Models and solving procedures for continuous-time production planning

The goal of this paper is to solve a continuous time production planning problem, where production rates are assumed to be piecewise constant. The problem is then to determine not only the rates, but also the times, called switching times, at which these rates may change. An iterative procedure is proposed where, at the first step, optimal rates are determined given the switching times and, at the second step, new switching times are added given the rates. A linear programming model is proposed and discussed for the first step. Several rules to remove or add switching times are also analyzed. Computational experiments are presented comparing two versions of the procedure and showing its efficiency.