In this paper we consider the uncapacitated economic lot-size model, where demand is a deterministic function of price. In the model a single price need to be set for all periods. The objective is to find an optimal price and ordering decisions simultaneously. In 1973 Kunreuther and Schrage proposed an heuristic algorithm to solve this problem. The contribution of our paper is twofold. First, w...

We give multi-stage stochastic programming formulations for lot-sizing problems where costs, demands and order lead times follow a general discrete-time stochastic process with finite support. We characterize the properties of an optimal solution and give a dynamic programming algorithm, polynomial in input size, when orders do not cross in time.

The lot–sizing polytope is a fundamental structure contained in many practical production planning problems. Here we study this polytope and identify facet–defining inequalities that cut off all fractional extreme points of its linear programming relaxation, as well as liftings from those facets. We give a polynomial– time combinatorial separation algorithm for the inequalities when capacities ...

We study the classical multistage lot sizing problem that arises in distribution and inventory systems. A celebrated result in this area is the 94% and 98% approximation guarantee provided by power-of-two policies. In this paper, we propose a simple randomized rounding algorithm to establish these performance bounds. We use this new technique to extend several results for the capacitated lot si...

Jobs can be batched if they share the same setup times on a machine in many practical situations. Another reason for batching arises when a machine can process several jobs at the same time. On the other hand, splitting a job or lot which consists of many identical items often increases customer service and decreases throughput time. Especially in CIM (Computer Integrated Manufacturing) these d...

Companies are trying to improve their ability to deliver and to reduce their production costs simultaneously. Nevertheless ongoing orders of customers are causing difficulties to deliver because of bottlenecks in the production. Furthermore constantly incoming customer orders effect that every actual optimal production plan with its already realized and planned guidelines has induced states tha...