Multi-objective decisions on capacity planning and production - Inventory control under uncertainty

In the presence of a changing and stochastic environment, firms must appropriately choose the timing and sizes of capacity acquisition as well as the production decisions to replenish inventory, such that various conflicting goals are satisfied. This paper considers multicriteria decision making on joint capacity planning and inventory control under uncertainty. We formulate this class of problems into a multi-objective Markov decision process, which simultaneously searches for both capacity and inventory policies that optimize multiple objectives. In a previous work, we developed a multi-objective dynamic programming algorithm to solve small problems by propagating Pareto optimal solutions recursively backward in time. The numerical intractability of the rigorous algorithm for large problems necessitates approximation approaches. However, and importantly, on the basis of the optimality equations constructed in the dynamic programming framework, we are able to obtain analytical insights into the structure of optimal solutions for certain simplified problems. For example, through convexity analysis, we show that such structural policies, as the target interval capacity policy and base-stock inventory policy, are optimal for a certain class of problems. We propose using these structural results to form a basis for parametric representation of suboptimal policies for more general problems. This approach greatly simplifies the optimization to that of finding a parameter vector that defines these optimal or suboptimal policies. We propose a simulation-based optimization framework to find the parameters that optimize multiple performance measures. Next we show how to exploit a multi-objective evolutionary algorithm to find a diverse set of Pareto optimal solutions in one single run, and finally we present numerical results from an example problem that we carry from formulation to solution.