The impact of customer returns on pricing and order decisions

In this paper, we address the simultaneous determination of price and inventory replenishment when customers return product to the firm. We examine cases when the quantity of returned product is a function of both the quantity sold and the price, in single and multi-period problems, with and without uncertainty in demand.     

Dynamic pricing of multiple home delivery options

Online grocers accept delivery bookings and have to deliver groceries to consumers’ residences. Grocery stores operate on very thin margins. Therefore, a critical question that an online grocery store needs to address is the cost of home delivery operations. In this paper, we develop a Markov decision process-based pricing model that recognizes the need to balance utilization of delivery capacity by the grocer and the need to have the goods delivered at the most convenient time for the customer. The model dynamically adjusts delivery prices as customers arrive and make choices. The optimal prices have the following properties. First, the optimal prices are such that the online grocer gains the same expected payoff in the remaining booking horizon, regardless of the delivery option independently chosen by a consumer. Second, with unit order sizes, delivery prices can increase due to dynamic substitution effects as there is less time left in the booking horizon.     

The effect of market segmentation with demand leakage between market segments on a firm’s price and inventory decisions

In this paper, we address the simultaneous determination of price and inventory replenishment in a newsvendor setting when the firm faces demand from two or more market segments in which the firm can set different prices. We allow for demand leakage from higher-priced segments to lower-priced segments and assume that unsatisfied demand can be backlogged. We examine the case where the demands occur concurrently without priority and are met from a single inventory. We consider customer’s buy-down behavior explicitly by modeling demand leakage as a function of segment price differentiation, and characterize the structure of optimal inventory and pricing policies.     

Optimal worst-case pricing for a logit demand model with network effects

We consider optimal pricing problems for a product that experiences network effects. Given a price, the sales quantity of the product arises as an equilibrium, which may not be unique. In contrast to previous studies that take a best-case view when there are multiple equilibrium sales quantities, we maximize the seller’s revenue assuming that the worst-case equilibrium quantity will arise in response to a chosen price. We compare the best- and worst-case solutions, and provide asymptotic analysis of revenues.     

Quantifying supply chain ineffectiveness under uncoordinated pricing decisions

We analyze a multiple-stage supply chain model of a seasonal product with pricing decisions. We develop closed-form expressions for the optimal expected profits of different stages. The results enable us to quantify the loss of supply chain profits if uncoordinated pricing decisions are made by supply chain agents.     

Electronic service matching: Failure of incentive compatibility in Vickrey auctions

We consider pricing schemes for matching customers and providers on double-sided markets for electronic services. While existing second-best solutions are incentive compatible, the associated payment functions are difficult to implement in real-world settings. Based on the Vickrey–Clarke–Groves (VCG) and the $k$-pricing mechanism, we propose two straightforward payment schemes that offer a practical alternative to the second-best solution. Our experiments provide evidence that the VCG payments fail to implement incentive compatibility. This failure is due to the interdependency of the participants’ utilities.     

Planning and approximation models for delivery route based services with price-sensitive demands

Classical vehicle routing problems typically do not consider the impact of delivery price on the demand for delivery services. Existing models seek the minimum sum of tour lengths in order to serve the demands of a given set of customers. This paper proposes approximation models to estimate the impacts of price on delivery services when demand for delivery service is price dependent. Such models can serve as useful tools in the planning phase for delivery service providers and can assist in understanding the economics of delivery services. These models seek to maximize profit from delivery service, where price determines demand for deliveries as well as the total revenue generated by satisfying demand. We consider a variant of the model in which each customer’s delivery volume is price sensitive, as well as the case in which customer delivery volumes are fixed, but the total number of customers who select the delivery service provider is price sensitive. A third model variant allows the delivery service provider to select a subset of delivery requests at the offered price in order to maximize profit.     

The setting of profit targets for target oriented divisions

Setting profit targets and striving to achieve them is fundamental to business survival and success. However, there has been little research on modeling profit-target setting. In this paper, we study analytic target setting under a common business scenario where a firm is in control of multiple divisions. Both the firm and the divisions maximize the profit probability, i.e., the probability of achieving some given profit target. The firm sets a profit target for each division which then acts as a price-setting newsvendor. We first obtain the optimal order quantity, the optimal retail price, and the maximal profit probability of a single division given its assigned target. We then derive the firm’s profit probability and focus on two specific cases to gain more managerial insights. In the first case of fair target setting, we show that when each division’s demand distribution has an increasing failure rate, if a division has a relatively high (low) production cost, its assigned profit target decreases (increases) with regard to its price elasticity. In the second case, if the firm is in control of two identical divisions, each division’s optimal profit target is just half of the firm’s profit target when the price elasticity is two or more, regardless of production cost and demand distribution.     

