Profitability of Service‐Level‐Based Price Differentiation with Inventory Rationing

In this paper, we study the profitability of service‐level‐based price differentiation (SLBPD) in an inventory‐rationing context. SLBPD implies that a company offers several combinations of prices and guaranteed service levels, from which customers self‐select; different customers choose different offerings because they incur different shortage costs if an order is not fulfilled immediately. We develop an analytical model for SLBPD and explore if and when such a service differentiation strategy yields higher profits than a single undifferentiated offering. The results of our analyses suggest that SLBPD is profitable only if a company faces pricing restrictions, e.g., because of competitive pressure or regulatory restrictions. We develop necessary and sufficient conditions under which a specific and relevant form of SLBPD (called “service‐level‐based upselling”) is profitable, and provide an algorithm to compute the optimal parameters of such a policy. Based on this algorithm we carry out numerical analyses that allow us to characterize the profit increment of service‐level‐based upselling. We derive managerial insights into the attractiveness of SLBPD and explain how our basic analytical framework can be extended to account for more complex practical features.     

Strategic Capacity Management When Customers Have Boundedly Rational Expectations

In retailing industries, such as apparel, sporting goods, customer electronics, and appliances, many firms deploy sophisticated modeling and optimization software to conduct dynamic pricing in response to uncertain and fluctuating market conditions. However, the possibility of markdown pricing creates an incentive for customers to strategize over the timing of their purchases. How should a retailing firm optimally account for customer behavior when making its pricing and stocking/capacity decisions? For example, is it optimal for a firm to create rationing risk by deliberately under stocking products? In this study, we develop a stylized modeling framework to answer these questions. In our model, customers strategize over the timing of their purchases. However, customers have boundedly rational expectations in the sense of anecdotal reasoning about the firm's fill rate, i.e., they have to rely on anecdotes, past experiences, or word‐of‐mouth to infer the firm's fill rate. In our modeling framework, we distinguish two settings: (i) capacity commitment, where the firm commits to its capacity level in the long run, or (ii) the firm dynamically changes it in each season. For both settings, within the simplest form of anecdotal reasoning, we prove that strategic capacity rationing is not optimal independent of customer risk preferences. Then, using a general form of anecdotal reasoning, we provide sufficient conditions for capacity rationing to be optimal for both settings, respectively. We show that the result of strategic capacity rationing being suboptimal is fairly robust to different valuation distributions and utility functions, heterogeneous sample size, and price optimization.     

Pareto‐Improving Contracts for Express Package Delivery Services

We address the problem of an express package delivery company in structuring a long‐term customer contract whose terms may include prices that differ by day‐of‐week and by speed‐of‐service. The company traditionally offered speed‐of‐service pricing to its customers, but without day‐of‐week differentiation, resulting in customer demands with considerable day‐of‐week seasonality. The package delivery company hoped that using day‐of‐week and speed‐of‐service price differentiation for contract customers would induce these customers to adjust their demands to become counter‐cyclical to the non‐contract demand. Although this usually cannot be achieved by pricing alone, we devise an approach that utilizes day‐of‐week and speed‐of‐service pricing as an element of a Pareto‐improving contract. The contract provides the lowest‐cost arrangement for the package delivery company while ensuring that the customer is at least as well off as he would have been under the existing pricing structure. The contract pricing smoothes the package delivery company's demand and reduces peak requirements for transport capacity. The latter helps to decrease capital costs, which may allow a further price reduction for the customer. We formulate the pricing problem as a biconvex optimization model, and present a methodology for designing the contract and numerical examples that illustrate the achievable savings.     

Transient and steady state results for two parallel queues

This paper lists numerical results for a system with two parallel queues in which arriving customers always join the shorter queue. These results enable us to discuss how fast the expected queue length converges toward its equilibrium, provided the arrivals are below the capacity of the service facility. It also shows how fast the expected queue length increases in case the traffic flow is at or above the capacity of the service facility. Finally, it is shown that the system under consideration behaves very similar to a two-server queue.     

