Lot Sizing and Sequencing for N Products on One Facility

The problem of determining both lot sizes and repeating sequences for N products on one facility is difficult due to the combinatorial and continuous nature of the problem. The work that has been done on the problem has made various assumptions ("zero-switch rule" or "equal lot size," for example) to simplify the problem. Several heuristics have been suggested that come fairly close to a computable lower bound on cost. This paper discusses a mathematical programming formulation of the entire problem, along with reasons for its (current) nonpracticality. Heuristics for reducing the problem to a manageable mathematical programming formulation are presented. Specifically, a formulation is given when the sequence is known with both (potentially unequal) lot sizes and idle time periods as variables. The formulation is a convex quadratic program. Heuristics for finding sequences (to feed to the quadratic program) are explored, and examples from previous literature demonstrate that the methods here give consistent results as good as and sometimes significantly better than previous methods. Finally, we discuss situations in which such methods might be important and situations in which easier methods should suffice.