Locational tying of complementary retail items

We study a selling practice that we refer to as locational tying (LT), which seems to be gaining wide popularity among retailers. Under this strategy, a retailer “locationally ties” two complementary items that we denote by “primary” and “secondary.” The retailer sells the primary item in an appropriate “department” of his or her store. To stimulate demand, the secondary item is offered in the primary item's department, where it is displayed in very close proximity to the primary item. We consider two variations of LT: In the multilocation tying strategy (LT‐M), the secondary item is offered in its appropriate department in addition to the primary item's department, whereas in the single‐location tying strategy (LT‐S), it is offered only in the primary item's location. We compare these LT strategies to the traditional independent components (IC) strategy, in which the two items are sold independently (each in its own department), but the pricing/inventory decisions can be centralized (IC‐C) or decentralized (IC‐D). Assuming ample inventory, we compare and provide a ranking of the optimal prices of the four strategies. The main insight from this comparison is that relative to IC‐D, LT decreases the price of the primary item and adjusts the price of the secondary item up or down depending on its popularity in the primary item's department. We also perform a comparative statics analysis on the effect of demand and cost parameters on the optimal prices of various strategies, and identify the conditions that favor one strategy over others in terms of profitability. Then we study inventory decisions in LT under exogenous pricing by developing a model that accounts for the effect of the primary item's stock‐outs on the secondary item's demand. We find that, relative to IC‐D, LT increases the inventory level of the primary item. We also link the profitability of different strategies to the trade‐off between the increase in demand volume of the secondary item as a result of LT and the potential increase in inventory costs due to decentralizing the inventory of the secondary item. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009     

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     

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.     

Contractual agreements for coordination and vendor‐managed delivery under explicit transportation considerations

We consider the coordination problem between a vendor and a buyer operating under generalized replenishment costs that include fixed costs as well as stepwise freight costs. We study the stochastic demand, single‐period setting where the buyer must decide on the order quantity to satisfy random demand for a single item with a short product life cycle. The full order for the cycle is placed before the cycle begins and no additional orders are accepted by the vendor. Due to the nonrecurring nature of the problem, the vendor's replenishment quantity is determined by the buyer's order quantity. Consequently, by using an appropriate pricing schedule to influence the buyer's ordering behavior, there is an opportunity for the vendor to achieve substantial savings from transportation expenses, which are represented in the generalized replenishment cost function. For the problem of interest, we prove that the vendor's expected profit is not increasing in buyer's order quantity. Therefore, unlike the earlier work in the area, it is not necessarily profitable for the vendor to encourage larger order quantities. Using this nontraditional result, we demonstrate that the concept of economies of scale may or may not work by identifying the cases where the vendor can increase his/her profits either by increasing or decreasing the buyer's order quantity. We prove useful properties of the expected profit functions in the centralized and decentralized models of the problem, and we utilize these properties to develop alternative incentive schemes for win–win solutions. Our analysis allows us to quantify the value of coordination and, hence, to identify additional opportunities for the vendor to improve his/her profits by potentially turning a nonprofitable transaction into a profitable one through the use of an appropriate tariff schedule or a vendor‐managed delivery contract. We demonstrate that financial gain associated with these opportunities is truly tangible under a vendor‐managed delivery arrangement that potentially improves the centralized solution. Although we take the viewpoint of supply chain coordination and our goal is to provide insights about the effect of transportation considerations on the channel coordination objective and contractual agreements, the paper also contributes to the literature by analyzing and developing efficient approaches for solving the centralized problem with stepwise freight costs in the single‐period setting. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Untruthful probabilistic demand forecasts in vendor‐managed revenue‐sharing contracts: Coordinating the chain

Vendor‐managed revenue‐sharing arrangements are common in the newspaper and other industries. Under such arrangements, the supplier decides on the level of inventory while the retailer effectively operates under consignment, sharing the sales revenue with his supplier. We consider the case where the supplier is unable to predict demand, and must base her decisions on the retailer‐supplied probabilistic forecast for demand. We show that the retailer's best choice of a distribution to report to his supplier will not be the true demand distribution, but instead will be a degenerate distribution that surprisingly induces the supplier to provide the system‐optimal inventory quantity. (To maintain credibility, the retailer's reports of daily sales must then be consistent with his supplied forecast.) This result is robust under nonlinear production costs and nonlinear revenue‐sharing. However, if the retailer does not know the supplier's production cost, the forecast “improves” and could even be truthful. That, however, causes the supplier's order quantity to be suboptimal for the overall system. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Competing with channel partners: Supply chain conflict when retailers introduce store brands

