Inventory allocation models for a two-stage, two-product, capacitated supplier and retailer problem with random demand

The objective of this research is to develop an optimal inventory allocation methodology for a supply chain consisting of a capacitated retailer with limited shelf space, and two unreliable capacitated suppliers in an uncertain environment. We develop conceptual and analytical models that provide allocation preferences between shelf-space and warehouse in both deterministic and stochastic demand cases, and develop managerial insights based on them. For each case, we provide both a closed-form solution and a heuristic method, and illustrate the bounds on the optimal solution. Further, we show that the cost function is L^⋄-convex in some cases. Finally, we prove that the expected profit decreases as the variance of demand increases.