Mathematical Programming Models and Formulations for Deterministic Production Planning Problems

Abstract. We study in this lecture the literature on mixed integer programming models and formulations for a specific problem class, namely deterministic production planning problems. The objective is to present the classical optimization approaches used, and the known models, for dealing with such management problems. We describe first production planning models in the general context of manufacturing planning and control systems, and explain in which sense most optimization solution approaches are based on the decomposition of the problem into single-item subproblems. Then we study in detail the reformulations for the core or simplest subproblem in production planning, the single-item uncapacitated lot-sizing problem, and some of its variants. Such reformulations are either obtained by adding variables – to obtain so called extended reformulations – or by adding constraints to the initial formulation. This typically allows one to obtain a linear description of the convex hull o...

• Type: Conference
• Year: 2001
• Where: CCO
• Authors: Yves Pochet
• Keywords: CCO 2001, Combinatorics, Planning Problems, Production Planning, Production Planning Models