Private‐label products are of increasing importance in many retail categories. While national‐brand products are designed by the manufacturer and sold by the retailer, the positioning of store‐brand products is under the complete control of the retailer. We consider a scenario where products differ on a performance quality dimension and we analyze how retailer–manufacturer interactions in product positioning are affected by the introduction of a private‐label product. Specifically, we consider a national‐brand manufacturer who determines the quality of its product as well the product's wholesale price charged to the retailer. Given the national‐brand quality and wholesale price, the retailer then decides the quality level of its store brand and sets the retail prices for both products. We find that a manufacturer can derive substantial benefits from considering a retailer's store‐brand introduction when determining the national brand's quality and wholesale price. If the retailer has a significant cost disadvantage in producing high‐quality products, the manufacturer does not need to adjust the quality of the national‐brand product, but he should offer a wholesale price discount to ensure its distribution through the retailer. If the retailer is competitive in providing products of high‐quality, the manufacturer should reduce this wholesale price discount and increase the national‐brand quality to mitigate competition. Interestingly, we find the retailer has incentive to announce a store‐brand introduction to induce the manufacturer's consideration of these plans in determining the national‐brand product quality and wholesale price. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Excess procurement strategies by a dominant buyer under constrained supply

Supply chains are often characterized by the presence of a dominant buyer purchasing from a supplier with limited capacity. We study such a situation where a single supplier sells capacity to an established and more powerful buyer and also to a relatively less powerful buyer. The more powerful buyer enjoys the first right to book her capacity requirements at supplier's end, and then the common supplier fulfills the requirement of the less powerful buyer. We find that when the supplier's capacity is either too low (below the lower threshold) or too high (above the higher threshold), there is no excess procurement as compared to the case when supplier has infinite capacity. When the supplier's capacity is between these two thresholds, the more powerful buyer purchases an excess amount in comparison to the infinite capacity case.     

Oligopolistic contracting: Channel coordination under competition

We study contracts between a single retailer and multiple suppliers of two substitutable products, where suppliers have fixed capacities and present the retailer cost contracts for their supplies. After observing the contracts, the retailer decides how much capacity to purchase from each supplier, to maximize profits from the purchased capacity from the suppliers plus his possessed inventory (endowment). This is modeled as a noncooperative, nonzero‐sum game, where suppliers, or principals, move simultaneously as leaders and the retailer, the common agent, is the sole follower. We are interested in the form of the contracts in equilibrium, their effect on the total supply chain profit, and how the profit is split between the suppliers and the retailer. Under mild assumptions, we characterize the set of all equilibrium contracts and discuss all‐unit and marginal‐unit quantity discounts as special cases. We also show that the supply chain is coordinated in equilibrium with a unique profit split between the retailer and the suppliers. Each supplier's profit is equal to the marginal contribution of her capacity to supply chain profits in equilibrium. The retailer's profit is equal to the total revenue collected from the market minus the payments to the suppliers and the associated sales costs.     

Supplier‐buyer contracting: Asymmetric cost information and cutoff level policy for buyer participation

We consider the problem of designing a contract to maximize the supplier's profit in a one‐supplier–one‐buyer relationship for a short‐life‐cycle product. Demand for the finished product is stochastic and price‐sensitive, and only its probability distribution is known when the supply contract is written. When the supplier has complete information on the marginal cost of the buyer, we show that several simple contracts can induce the buyer to choose order quantity that attains the single firm profit maximizing solution, resulting in the maximum possible profit for the supplier. When the marginal cost of the buyer is private information, we show that it is no longer possible to achieve the single firm solution. In this case, the optimal order quantity is always smaller while the optimal sale price of the finished product is higher than the single firm solution. The supplier's profit is lowered while that of the buyer is improved. Moreover, a buyer who has a lower marginal cost will extract more profit from the supplier. Under the optimal contract, the supplier employs a cutoff level policy on the buyer's marginal cost to determine whether the buyer should be induced to sign the contract. We characterize the optimal cutoff level and show how it depends on the parameters of the problem. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 41–64, 2001     

Dynamic coordination of production planning and sales admission control in the presence of a spot market

We consider the decision‐making problem of dynamically scheduling the production of a single make‐to stock (MTS) product in connection with the product's concurrent sales in a spot market and a long‐term supply channel. The spot market is run by a business to business (B2B) online exchange, whereas the long‐term channel is established by a structured contract. The product's price in the spot market is exogenous, evolves as a continuous time Markov chain, and affects demand, which arrives sequentially as a Markov‐modulated Poisson process (MMPP). The manufacturer is obliged to fulfill demand in the long‐term channel, but is able to rein in sales in the spot market. This is a significant strategic decision for a manufacturer in entering a favorable contract. The profitability of the contract must be evaluated by optimal performance. The current problem, therefore, arises as a prerequisite to exploring contracting strategies. We reveal that the optimal strategy of coordinating production and sales is structured by the spot price dependent on the base stock and sell‐down thresholds. Moreover, we can exploit the structural properties of the optimal strategy to conceive an efficient algorithm. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Timely exposure of a secret project: Which activities to monitor?

