I n this research, we apply robust optimization (RO) to the problem of locating facilities in a network facing uncertain demand over multiple periods. We consider a multi-period fixed-charge network location problem for which we find (1) the number of facilities, their location and capacities, (2) the production in each period, and (3) allocation of demand to facilities. Using the RO approach we formulate the problem to include alternate levels of uncertainty over the periods. We consider two models of demand uncertainty: demand within a bounded and symmetric multi-dimensional box, and demand within a multi-dimensional ellipsoid. We evaluate the potential benefits of applying the RO approach in our setting using an extensive numerical study. We show that the alternate models of uncertainty lead to very different solution network topologies, with the model with box uncertainty set opening fewer, larger facilities. Through sample path testing, we show that both the box and ellipsoidal uncertainty cases can provide small but significant improvements over the solution to the problem when demand is deterministic and set at its nominal value. For changes in several environmental parameters, we explore the effects on the solution performance.

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W e study a supply chain of a manufacturer selling to two asymmetric retailers engaged in inventory (order quantity) competition in the presence of demand uncertainty and an exogenously given retail price. The effective demand of each retailer includes its primary demand and reallocated demand from its competitor. We model two salient features causing asymmetry: (i) the weak retailer is capital-constrained and (ii) the bargaining power of the dominant retailer implies that it enjoys a lower wholesale price. The manufacturer offers trade credit to the weak, capital-constrained retailer. We show that such trade credit can be used by the manufacturer as a strategic response to the bargaining power of its dominant retailer. Computational examples reveal that under inventory competition, the capital-constrained retailer benefits from the trade credit, leaving the dominant retailer worse off. We show that demand substitution increases the profit of the dominant retailer and the manufacturer but, somewhat surprisingly, decreases the weak retailer's profit. When both bank and trade credit are available, we show conditions under which trade credit is preferred over bank credit by the manufacturer. Compared with a trade credit with an endogenous interest rate (and an exogenously given wholesale price), a trade credit with an endogenous wholesale price (and an exogenously given interest rate) is preferred by the manufacturer, but is only preferred by the system when the weak retailer's initial working capital is small.

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We analyze the problem of optimal location of a set of facilities in the presence of stochastic demand and congestion. Customers travel to the closest facility to obtain service; the problem is to determine the number, locations, and capacity of the facilities. Under rather general assumptions (spatially distributed continuous demand, general arrival and service processes, and nonlinear location and capacity costs) we show that the problem can be decomposed, and construct an efficient optimization algorithm. The analysis yields several insights, including the importance of equitable facility configurations (EFCs), the behavior of optimal and near-optimal capacities, and robust class of solutions that can be constructed for this problem.facility location, stochastic demand, queueing, service level