A lot-sizing problem in deliberated and controlled co-production systems
研究了联合生产系统中无产能限制的批量问题，证明其强NP难性，提出混合整数线性规划模型、分离算法、下界和启发式算法，并基于分支切割算法求解。
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) formulations 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.