A defender wants to detect as quickly as possible whether some attacker is secretly conducting a project that could harm the defender. Security services, for example, need to expose a terrorist plot in time to prevent it. The attacker, in turn, schedules his activities so as to remain undiscovered as long as possible. One pressing question for the defender is: which of the project's activities to focus intelligence efforts on? We model the situation as a zero‐sum game, establish that a late‐start schedule defines a dominant attacker strategy, and describe a dynamic program that yields a Nash equilibrium for the zero‐sum game. Through an innovative use of cooperative game theory, we measure the harm reduction thanks to each activity's intelligence effort, obtain insight into what makes intelligence effort more effective, and show how to identify opportunities for further harm reduction. We use a detailed example of a nuclear weapons development project to demonstrate how a careful trade‐off between time and ease of detection can reduce the harm significantly.     

Price and capacity decisions of service systems with boundedly rational customers

We consider price and capacity decisions for a profit‐maximizing service provider in a single server queueing system, in which customers are boundedly rational and decide whether to join the service according to a multinomial logit model. We find two potential price‐capacity pair solutions for the first‐order condition of the profit‐maximizing problem. Profit is maximized at the solution with a larger capacity, but minimized at the smaller one. We then consider a dynamically adjusting capacity system to mimic a real‐life situation and find that the maximum can be reached only when the initial service rate is larger than a certain threshold; otherwise, the system capacity and demand shrink to zero. We also find that a higher level of customers’ bounded rationality does not necessarily benefit a firm, nor does it necessarily allow service to be sustained. We extend our analysis to a setting in which customers’ bounded rationality level is related to historical demand and find that such a setting makes service easier to sustain. Finally we find that bounded rationality always harms social welfare.     

Quality risk in outsourcing: Noncontractible product quality and private quality cost information

This article addresses the concept of quality risk in outsourcing. Recent trends in outsourcing extend a contract manufacturer's (CM's) responsibility to several functional areas, such as research and development and design in addition to manufacturing. This trend enables an original equipment manufacturer (OEM) to focus on sales and pricing of its product. However, increasing CM responsibilities also suggest that the OEM's product quality is mainly determined by its CM. We identify two factors that cause quality risk in this outsourcing relationship. First, the CM and the OEM may not be able to contract on quality; second, the OEM may not know the cost of quality to the CM. We characterize the effects of these two quality risk factors on the firms' profits and on the resulting product quality. We determine how the OEM's pricing strategy affects quality risk. We show, for example, that the effect of noncontractible quality is higher than the effect of private quality cost information when the OEM sets the sales price after observing the product's quality. We also show that committing to a sales price mitigates the adverse effect of quality risk. To obtain these results, we develop and analyze a three‐stage decision model. This model is also used to understand the impact of recent information technologies on profits and product quality. For example, we provide a decision tree that an OEM can use in deciding whether to invest in an enterprise‐wide quality management system that enables accounting of quality‐related activities across the supply chain. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009     

The effects of information on a queue with balking and phase‐type service times

This article generalizes the models in Guo and Zipkin, who focus on exponential service times, to systems with phase‐type service times. Each arriving customer decides whether to stay or balk based on his expected waiting cost, conditional on the information provided. We show how to compute the throughput and customers' average utility in each case. We then obtain some analytical and numerical results to assess the effect of more or less information. We also show that service‐time variability degrades the system's performance. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Capacity allocation with traditional and Internet channels

In this paper we study a capacity allocation problem for two firms, each of which has a local store and an online store. Customers may shift among the stores upon encountering a stockout. One question facing each firm is how to allocate its finite capacity (i.e., inventory) between its local and online stores. One firm's allocation affects the decision of the rival, thereby creating a strategic interaction. We consider two scenarios of a single‐product single‐period model and derive corresponding existence and stability conditions for a Nash equilibrium. We then conduct sensitivity analysis of the equilibrium solution with respect to price and cost parameters. We also prove the existence of a Nash equilibrium for a generalized model in which each firm has multiple local stores and a single online store. Finally, we extend the results to a multi‐period model in which each firm decides its total capacity and allocates this capacity between its local and online stores. A myopic solution is derived and shown to be a Nash equilibrium solution of a corresponding “sequential game.” © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Decomposing inventory routing problems with approximate value functions

