Multi-Stage Multi-Product Production and Inventory Planning for Cold Rolling under Random Yield

This paper studies a multi-stage multi-product production and inventory planning problem with random yield derived from the cold rolling process in the steel industry. The cold rolling process has multiple stages, and intermediate inventory buffers are kept between stages to ensure continuous operation. Switching products during the cold rolling process is typically very costly. Backorder costs are incurred for unsatisfied demand while inventory holding costs are incurred for excess inventory. The process also experiences random yield. The objective of the production and inventory planning problem is to minimize the total cost including the switching costs, inventory holding costs, and backorder costs. We propose a stochastic formulation with a nonlinear objective function. Two lower bounds are proposed, which are based on full information relaxation and Jensen's inequality, respectively. Then, we develop two heuristics from the proposed lower bounds. In addition, we propose a two-stage procedure motivated by newsvendor logic. To verify the performance of the proposed bounds and heuristics, computational tests are conducted on synthetic instances. The results show the efficiency of the proposed bounds and heuristics.