve production efficiency. Underpinning ZI is set up reduction and this paper examines what eventuates when set up costs are cut. The folklore is that set up reduction lowers inventory and costs. We obtain results contrary to that....

Continuous improvement (CI) unceasingly strives to improve the performance of production and service firms. The learning curve (LC) provides1988 Department of Industrial Engineering and a means to observe and track that improvement. At present, however, the concepts of CI are abstract and...