Optimal static pricing for a service facility with holding costs

We study a service facility modelled as a single-server queueing system with Poisson arrivals and limited or unlimited buffer size. In systems with unlimited buffer size, the service times have general distributions, whereas in finite buffered systems service times are exponentially distributed. Arriving customers enter if there is room in the facility and if they are willing to pay the posted price. The same price is charged to all customers at all times (static pricing). The service provider is charged a holding cost proportional to the time that the customers spend in the system. We demonstrate that there is a unique optimal price that maximizes the long-run average profit per unit time. We also investigate how optimal prices vary as system parameters change. Finally, we consider buffer size as an additional decision variable and show that there is an optimal buffer size level that maximizes profit.     

A competitive dynamic pricing model when demand is interdependent over time

In this study, we contribute to the dynamic pricing literature by developing a finite horizon model for two firms offering substitutable and nonperishable products with different quality levels. Customers can purchase and store the products, even if they do not need them at the time, in order to use them in future. The stockpile of the products generated by customers affects the demand in future periods. Therefore, the demand for each product not only is a function of prices and quality levels, but also of the products’ stockpile levels. In addition, the stockpile levels change the customers’ consumption behavior; more product in a stockpile leads to more consumption. Therefore, we address not only the price and demand relationship but also the stockpiling and consumption relationship in a competitive environment.     

Designing a quantity discount scheme for a newsvendor-type product with numerous heterogeneous retailers

This paper presents a practical approach for designing a quantity-discount (“qd”) scheme for a manufacturer who supplies a newsvendor-type product to a large number of heterogeneous retailers. The main components of our approach are: (i) an information structure for handling a large number of heterogeneous retailers with changing identities; and (ii) expected-profit expressions for any given qd scheme. We show that these expected-profit expressions can be easily optimized to produce attractive qd schemes; also, these schemes are shown to be quite robust against errors in parameter estimation.     

Lease expiration management for a single lease term in the apartment industry

Lease expiration management (LEM) in the apartment industry aims to control the number of lease expirations and thus achieve maximal revenue growth. We examine rental rate strategies in the context of LEM for apartment buildings that offer a single lease term and face demand uncertainty. We show that the building may incur a significant revenue loss if it fails to account for LEM in the determination of the rental rate. We also show that the use of LEM is a compromise approach between a limited optimization, where no future demand information is available, and a global optimization, where complete future demand information is available. We show that the use of LEM can enhance the apartment building’s revenue by as much as 8% when the desired number of expirations and associated costs are appropriately estimated. Numerical examples are included to illustrate the major results derived from our models and the impact on the apartment’s revenue of sensitivity to the desired number of expirations and associated costs.     

Multi-tier binary solution method for multi-product newsvendor problem with multiple constraints

This paper considers a multi-product newsvendor problem with multiple constraints. Multiple constraints in the problem make it more challenging to solve. Previous research has attempted to solve the problem by considering two-constraint case or/and using approximation techniques or active sets methods. The solution methods in literature for solving multi-constraint problem are limited or cumbersome. In this paper, by analyzing structural properties of the multi-constraint multi-product newsvendor problem, we develop a multi-tier binary solution method for yielding the optimal solution to the problem. The proposed method is applicable to the problem with any continuous demand distribution and more than two constraints, and its computational complexity is polynomial in the number of products. Numerical results are presented for showing the effectiveness of our method.     

A note on “Seller’s optimal credit period and cycle time in a supply chain for deteriorating items with maximum lifetime”

In 2014, Wang et al. (2014) extended the model of Lou and Wang (2012) to incorporate the credit period dependent demand and default risk for deteriorating items with maximum lifetime. However, the rates of demand, default risk and deterioration in the model of Wang et al. (2014) are assumed to be specific functions of credit period which limits the contributions. In this note, we first generalize the theoretical results of Wang et al. (2014) under some certain conditions. Furthermore, we also present some structural results instead of a numerical analysis on variation of optimal replenishment and trade credit strategies with respect to key parameters.     

