Inventory Competition in Make-to-Stock Systems

We present models for competition among multiple suppliers for demand from a single manufacturer. The suppliers produce to stock a single product and are allocated demand by the manufacturer based on the amount the amount of inventory they hold. We prove the existence of a Nash equilibrium for a broad class of market allocation schemes. For the special case of identical suppliers under either a stock-proportional or fill rate-proportional allocation, we show the uniqueness of the Nash equilibrium. Analysis of the Nash equilibrium for this case reveals that (a) the manufacturer benefits from competition (in the form of higher fill rates), (b) the manufacturer benefits more from a stock-proportional allocation than a fill rate-proportional allocation, and (c) the manufacturer benefits the most when the number of suppliers is two

Outsourcing to Non-Identical Suppliers via Service Competition

In this paper, we consider a single buyer who wishes to outsource a fixed demand for a manufactured good or service at a fixed price to a set of N suppliers. We examine the value of competition as a mechanism for the buyer to elicit good service quality from her suppliers. In particular, we consider a scheme in which the buyer allocates a proportion of demand to each supplier, with the proportion a supplier receives increasing in the service level she offers. Suppliers compete for expected market share, which increases in the offered service level. The suppliers affect their service levels by exerting effort once they receive a positive portion of demand, with the cost of effort increasing in the service level offered and the demand allocated. Each supplier chooses a service level to maximize her own expected profit, subject to the behavior of other competing suppliers. In making this decision, the supplier effectively weighs the market share benefits of each service level against its associated cost. The possibility of inducing service quality through competition raises several important questions. For example, under what conditions does service competition lead to an equilibrium? How does the number and type of suppliers affect the buyer’s service quality and the suppliers’ expected profits? Is it more desirable for the buyer to contract with suppliers that are equally efficient or to have a mix of suppliers with varying capabilities? How should the buyer choose parameters for the competition to maximize the quality of service she receives? In particular, what is the impact of the allocation functions on the buyer’s quality of service and is it possible for the buyer to choose an allocation function that forces the suppliers to provide the maximum feasible service level? In this paper, we address these and other related questions

Optimal Service-Based Competition with Heterogeneous Suppliers

We investigate how a competition can be designed to maximize expected profit for a buyer who wishes to allocate demand among a diverse set of suppliers when his profit is dependent on the supplier’s service levels. The candidate suppliers are heterogeneous in their capacities and cost structures, and compete for shares of the buyer’s demand based on their promised service levels. To characterize the optimal competition, we first identify a family of allocation functions that are service maximizing, meaning they can intensify the competition to a point where each supplier provides its maximum feasible service level and the outcome of the competition is a predefined set of demand shares. We show that using a service maximizing allocation function is a necessary condition for solving the buyer’s problem. We then characterize the optimal demand allocation set and, when they are endogenous, the optimal procurement prices. When both demand allocation and procurement prices can be chosen by the buyer, we find that the competition also maximizes supply chain profit. Through a set of numerical examples, we show that the benefit of using this optimal competition design, including its specified demand allocation function and suggested procurement prices, can be significant

Service Systems with Finite and Heterogeneous Customer Arrivals

International audienceW e consider service systems with a finite number of customer arrivals, where customer interarrival times and service times are both stochastic and heterogeneous. Applications of such systems are numerous and include systems where arrivals are driven by events or service completions in serial processes as well as systems where servers are subject to learning or fatigue. Using an embedded Markov chain approach, we characterize the waiting time distribution for each customer, from which we obtain various performance measures of interest, including the expected waiting time of a specific customer, the expected waiting time of an arbitrary customer, and the expected completion time of all customers. We carry out extensive numerical experiments to examine the effect of heterogeneity in interarrival and service times. In particular, we examine cases where interarrival and service times increase with each subsequent arrival or service completion, decrease, increase and then decrease, or decrease and then increase. We derive several managerial insights and discuss implications for settings where such features can be induced. We validate the numerical results using a fluid approximation that yields closed-form expressions

A customer-item decomposition approach to stochastic inventory systems with correlation

We consider an inventory system with a single stage, periodic review, correlated, non-stationary stochastic demand and correlated, non-stationary stochastic and sequential leadtimes. We use the customer-item decomposition approach to decompose the problem into sub-problems, each involving a single customer-item pair. We then formulate each subproblem as an optimal stopping problem. We use properties that arise from this formulation to show that the optimal policy is a state-dependent base-stock policy and to show, for several cases, that the optimal policy can be obtained via a polynomial time algorithm. We also use the formulation to construct a myopic heuristic which leads to an explicit solution for the optimal policy in the form of a critical fractile. We characterize conditions under which the myopic heuristic is optimal

Queueing systems with appointment-driven arrivals, nonpunctual customers and no-shows. Working Paper

Abstract We consider queueing systems where a finite number of customers arrive over time to a service system, consisting of either a single or multiple servers. The arrival of customers is driven by appointments, with a scheduled appointment time associated with each customer. However, customers are not necessarily punctual and may arrive either earlier or later than their scheduled appointment times. Customers may also not show up altogether. The arrival times of customers (relative to their scheduled appointments) and their service times are both stochastic. Customers are not homogeneous in their punctuality, show-up probabilities, and time between previous and subsequent appointments, which may vary from customer to customer. We develop an exact analytical approach to obtain various performance measures of interest and illustrate the usefulness of the approach by describing numerical results that examine the impact of not accounting for non-punctuality and no-shows. We also illustrate how our approach can be used to support individualized appointment scheduling, and show how such a scheduling scheme can significantly outperform schemes where all appointment times are equally spaced