A DECOMPOSITION SCHEME IN PRODUCTION PLANNING BASED ON LINEAR PROGRAMMING THAT INCORPORATES THE CONCEPT OF A DYNAMIC PLANNING ENVIRONMENT

Abstract

. The present work proposes a decomposition scheme in production planning based on linear programming, which couples the concept of clearing function and supposes a dynamic environment to plan a production along a planning horizon. Where planning parameters such as demand, production capacity, production resources, and other parameters change over the planning horizon. In general, this requires the planner, freeze the production plan for some blocks of periods or rethink the production plan of each period, with obvious implications on production planning costs. The Plan shall be designed and implemented in the following way: At the beginning of any period of the planning horizon, from the first, a set of decisions on a production is taken based on available information under a supervision of a decision support system represented by the mathematical model that acts according to the latest available information, period to period. This mechanism suggest that the number of planned periods is of the magnitude of n squared, much larger than the number of periods to be performed, because for each execution period, the remainder of the planning horizon is re-planned. The scheme we are proposing in this paper addresses this drawback and provides a lower cost solution to this production planning problem. This proposed scheme is implemented by an algorithm which is analyzed in detail and after, numerically illustrated.