Francis de Véricourt

Optimal Stock Allocation for a Capacitated Supply System

We consider a capacitated supply system that produces a single item that is demanded by several classes of customers. Each customer class may have a different backorder cost, so stock allocation arises as a key decision problem. We model the supply system as a multi customer make-to-stock queue. Using dynamic programming, we show that the optimal allocation policy has a simple and intuitive structure. In addition, we present an efficient algorithm to compute the parameters of this optimal allocation policy. Finally, for a typical supply chain design problem, we illustrate that ignoring the stock allocation dimension--a frequently encountered simplifying assumption--can lead to incorrect managerial decisions.

Using Imperfect Advance Demand Information in Production-Inventory Systems with Multiple Customer Classes

We consider a make-to-stock supplier that operates a production facility with limited capacity. The supplier receives orders from customers belonging to several demand classes. Some of the customer classes share advance demand information with the supplier by announcing their orders ahead of their due date. However, this advance demand information is not perfect because the customer may decide to order prior to or later than the expected due date or may decide to cancel the order altogether. Customer classes vary in their demand rates, expected due dates, cancellation probabilities, and shortage costs. The supplier must decide when to produce and, whenever an order becomes due, whether or not to satisfy it from on-hand inventory. Hence, the supplier is faced with a joint production-control and inventory-allocation problem. We formulate the problem as a Markov decision process and characterize the structure of the optimal policy. We show that the optimal production policy is a state-dependent base-stock policy with a base-stock level that is nondecreasing in the number of announced orders. We show that the optimal inventory-allocation policy is a state-dependent multilevel rationing policy, with the rationing level for each class nondecreasing in the number of announced orders (regardless of whether the class provides advance information). From numerical results, we obtain several insights into the value of advance demand information for both supplier and customers.

Call Center Outsourcing Contract Analysis and Choice

This paper considers a call center outsourcing contract analysis and choice problem faced by a contractor and a service provider. The service provider receives an uncertain call volume over multiple periods and is considering outsourcing all or part of these calls to a contractor. Each call brings in a fixed revenue to the service provider. Answering calls requires having service capacity; thus implicit in the outsourcing decision is a capacity decision. Insufficient capacity implies that calls cannot be answered, which in turn means there will be a revenue loss. Faced with a choice between a volume-based and a capacity-based contract offered by a contractor that has pricing power, the service provider determines optimal capacity levels. The optimal price and capacity of the contractor together with the optimal capacity of the service provider determine optimal profits of each party under the two contracts being considered. This paper characterizes optimal capacity levels and partially characterizes optimal pricing decisions under each contract. The impact of demand variability and the economic parameters on contract choice are explored through numerical examples. It is shown that no contract type is universally preferred and that operating environments as well as cost-revenue structures have an important effect.

Dynamic Scheduling in a Make-to-Stock System: A Partial Characterization of Optimal Policies

We consider the problem of dynamically allocating production capacity between two products to minimize the average inventory and backorder costs per unit time in a make-to-stock single machine system. Using sample path comparisons and dynamic programming, we give a characterization of the optimal hedging point policy for a certain region of the state space. The characterization is simple enough to lead to easily implementable heuristics and provides a formal justification of some of the earlier heuristics proposed.

Managing Response Time in a Call-Routing Problem with Service Failure

Traditional research on routing in queueing systems usually ignores service quality related factors. In this paper, we analyze the routing problem in a system where customers call back when their problems are not completely resolved by the customer service representatives (CSRs). We introduce the concept of call resolution probability, and we argue that it constitutes a good proxy for call quality. For each call, both the call resolution probability (p) and the average service time (1/µ) are CSR dependent. We use a Markov decision process formulation to obtain analytical results and insights about the optimal routing policy that minimizes the average total time of call resolution, including callbacks. In particular, we provide sufficient conditions under which it is optimal to route to the CSR with the highest call resolution rate (pµ) among those available. We also develop efficient heuristics that can be easily implemented in practice.