Optimal Dynamic Pricing of Perishable Items by a Monopolist Facing Strategic Consumers

We introduce a dynamic pricing model for a monopolistic company selling a perishable product to a finite population of strategic consumers (customers who are aware that pricing is dynamic and may time their purchases strategically). This problem is modeled as a stochastic dynamic game in which the company's objective is to maximize total expected revenues, and each customer maximizes the expected present value of utility. We prove the existence of a unique subgame‐perfect equilibrium pricing policy, provide equilibrium optimality conditions for both customer and seller, and prove monotonicity results for special cases. We demonstrate through numerical examples that a company that ignores strategic consumer behavior may receive much lower total revenues than one that uses the strategic equilibrium pricing policy. We also show that, when the initial capacity is a decision variable, it can be used together with the appropriate pricing policy to effectively reduce the impact of strategic consumer behavior. The proposed model is computationally tractable for problems of realistic size.     

Efficient frontiers for electricity procurement by an LDC with multiple purchase options

In meeting its retail sales obligations, management of a local distribution company (LDC) must determine the extent to which it should rely on spot markets, forward contracts, and the increasingly popular long-term tolling agreements under which it pays a fee to reserve generator capacity. We address these issues by solving a mathematical programming model to derive the efficient frontier that summarizes the optimal tradeoffs available to the LDC between procurement risk and expected cost. To illustrate the approach, we estimate the expected procurement costs and associated variances that proxy for risk through a spot-price regression for the spot-purchase alternative and a variable-cost regression for the tolling-agreement alternative. The estimated regressions yield the estimates required to determine the efficient frontier. We develop several such frontiers under alternative assumptions as to the forward-contract price and the tolling agreement's capacity payment, and discuss the implications of our results for LDC management.     

Impeding the Juggernaut of Innovation Diffusion: A Production‐Constrained Model

Models of innovation diffusion typically depict an inexorable momentum once the process begins to roll. Limited production capacity, however, can place a cap on this process, leading to waiting lines of potential customers, thus diminishing overall service quality and the speed of diffusion. Identifying the minimum production capacity needed for unimpeded and unimpaired diffusion can ensure that there are no customers waiting to adopt the product. We propose a production‐capacity‐constrained diffusion model that considers an exogenous industry production capacity and accounts for word‐of‐mouth effects from adopters as well as waiting customers. We derive analytical expressions for minimum capacity needed under multiple production scenarios. We present a dual‐objective non‐linear least squares procedure with large‐scale grid search for estimating the parameters. We apply our model to several new product innovation data sets, ranging from vacuum cleaners to sports utility vehicles in the United States to iPhones globally. Our estimates show that product shortages exist, ranging from mild to severe, in all of these product markets. We are able to corroborate some of our findings with independent external sources of evidence. We find that information on industry capacity can be recovered with as few as 5 years of sales data. Our model has practical implications for policy makers and can help equity analysts triangulate industry capacity better, particularly when such information is closely held.     

Rationing Capacity Between Two Product Classes*

In this paper, we study the capacity allocation problem faced by make-to-order manufacturing firms encountering expected total demand in excess of available capacity. Specifically, we focus on firms' manufacturing short-life-cycle or seasonal products such as high fashion apparel. Using a decision-theory-based approach, we develop a capacity allocation policy that allows such firms to discriminate between two classes of products (one yielding a higher profit contribution per unit of capacity allocated to it than the other), resulting in selective rejection of orders for the class with the lower unit contribution. The effectiveness of capacity rationing is investigated under a wide array of conditions characterized by variations in factors such as the ratio of unit profit contributions of the two product classes, the ratio of total available capacity to expected total demand, the ratio of expected demands between the two classes, and the variability in demand for each product class. The results indicate that capacity rationing is very effective in increasing the total profit, and could therefore serve as a valuable decision tool for managers in such firms.     

The limits of price leadership: needs-based positioning strategy and the long-term competitiveness of Europe’s low fare airlines

This article argues that a strategy of low operating costs and cheap prices is not sufficient in and of itself to establish long term competitive advantage for a growing company. Companies also need to leverage their distinctive corporate capabilities and unique experiences. In the case of service sector companies such as airlines, capabilities derive from the relationship which exists between the company, its employees, and its customers, as well as the reputation which is gradually established on the basis of reliability and quality of service. Unique experiences arise from the corporate culture and route network which an airline builds over time.     

