Simultaneous price,location, and capacity decisions on a line of time‐sensitive customers

Consider a monopolist who sells a single product to time‐sensitive customers located on a line segment. Customers send their orders to the nearest distribution facility, where the firm processes (customizes) these orders on a first‐come, first‐served basis before delivering them. We examine how the monopolist would locate its facilities, set their capacities, and price the product offered to maximize profits. We explicitly model customers' waiting costs due to both shipping lead times and queueing congestion delays and allow each customer to self‐select whether she orders or not, based on her reservation price. We first analyze the single‐facility problem and derive a number of interesting insights regarding the optimal solution. We show, for instance, that the optimal capacity relates to the square root of the customer volume and that the optimal price relates additively to the capacity and transportation delay costs. We also compare our solutions to a similar problem without congestion effects. We then utilize our single‐facility results to treat the multi‐facility problem. We characterize the optimal policy for serving a fixed interval of customers from multiple facilities when customers are uniformly distributed on a line. We also show how as the length of the customer interval increases, the optimal policy relates to the single‐facility problem of maximizing expected profit per unit distance. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Delivery‐date and capacity management in a decentralized internal market

We study competitive due‐date and capacity management between the marketing and engineering divisions within an engineer‐to‐order (ETO) firm. Marketing interacts directly with the customers and quotes due‐dates for their orders. Engineering is primarily concerned with the efficient utilization of resources and is willing to increase capacity if the cost is compensated. The two divisions share the responsibility for timely delivery of the jobs. We model the interaction between marketing and engineering as a Nash game and investigate the effect of internal competition on the equilibrium decisions. We observe that the internal competition not only degrades the firm's overall profitability but also the serviceability. Finally, we extend our analysis to multiple‐job settings that consider both flexible and inflexible capacity. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

A produce‐to‐stock system with advance demand information and secondary customers

We consider a manufacturer (i.e., a capacitated supplier) that produces to stock and has two classes of customers. The primary customer places orders at regular intervals of time for a random quantity, while the secondary customers request a single item at random times. At a predetermined time the manufacturer receives advance demand information regarding the order size of the primary customer. If the manufacturer is not able to fill the primary customer's demand, there is a penalty. On the other hand, serving the secondary customers results in additional profit; however, the manufacturer can refuse to serve the secondary customers in order to reserve inventory for the primary customer. We characterize the manufacturer's optimal production and stock reservation policies that maximize the manufacturer's discounted profit and the average profit per unit time. We show that these policies are threshold‐type policies, and these thresholds are monotone with respect to the primary customer's order size. Using a numerical study we provide insights into how the value of information is affected by the relative demand size of the primary and secondary customers. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Production‐inventory systems with imperfect advance demand information and updating

We consider a supplier with finite production capacity and stochastic production times. Customers provide advance demand information (ADI) to the supplier by announcing orders ahead of their due dates. However, this information is not perfect, and customers may request an order be fulfilled prior to or later than the expected due date. Customers update the status of their orders, but the time between consecutive updates is random. We formulate the production‐control problem as a continuous‐time Markov decision process and prove there is an optimal state‐dependent base‐stock policy, where the base‐stock levels depend upon the numbers of orders at various stages of update. In addition, we derive results on the sensitivity of the state‐dependent base‐stock levels to the number of orders in each stage of update. In a numerical study, we examine the benefit of ADI, and find that it is most valuable to the supplier when the time between updates is moderate. We also consider the impact of holding and backorder costs, numbers of updates, and the fraction of customers that provide ADI. In addition, we find that while ADI is always beneficial to the supplier, this may not be the case for the customers who provide the ADI. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

Scheduling and due‐date quotation in a make‐to‐order supply chain

We consider a manufacturer, served by a single supplier, who has to quote due dates to arriving customers in a make‐to‐order production environment. The manufacturer is penalized for long lead times and for missing due dates. To meet due dates, the manufacturer has to obtain components from a supplier. We model this manufacturer and supplier as a two‐machine flow shop, consider several variations of this problem, and design effective due‐date quotation and scheduling algorithms for centralized and decentralized versions of the model. We perform extensive computational testing to assess the effectiveness of our algorithms and to compare the centralized and decentralized models to quantify the value of centralized control in a make‐to‐order supply chain. Since complete information exchange and centralized control is not always practical or cost‐effective, we explore the value of partial information exchange for this system. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Analysis of the finite‐source multiclass priority queue with an unreliable server and setup time

