The single-item discrete lotsizing and scheduling problem: Optimization by linear and dynamic programming

This paper considers the single-item discrete lotsizing and scheduling problem (DLSP). DLSP is the problem of determining a minimal cost production schedule, that satisfies demand without backlogging and does not violate capacity constraints. The authors formulate DLSP as an integer programming problem and present two solution procedures. The first procedure is based on a reformulation of DLSP as a linear programming assignment problem, with additional restrictions to reflect the specific (setup) cost structure. For this linear programming formulation it is shown that, under certain conditions on the objective, the solution is all integer. The second procedure is based on dynamic programming (DP). Under certain conditions on the objective function, the DP algorithm can be made to run very fast by using special properties of optimal solutions.