A methodology for probabilistic inventory-production-distribution problems

We consider a supply chain operating in an uncertain environment. The objective is to construct a robust inventory-production-distribution plan over a multi-period planning horizon. Each supply chain entity deals with a discretely distributed stochastic demand, and cannot backlog the unsatisfied demand. A probabilistic programming methodology is adopted.; The plan minimizes the costs of the supply chain, while enabling it to reach a prescribed service level. It is a strategic plan that hedges against undesirable outcomes, and that can be adjusted to account for possible favorable realizations of uncertain quantities.; For each service level considered, a modular, integrated, and computationally tractable solving methodology is proposed, that is not limited by any independence restriction on the random demand. The methodologies are validated on an industrial problem faced by a chemical supply chain; they allow the finding of efficient solutions with minimal optimality gaps, and result in substantial cost savings.; The model associated with the non-stockout service level contains joint probabilistic constraints enforcing the probability of the joint fulfillment of a system of linear inequalities with dependent random right-hand side variables to be above a prescribed probability level.; In the first module of the methodology, the concept of p-efficiency is shown to be useful for approximating the joint probabilistic constraints. Its application to a stochastic supply chain involves the construction of p-efficient demand trajectories. We complement this concept by designing preprocessing methods that drastically reduce the number of considered demand trajectories.; The second module is devoted to the construction of valid inequalities, used to support the branch-and-bound algorithm. In particular, a new family of cover inequalities for binary-integer knapsack-constraints is developed, allowing the finding of substantially better integer solutions.; The third module finds the best p-efficient demand trajectory. A congestion-relief column generation algorithm is implemented, limiting inefficiencies due to bottleneck of distribution resources.; The model associated with the fill rate service level contains normalized expected shortfall constraints. The solving methodology involves the identification of the critical fill rate supply path. It is also shown that the non-stockout cycle service level is more demanding than the fill rate one.