Strategic Capacity Allocation under Uncertainty by Using a Two-Stage Stochastic Decomposition Algorithm with Incumbent Solutions

This paper addresses the optimization of strategic capacity allocation problems under uncertainty. Uncertain parameters include the availabilities and the demands of chemicals. The optimization problem is formulated as a two-stage mixed-integer stochastic program (first-stage integer) that maximizes the expected net present value of the project over the time horizon. The net present value includes the discounted investment costs, operating costs, and revenues from sales in the markets. The decisions about the selection of processes and about the plant capacities are defined as the first stage decision variables; given such first stage decisions, recourse is then provided by calculating the operating costs in the second stage. The paper presents the two-stage model and the solution framework. A stochastic decomposition algorithm (SD) based on incumbent solution is used as the Solution algorithm. The use of incumbent solutions as convergence criterion allows us to solve the problem in reasonable computational time. Two capacity allocation problems are used as case studies: the first one is a small size problem and is used to compare the stochastic optimal solution against other solution methods; the second one is a larger problem, with an increased number of variables and stochastic parameters. The results show that the stochastic decomposition algorithm with incumbent solutions is stable and robust and greatly reduces the number of samples required for convergence.