Demand Allocation in Multiple-Product, Multiple-Facility, Make-to-Stock Systems

We consider the problem of allocating demand arising from multiple products to multiple production facilities with finite capacity and load-dependent lead times. Production facilities can choose to manufacture items either to stock or to order. Products vary in their demand rates, holding and backordering costs, and service-level requirements. We develop models and solution procedures to determine the optimal allocation of demand to facilities and the optimal inventory level for products at each facility. We consider two types of demand allocation, one in which we allow the demand for a product to be split among multiple facilities and the other in which demand from each product must be entirely satisfied by a single facility. We also consider two forms of inventory warehousing, one in which inventory locations are factory based and one in which they are centralized. For each case, we offer a solution procedure to obtain optimal demand allocations and optimal inventory base-stock levels. For systems with multiple customer classes, we also determine optimal inventory rationing levels for each class for each product. We use the models to characterize analytically several properties of the optimal solution. In particular, we highlight eight principles that relate the effects of cost, congestion, inventory pooling, multiple sourcing, customer segmentation, inventory rationing, and process and demand variability.

Nurse Staffing in Medical Units: A Queueing Perspective

In this paper, we present a closed queueing model to determine efficient nurse staffing policies. We explicitly model the workload experienced by s nurses within a single medical unit with n homogeneous patients as a closed M/M/s//n queueing system, where each patient alternates between requiring assistance and not. The performance of the medical unit is based on the probability of excessive delay, the relative frequency with which the delay between the onset of patient neediness and the provision of care from a nurse exceeds a given time threshold. Using new many-server asymptotic results, we find that effective staffing policies should deviate from threshold-specific nurse-to-patient ratios by factors that take into account the total number of patients present in the unit. In particular, our staffing rule significantly differs from California Bill AB 394, legislation that mandates fixed nurse-to-patient staffing ratios. Simulations show that our results are robust to delay-dependent service times, generally distributed service times, and nonhomogeneous patients, i.e., those with different acuity levels.

Assessing the Benefits of Different Stock-Allocation Policies for a Make-to-Stock Production System

We consider a manufacturing facility that produces a single item that is demanded by several different classes of customers. The inventory-related cost performance of such a system can be improved by effective allocation of production and inventories. We obtain the optimal parameters for three easily implementable allocation policies. Our results cover the case of linear backorder costs as well as fill-rate constraints. We compare the optimal performance of these control policies to gain insights into the benefits of different production and stock-allocation rules.

Resource and Revenue Management in Nonprofit Operations

Nonprofit firms sometimes engage in for-profit activities for the purpose of generating revenue to subsidize their mission activities. The organization is then confronted with a consumption versus investment trade-off, where investment corresponds to providing capacity for revenue customers, and consumption corresponds to serving mission customers. Exemplary of this approach are the Aravind Eye Hospitals in India, where profitable paying hospitals are used to subsidize care at free hospitals. We model this problem as a multiperiod stochastic dynamic program. In each period, the organization must decide how much of the current assets should be invested in revenue-customer service capacity, and at what price the service should be sold. We provide sufficient conditions under which the optimal capacity and pricing decisions are of threshold type. Similar results are derived when the selling price is fixed, but the banking of assets from one period to the next is allowed. We compare the performance of the optimal threshold policy with heuristics that may be more appealing to managers of nonprofit organizations, and we assess the value of banking and of dynamic pricing through numerical experiments.

Diagnostic Accuracy Under Congestion

In diagnostic services, agents typically need to weigh the benefit of running an additional test and improving the accuracy of diagnosis against the cost of delaying the provision of services to others. Our paper analyzes how to dynamically manage this accuracy/congestion trade-off. To that end, we study an elementary congested system facing an arriving stream of customers. The diagnostic process consists of a search problem in which the service provider conducts a sequence of imperfect tests to determine the customers type. We find that the agent should continue to perform the diagnosis as long as her current belief that the customer is of a given type falls into an interval that depends on the congestion level as well as the number of performed tests thus far. This search interval should shrink as congestion intensifies and as the number of performed tests increases if additional conditions hold. Our study reveals that, contrary to diagnostic services without congestion, the base rate i.e., the prior probability of the customer type has an effect on the agents search strategy. In particular, the optimal search interval shrinks when customer types are more ambiguous a priori, i.e., as the base rate approaches the value at which the agent is indifferent between types. Finally, because of congestion effects, the agent should sometimes diagnose the customer as being of a given type, even if test results indicate otherwise. All these insights disappear in the absence of congestion. This paper was accepted by Martin Lariviere, operations management.