In this article, we study a queueing system serving multiple classes of customers. Each class has a finite‐calling population. The customers are served according to the preemptive‐resume priority policy. We assume general distributions for the service times. For each priority class, we derive the steady‐state system size distributions at departure/arrival and arbitrary time epochs. We introduce the residual augmented process completion times conditioned on the number of customers in the system to obtain the system time distribution. We then extend the model by assuming that the server is subject to operation‐independent failures upon which a repair process with random duration starts immediately. We also demonstrate how setup times, which may be required before resuming interrupted service or picking up a new customer, can be incorporated in the model. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

Scheduling a production–distribution system to optimize the tradeoff between delivery tardiness and distribution cost

We consider a make‐to‐order production–distribution system with one supplier and one or more customers. A set of orders with due dates needs to be processed by the supplier and delivered to the customers upon completion. The supplier can process one order at a time without preemption. Each customer is at a distinct location and only orders from the same customer can be batched together for delivery. Each delivery shipment has a capacity limit and incurs a distribution cost. The problem is to find a joint schedule of order processing at the supplier and order delivery from the supplier to the customers that optimizes an objective function involving the maximum delivery tardiness and the total distribution cost. We first study the solvability of various cases of the problem by either providing an efficient algorithm or proving the intractability of the problem. We then develop a fast heuristic for the general problem. We show that the heuristic is asymptotically optimal as the number of orders goes to infinity. We also evaluate the performance of the heuristic computationally by using lower bounds obtained by a column generation approach. Our results indicate that the heuristic is capable of generating near optimal solutions quickly. Finally, we study the value of production–distribution integration by comparing our integrated approach with two sequential approaches where scheduling decisions for order processing are made first, followed by order delivery decisions, with no or only partial integration of the two decisions. We show that in many cases, the integrated approach performs significantly better than the sequential approaches. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005     

Competitive location and capacity decisions for firms serving time‐sensitive customers

In this article we explore how two competing firms locate and set capacities to serve time‐sensitive customers. Because customers are time‐sensitive, they may decline to place an order from either competitor if their expected waiting time is large. We develop a two‐stage game where firms set capacities and then locations, and show that three types of subgame perfect equilibria are possible: local monopoly (in which each customer is served by a single firm, but some customers may be left unserved), constrained local monopoly (in which firms serve the entire interval of customers but do not compete with each other), and constrained competition (in which firms also serve the entire interval of customers, but now compete for some customers). We perform a comparative statics analysis to illustrate differences in the equilibrium behavior of a duopolist and a coordinated monopolist. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Supply contracts in manufacturer‐retailer interactions with manufacturer‐quality and retailer effort‐induced demand

We consider a decentralized distribution channel where demand depends on the manufacturer‐chosen quality of the product and the selling effort chosen by the retailer. The cost of selling effort is private information for the retailer. We consider three different types of supply contracts in this article: price‐only contract where the manufacturer sets a wholesale price; fixed‐fee contract where manufacturer sells at marginal cost but charges a fixed (transfer) fee; and, general franchise contract where manufacturer sets a wholesale price and charges a fixed fee as well. The fixed‐fee and general franchise contracts are referred to as two‐part tariff contracts. For each contract type, we study different contract forms including individual, menu, and pooling contracts. In the analysis of the different types and forms of contracts, we show that the price only contract is dominated by the general franchise menu contract. However, the manufacturer may prefer to offer the fixed‐fee individual contract as compared to the general franchise contract when the retailer's reservation utility and degree of information asymmetry in costs are high. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Optimal control of a production‐inventory system with both backorders and lost sales