We present a time decomposition for inventory routing problems. The methodology is based on valuing inventory with a concave piecewise linear function and then combining solutions to single‐period subproblems using dynamic programming techniques. Computational experiments show that the resulting value function accurately captures the inventory's value, and solving the multiperiod problem as a sequence of single‐period subproblems drastically decreases computational time without sacrificing solution quality. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

The effect of a temporary product distribution channel on supply chain performance

We analyze a supply chain of a manufacturer and two retailers, a permanent retailer who always stocks the manufacturer's product and an intermittent deal‐of‐the day retailer who sells the manufacturer's product online for a short time. We find that without a deal‐of‐the‐day (DOTD) retailer, it is suboptimal for the manufacturer to offer a quantity discount while it is optimal for the retailer to offer periodic price discounts to consumers. With the addition of a DOTD retailer, it is likely to be optimal for the manufacturer to offer a quantity discount. We show that even without market expansion, i.e., no exclusive DOTD retailer consumers, opening the intermittent channel can leave the permanent retailer no worse‐off while increasing the manufacturer's profit. We identify the regular and discounted wholesale prices and the threshold quantity at which the manufacturer should give the discount. We also identify the optimal retail prices. We find that opening the intermittent channel increases the profit of the manufacturer, is likely to decrease the average retail price and to increase sales, and may increase the permanent retailer's profit. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 505–528, 2016     

Dynamic pricing under first order Markovian competition

We evaluate the effect of competition on prices, profits, and consumers' surplus in multiperiod, finite horizon, dynamic pricing settings. In our base model, a single myopic consumer visits two competing retailers, who offer identical goods, in a (first order Markovian) probabilistic fashion—if the posted price exceeds the consumer's valuation for the good, he returns to the same store in the following period with a certain probability. We find that even a small reduction in the return probability from one—which corresponds to the monopoly case at which prices decline linearly—is sufficient to revert the price decline from a linear into an exponential shape. Each retailer's profit is particularly sensitive to changes in his return probability when it is relatively high, and is maximized under complete loyalty behavior (i.e., return probability is one). On the other hand, consumer surplus is maximized under complete switching behavior (i.e., return probability is zero). In the presence of many similar consumers, the insights remain valid. We further focus on the extreme scenario where all consumers follow a complete switching behavior, to derive sharp bounds, and also consider the instance where, in this setting, myopic consumers are replaced with strategic consumers. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

Dynamic pricing in a dual‐market environment

This article is concerned with the determination of pricing strategies for a firm that in each period of a finite horizon receives replenishment quantities of a single product which it sells in two markets, for example, a long‐distance market and an on‐site market. The key difference between the two markets is that the long‐distance market provides for a one period delay in demand fulfillment. In contrast, on‐site orders must be filled immediately as the customer is at the physical on‐site location. We model the demands in consecutive periods as independent random variables and their distributions depend on the item's price in accordance with two general stochastic demand functions: additive or multiplicative. The firm uses a single pool of inventory to fulfill demands from both markets. We investigate properties of the structure of the dynamic pricing strategy that maximizes the total expected discounted profit over the finite time horizon, under fixed or controlled replenishment conditions. Further, we provide conditions under which one market may be the preferred outlet to sale over the other. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 531–549, 2015     

Pricing and capacity allocation strategies: Implications for manufacturers with product sharing

Emerging sharing modes, like the consumer-to-consumer (C2C) sharing of Uber and the business-to-consumer (B2C) sharing of GoFun, have considerably affected the retailing markets of traditional manufacturers, who are motivated to consider product sharing when making pricing and capacity decisions, particularly electric car manufacturers with limited capacity. In this paper, we examine the equilibrium pricing for a capacity-constrained manufacturer under various sharing modes and further analyze the impact of capacity constraint on the manufacturer's sharing mode selection as well as equilibrium outcomes. We find that manufacturers with low-cost products prefer B2C sharing while those with high-cost products prefer C2C sharing except when the sharing price is moderate. However, limited capacity motivates manufacturers to enter into the B2C sharing under a relatively low sharing price, and raise the total usage level by sharing high-cost products. We also show that the equilibrium capacity allocated to the sharing market with low-cost products first increases and then decreases. Finally, we find that sharing low-cost products with a high limited capacity leads to a lower retail price under B2C sharing, which creates a win-win situation for both the manufacturer and consumers. However, sharing high-cost products with a low limited capacity creates a win-lose situation for them.