Seller’s optimal credit period and cycle time in a supply chain for deteriorating items with maximum lifetime

Due to evaporation, obsolescence, spoilage, etc., some products (e.g., fruits, vegetables, pharmaceuticals, volatile liquids, and others) not only deteriorate continuously but also have their expiration dates. To attract new buyers and increase sales, a seller frequently offers its buyers a trade credit period to settle the purchase amount. There is no interest charge to a buyer if the purchasing amount is paid within the credit period, and vice versa. On the other hand, granting a credit period from a seller to its buyers increases default risk. In this paper, we propose an economic order quantity model for a seller by incorporating the following relevant facts: (1) deteriorating products not only deteriorate continuously but also have their maximum lifetime, and (2) credit period increases not only demand but also default risk. We then characterize the seller’s optimal credit period and cycle time. Furthermore, we discuss a special case for non-deteriorating items. Finally, we run several numerical examples to illustrate the problem and provide some managerial insights.     

Manufacturer’s return policy in a two-stage supply chain with two risk-averse retailers and random demand

This paper studies the manufacturer’s return policy and the retailers’ decisions in a supply chain consisting of one manufacturer and two risk-averse retailers under a single-period setting with price-sensitive random demand. We characterize each retailer’s risk-embedded objective via conditional value-at-risk, and construct manufacturer-Stackelberg games with and without horizontal price competition between the retailers. We explore, through numerical studies, the effects of the retailers’ aversion to risk and other parameters on the manufacturer’s return policy and profit and the retailers’ decisions. We further investigate the effect of distribution asymmetry by comparing the results with normal and lognormal demand.     

A continuous-time dynamic pricing model knowing the competitor’s pricing strategy

In this paper we consider a dynamic pricing model for a firm knowing that a competitor adopts a static pricing strategy. We establish a continuous time model to analyze the effect of dynamic pricing on the improvement in expected revenue in the duopoly. We assume that customers arrive to purchase tickets in accordance with a geometric Brownian motion. We derive an explicit closed-form expression for an optimal pricing policy to maximize the expected revenue. It is shown that when the competitor adopts a static pricing policy, dynamic pricing is not always effective in terms of maximizing expected revenue compared to a fixed pricing strategy. Moreover, we show that the size of the reduction in the expected revenue depends on the competitor’s pricing strategy. Numerical results are presented to illustrate the dynamic pricing policy.     

On the application of a transportation model for revenue optimization in waste management: a case study

This paper describes an interactive decision support system called Opti-Link which has been developed for a company operating in the area of waste and raw material management. Built around a specific transportation problem, the system is used to maximize the revenue generated by selling waste paper to paper mills. Furthermore, the dual variables of the linear program allow the planner to identify upper bounds for setting bid prices to buy waste paper from waste collection companies. First operational results indicate a significant increase in profit while at the same time the duration of the planning process could be cut by more than half.     

An optimal production-inventory model for deteriorating items with multiple-market demand

The global markets of today offer more selling opportunities to the deteriorating items’ manufacturers, but also pose new challenges in production and inventory planning. From a production management standpoint, opportunities to exploit the difference in the timing of the selling season between geographically dispersed markets for deteriorating items are important to improving a firm’s profitability. In this paper, we examined the above issue with an insightful production-inventory model of a deteriorating items manufacturer selling goods to multiple-markets with different selling seasons. We also provided a solution procedure to find the optimal replenishment schedule for raw materials and the optimal production plan for finished products. A numerical example was then used to illustrate the model and the solution procedure. Finally, sensitivity analysis of the optimal solution with respect to major parameters was carried out.     

Retailer’s optimal replenishment decisions with credit-linked demand under permissible delay in payments

Usually it is assumed that the supplier would offer a fixed credit period to the retailer but the retailer in turn would not offer any credit period to its customers, which is unrealistic, because in real practice retailer might offer a credit period to its customers in order to stimulate his own demand. Moreover, it is observed that credit period offered by the retailer to its customers has a positive impact on demand of an item but the impact of credit period on demand has received a very little attention by the researchers. To incorporate this phenomenon, we assume that demand is linked to credit period offered by the retailer to the customers.