We consider the optimal control of a production inventory‐system with a single product and two customer classes where items are produced one unit at a time. Upon arrival, customer orders can be fulfilled from existing inventory, if there is any, backordered, or rejected. The two classes are differentiated by their backorder and lost sales costs. At each decision epoch, we must determine whether or not to produce an item and if so, whether to use this item to increase inventory or to reduce backlog. At each decision epoch, we must also determine whether or not to satisfy demand from a particular class (should one arise), backorder it, or reject it. In doing so, we must balance inventory holding costs against the costs of backordering and lost sales. We formulate the problem as a Markov decision process and use it to characterize the structure of the optimal policy. We show that the optimal policy can be described by three state‐dependent thresholds: a production base‐stock level and two order‐admission levels, one for each class. The production base‐stock level determines when production takes place and how to allocate items that are produced. This base‐stock level also determines when orders from the class with the lower shortage costs (Class 2) are backordered and not fulfilled from inventory. The order‐admission levels determine when orders should be rejected. We show that the threshold levels are monotonic (either nonincreasing or nondecreasing) in the backorder level of Class 2. We also characterize analytically the sensitivity of these thresholds to the various cost parameters. Using numerical results, we compare the performance of the optimal policy against several heuristics and show that those that do not allow for the possibility of both backordering and rejecting orders can perform poorly.© 2010 Wiley Periodicals, Inc. Naval Research Logistics 2010     

Irreducibility of joint inventory positions in an assemble‐to‐order system under (r,nQ) policies

In a typical assemble‐to‐order system, a customer order may request multiple items, and the order may not be filled if any of the requested items are out of stock. A key customer service measure when unfilled orders are backordered is the order‐based backorder level. To evaluate this crucial performance measure, a fundamental question is whether the stationary joint inventory positions follow an independent and uniform distribution. In this context, this is equivalent to the irreducibility of the Markov chain formed by the joint inventory positions. This article presents a necessary and sufficient condition for the irreducibility of such a Markov chain through a set of simultaneous Diophantine equations. This result also leads to sufficient conditions that are more general than those in the published reports. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

A location‐inventory model with lateral transshipments

We study an infinite horizon periodic stochastic inventory system consisting of retail outlets and customers located on a homogenous line segment. In each period, the total demand, generated by the customers on the line, is normally distributed. To better match supply and demand, we incorporate lateral transshipments. We propose a compact model in which the strategic decisions—the number and locations of retail outlets—are determined simultaneously with the operational decisions—the inventory replenishment and transshipment quantities. We find the optimal balance between the risk‐pooling considerations, which drive down the optimal number of retail outlets, and lateral transshipments, which drive up the optimal number of retail outlets. We also explore the sensitivity of the optimal number of retail outlets to various problem parameters. This article presents a novel way of integrating lateral transshipments in the context of an inventory‐location model. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

The loss‐averse newsvendor problem with supply options

In this article, we consider a loss‐averse newsvendor with stochastic demand. The newsvendor might procure options when demand is unknown, and decide how many options to execute only after demand is revealed. If the newsvendor reserves too many options, he would incur high reservation costs. Yet reserving too few could result in lost sales. So the newsvendor faces a trade‐off between reservation costs and losing sales. When there are multiple options available, the newsvendor has to consider how many units of each to reserve by studying the trade‐off between flexibility and costs. We show how the newsvendor's loss aversion behavior affects his ordering decision, and propose an efficient algorithm to compute his optimal solution in the general case with n options. We also present examples showing how the newsvendor's ordering strategy changes as loss aversion rises. © 2014 Wiley Periodicals, Inc. 62:46–59, 2015     

Optimal control policies for an inventory system with commitment lead time

We consider a firm which faces a Poisson customer demand and uses a base‐stock policy to replenish its inventories from an outside supplier with a fixed lead time. The firm can use a preorder strategy which allows the customers to place their orders before their actual need. The time from a customer's order until the date a product is actually needed is called commitment lead time. The firm pays a commitment cost which is strictly increasing and convex in the length of the commitment lead time. For such a system, we prove the optimality of bang‐bang and all‐or‐nothing policies for the commitment lead time and the base‐stock policy, respectively. We study the case where the commitment cost is linear in the length of the commitment lead time in detail. We show that there exists a unit commitment cost threshold which dictates the optimality of either a buy‐to‐order (BTO) or a buy‐to‐stock strategy. The unit commitment cost threshold is increasing in the unit holding and backordering costs and decreasing in the mean lead time demand. We determine the conditions on the unit commitment cost for profitability of the BTO strategy and study the case with a compound Poisson customer demand.     

