Applications of Combinatorial Optimization, 2nd Edition

Chapter 4

Production Planning

4.1. Introduction

Mathematical programming and production planning have been closely linked since their beginnings. The work of Kantorovich [KAN 60] on “mathematical methods in production organization and planning”, published in 1939, already contained the seeds of the developments in linear programming which took place in the following decades. Many methods derived from this approach have been effectively applied in practice, for example:

– inventory and supply management;

– material resource planning (MRP);

– the many industrial applications of linear programming since the 1950s in the petroleum industry (production and distribution planning), food industry (transportation, blending), steel industry (process planning and scheduling), mechanical industry (scheduling), etc.

Production planning has evolved considerably since the 1960s. Companies have had to refocus in order to increase their flexibility and reactivity and thus accelerate the renewal of their products on the market. To reduce costs, they attempt to remove all superfluous activities through just-in-time production, lean production, and by realigning the concepts of quality and deadlines. Production planning, in a wide sense, includes all the activities in what we today call a “supply chain”. According to [GOV 02], a supply chain can in general be decomposed into five macroactivities: Procurement –Transport – Production – Inventory – Distribution.

The aim of this chapter is to highlight ...