Optimal Allocation of Stock Levels and Stochastic Customer Demands to a Capacitated Resource Shuang Chen and Joseph Geunes Department of Industrial and Systems Engineering University of Florida, PO Box 116595, Gainesville, FL, 32611 scljj@ufl.edu, geunes@ise.ufl.edu August 24, 2009 Abstract This paper considers a class of stochastic resource allocation problems that requires simulta- neously determining the customers that a capacitated resource must serve and the stock levels of multiple items that may be used in meeting these customers’ demands. Our model consid- ers a reward (revenue) for serving each assigned customer, a variable cost for allocating each item to the resource, and a shortage cost for each unit of unsatisfied customer demand in a single-period context. The model maximizes the expected profit resulting from the assignment of customers and items to the resource while obeying the resource capacity constraint. We provide an exact solution method for this mixed integer nonlinear optimization problem using a Generalized Benders Decomposition approach. This decomposition approach uses Lagrangian relaxation to solve a constrained multi-item newsvendor subproblem and uses CPLEX to solve a mixed-integer linear Master Problem. We generate Benders cuts for the master problem by obtaining a series of subgradients of the subproblem’s convex objective function. In addition, we present a family of heuristic solution approaches and compare our methods with a commercial solver in order to benchmark their efficiency and quality. Keywords: Stochastic resource allocation; Generalized Benders decomposition; Lagrangian relaxation; Mixed integer nonlinear optimization. 1 Introduction The optimal deployment of constrained resources lies at the heart of nearly all operations problems. Many operations settings require the assignment of uncertain customer demands to a resource with limited capacity. One such problem is faced by service technicians who must perform on-site diagnosis and repair of customer equipment and/or facilities. That is, given a set of customers requiring a service visit, a service operations planner must determine how to allocate these visits to service technicians, and which parts each service technician should stock in their corresponding vehicles prior to making the service calls. Because customer service requirements require on-site diagnosis prior to service, the required parts to provide service to each customer are not known with certainty prior to dispatching the service technician. Although the degree of uncertainty in customer parts requirements can be decreased via an initial telephone- or Internet-based pre- 1