A framework for multi-objective stochastic lot sizing with multiple decision stages

In stochastic lot sizing subject to dynamic and random demand, the minimization of operational costs is not the only conceivable objective. Minimizing the tardiness in customer demand satisfaction is no less important. Furthermore, the decision maker is interested in production plan stability. Therefore, we consider those three objectives simultaneously and propose a multi-objective model formulation and decision-making framework of the stochastic capacitated lot sizing problem (MOSCLSP). Demand is modeled via the Martingale Model of Forecast Evolution to allow gradual adaptations of the demand forecasts due to sequential market observations. We propose an interactive multi-objective optimization algorithm for solving the MO-SCLSP, that systematically takes prior demand realization information into account. In multiple decision stages, periodic re-optimizations are carried out, allowing to adjust the production plan to the actual demand realizations. In each decision stage, methods from multi-objective optimization are applied to derive a set of Pareto-optimal solutions. These Pareto-optimal solutions outline the attainable objective space, thus supporting the decision maker in taking an informed and economically profound position between prioritizing low operational costs, high delivery reliability and low production plan nervousness.