Multi-item capacitated lot-sizing problems are reformulated using a class of valid inequalities, which are facets for the single-item uncapacitated problem. Computational results using this reformulation are reported, and problems vnth up to 20 items and 13 periods have been solved to optimality using a commercial mixed integer code. We also show how the valid inequalities can easily be generat...

A dynamic knapsack set is a natural generalization of the 0-1 knapsack set with a continuous variable studied recently. For dynamic knapsack sets a large family of facet-defining inequalities, called dynamic knapsack inequalities, are derived by fixing variables to one and then lifting. Surprisingly such inequalities have the simultaneous lifting property, and for small instances provide a sign...

In the present paper, we discuss one of the many processes arising in the context of supply chain management, namely production planning. We focus on one type of production planning models called capacitated lot sizing models. These models appear to be well suited for the usually rather in exible production resources found in the process industries. We review the literature on single-level sing...

One of the fundamental problems in operations management is to determine the optimal investment in capacity. Capacity investment consumes resources and the decision is often irreversible. Moreover, the available capacity level affects the action space for production and inventory planning decisions directly. In this paper, we address the joint capacitated lot sizing and capacity acquisition pro...

Ravindra K. Ahuja and Dorit S. Hochbaum Abstract In this paper, we study capacitated dynamic lot sizing problems with or without backorders, under the assumption that production costs are linear, that is, there are no set up costs. These two dynamic lot sizing problems (with or without backorders) are minimum cost flow problems on an underlying network that possess a special structure. We show ...

As a traditional model in the operations research and management science domain, deterministic lot-sizing problem is embedded in many application problems such as production and inventory planning and has been consistently drawing attentions from researchers. In this paper we consider basic versions of lot-sizing models in which problem parameters are stochastic and develop corresponding scenar...

Coordinated replenishment problems are common in manufacturing and distribution when a family of items shares a common production line, supplier, or a mode of transportation. In these situations the coordination of shared, and often limited, resources across items is economically attractive. This paper describes a mixed-integer programming formulation and Lagrangian relaxation solution procedur...