A Lot-Sizing Problem in Deliberated and Controlled Co-Production Systems - Kabakulak, Banu; Ağralı, Semra; Taşkın, Z. Caner; Pamuk, Bahadır (Taylor and Francis, 2022)
We consider an uncapacitated lot sizing problem in co-production systems, in which it is possible to produce multiple items simultaneously in a single production run. Each product has a deterministic demand to be satisfied on time. The decision is to choose which items to co-produce and the amount of production throughout a predetermined planning horizon. We show that the lot sizing problem with co-production is strongly NP-Hard. Then, we develop various mixed-integer linear programming (MILP) formulation of the problem and show that LP relaxations of all MILPs are equal. We develop a separation algorithm based on a set of valid inequalities, lower bounds based on a dynamic lot-sizing relaxation of our problem and a constructive heuristic that is used to obtain an initial solution for the solver, which form the basis of our proposed Branch & Cut algorithm for the problem. We test our models and algorithms on different data sets and provide the results.
Keywords: Lot-sizing; Milp; Co-production; Branch & cut