A sequential dynamic pricing model and its applications

Consider a sequential dynamic pricing model where a seller sells a given stock to a random number of customers. Arriving one at a time, each customer will purchase one item if the product price is lower than her personal reservation price. The seller's objective is to post a potentially different price for each customer in order to maximize the expected total revenue. We formulate the seller's problem as a stochastic dynamic programming model, and develop an algorithm to compute the optimal policy. We then apply the results from this sequential dynamic pricing model to the case where customers arrive according to a continuous‐time point process. In particular, we derive tight bounds for the optimal expected revenue, and develop an asymptotically optimal heuristic policy. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

The effect of catastrophes on the strategic customer behavior in queueing systems

We consider the single server Markovian queue subject to Poisson generated catastrophes. Whenever a catastrophe occurs, all customers are forced to abandon the system, the server is rendered inoperative and an exponential repair time is set on. During the repair time new arrivals are allowed to join the system. We assume that the arriving customers decide whether to join the system or balk, based on a natural linear reward‐cost structure with two types of rewards: A (usual) service reward for those customers that receive service and a (compensation) failure reward for those customers that are forced to abandon the system due to a catastrophe. We study the strategic behavior of the customers regarding balking and derive the corresponding (Nash) equilibrium strategies for the observable and unobservable cases. We show that both types of strategic behavior may be optimal: to avoid the crowd or to follow it. The crucial factor that determines the type of customer behavior is the relative value of the service reward to the failure compensation. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

Single machine just‐in‐time scheduling problems with two competing agents

In scheduling problems with two competing agents, each one of the agents has his own set of jobs to be processed and his own objective function, and both share a common processor. In the single‐machine problem studied in this article, the goal is to find a joint schedule that minimizes the total deviation of the job completion times of the first agent from a common due‐date, subject to an upper bound on the maximum deviation of job completion times of the second agent. The problem is shown to be NP‐hard even for a nonrestrictive due‐date, and a pseudopolynomial dynamic program is introduced and tested numerically. For the case of a restrictive due‐date (a sufficiently small due‐date that may restrict the number of early jobs), a faster pseudopolynomial dynamic program is presented. We also study the multiagent case, which is proved to be strongly NP‐hard. A simple heuristic for this case is introduced, which is tested numerically against a lower bound, obtained by extending the dynamic programming algorithm. © 2013 Wiley Periodicals, Inc. Naval Research Logistics 61: 1–16, 2014     

Stein–Chen approximation and error bounds for order fill rates in assemble‐to‐order systems

Assemble‐to‐order (ATO) is an important operational strategy for manufacturing firms to achieve quick response to customer orders while keeping low finished good inventories. This strategy has been successfully used not only by manufacturers (e.g., Dell, IBM) but also by retailers (e.g., Amazon.com). The evaluation of order‐based performance is known to be an important but difficult task, and the existing literature has been mainly focused on stochastic comparison to obtain performance bounds. In this article, we develop an extremely simple Stein–Chen approximation as well as its error‐bound for order‐based fill rate for a multiproduct multicomponent ATO system with random leadtimes to replenish components. This approximation gives an expression for order‐based fill rate in terms of component‐based fill rates. The approximation has the property that the higher the component replenishment leadtime variability, the smaller the error bound. The result allows an operations manager to analyze the improvement in order‐based fill rates when the base‐stock level for any component changes. Numerical studies demonstrate that the approximation performs well, especially when the demand processes of different components are highly correlated; when the components have high base‐stock levels; or when the component replenishment leadtimes have high variability. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012     

Modeling and analysis of flexible queueing systems

We consider queueing systems with multiple classes of customers and heterogeneous servers where customers have the flexibility of being processed by more than one server and servers possess the capability of processing more than one customer class. We provide a unified framework for the modeling and analysis of these systems under arbitrary customer and server flexibility and for a rich set of control policies that includes customer/server‐specific priority schemes for server and customer selection. We use our models to generate several insights into the effect of system configuration and control policies. In particular, we examine the relationship between flexibility, control policies and throughput under varying assumptions for system parameters. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

Optimal inventory control policy for periodic‐review inventory systems with inventory‐level‐dependent demand

We consider a setting in which inventory plays both promotional and service roles; that is, higher inventories not only improve service levels but also stimulate demand by serving as a promotional tool (e.g., as the result of advertising effect by the enhanced product visibility). Specifically, we study the periodic‐review inventory systems in which the demand in each period is uncertain but increases with the inventory level. We investigate the multiperiod model with normal and expediting orders in each period, that is, any shortage will be met through emergency replenishment. Such a model takes the lost sales model as a special case. For the cases without and with fixed order costs, the optimal inventory replenishment policy is shown to be of the base‐stock type and of the (s,S) type, respectively. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012