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.

We study a multi-product production and inventory planning problem with uncertain demand in the cold rolling stage of steel production processes. The problem is to determine the production amount of each product in each planning period so that the sum of production, inventory holding, and backorder costs is minimized. We first formulate it into a Markov decision process (MDP) model, considering dynamic demand. Aiming at the proposed large-scale MDP model, we develop the improved Approximated Dynamic Programming (ADP) algorithms, which are composed of the reformulation and the approximation functions for the value function in MDP. Linear and two quadratic approximate functions are proposed to approximate the value function. Numerical experiments show the optimal gaps of the different approximation methods and illustrate the efficiency of the proposed ADP methods.