Distribution with Quality of Service Considerations: The Capacitated Routing Problem with Profits and Service Level Requirements

Inspired by a problem arising in cash logistics, we propose the Capacitated Routing Problem with Profits and Service Level Requirements (CRPPSLR). The CRPPSLR extends the class of Routing Problems with Profits by considering customers requesting deliveries to their (possibly multiple) service points. Moreover, each customer imposes a service level requirement specifying a minimum-acceptable bound on the fraction of its service points being delivered. A customer-specific financial penalty is incurred by the logistics service provider when this requirement is not met. The CRPPSLR consists in finding vehicle routes maximizing the difference between the collected revenues and the incurred transportation and penalty costs in such a way that vehicle capacity and route duration constraints are met. A fleet of homogeneous vehicles is available for serving the customers. We design a branch-and-cut algorithm and evaluate the usefulness of valid inequalities that have been effectively used for the capacitated vehicle routing problem and, more recently, for other routing problems with profits. A real-life case study taken from the cash supply chain in the Netherlands highlights the relevance of the problem under consideration. Computational results illustrate the performance of the proposed solution approach under different input parameter settings for the synthetic instances. For instances of real-life problems, we distinguish between coin and banknote distribution, as vehicle capacities only matter when considering the former. Finally, we report on the effectiveness of the valid inequalities in closing the optimality gap at the root node for both the synthetic and the real-life instances and conclude with a sensitivity analysis on the most significant input parameters of our model.     

Maximizing the rate of return on the capital employed in shipping capacity renewal

Decisions regarding investments in capacity expansion/renewal require taking into account both the operating fitness and the financial performance of the investment. While several operating requirements have been considered in the operations research literature, the corresponding financial aspects have not received as much attention. We introduce a model for the renewal of shipping capacity which maximizes the Average Internal Rate of Return (AIRR). Maximizing the AIRR sets stricter return requirements on money expenditures than classic profit maximization models and may describe more closely shipping investors׳ preferences. The resulting nonlinear model is linearized to ease computation. Based on data from a shipping company we compare a profit maximization model with an AIRR maximization model. Results show that while maximizing profits results in aggressive expansions of the fleet, maximizing the return provides more balanced renewal strategies which may be preferable to most shipping investors.     

Optimal Workforce Mix in Service Systems with Two Types of Customers

We consider a service system with two types of customers. In such an environment, the servers can either be specialists (or dedicated) who serve a specific customer type, or generalists (or flexible) who serve either type of customers. Cross‐trained workers are more flexible and help reduce system delay, but also contribute to increased service costs and reduced service efficiency. Our objective is to provide insights into the choice of an optimal workforce mix of flexible and dedicated servers. We assume Poisson arrivals and exponential service times, and use matrix‐analytic methods to investigate the impact of various system parameters such as the number of servers, server utilization, and server efficiency on the choice of server mix. We develop guidelines for managers that would help them to decide whether they should be either at one of the extremes, i.e., total flexibility or total specialization, or some combination. If it is the latter, we offer an analytical tool to optimize the server mix.     

Managing Clearance Sales in the Presence of Strategic Customers

We study the effect of strategic customer behavior on pricing and rationing decisions of a firm selling a single product over two periods. The seller may limit the availability of the product (that is, ration) in the second (clearance) period. Some customers are strategic and respond to the firm's decisions by timing their purchases. When capacity is nonconstraining and the seller has pricing flexibility, we show that rationing in the clearance period cannot improve revenue. However, when prices are fixed in advance, rationing can improve revenue. In the latter case, we conduct a detailed analysis for linear and exponential demand curves and derive explicit expressions for optimal rationing levels. We find that the policy of doing the better of not restricting availability at the clearance price or not offering the product at the clearance price is typically near optimal. Our analysis also suggests that rationing—although sometimes offering considerable benefit over allowing unrestricted availability in the clearance period—may allow the seller to obtain only a small fraction of the optimal revenue when the prices are chosen optimally without rationing. We extend the analysis to cases where the capacity is constraining and obtain similar results.     

Pricing and Capacity Rationing with Customer Disappointment Aversion

Customers are averse to disappointment that arises when economic outcomes fall short of expectations. In this study, we study a two‐period model in which the firm may create rationing in either period. In the anticipation of possible disappointment due to stock‐outs, strategic customers decide when to purchase and the firm determines the prices and rationing levels in each period. We explore the impact of disappointment aversion on customers' strategic purchasing behavior and the firm's pricing and rationing decisions. Without disappointment aversion, it is optimal for the firm to adopt a uniform pricing policy without rationing. However, when strategic customers are averse to disappointment, a firm may be able to increase profits with an appropriate level of rationing. We analyze both the mark‐up and mark‐down policies. We show that, in a mark‐down scenario, the firm always benefits from disappointment aversion behavior by using an appropriate level of rationing in a low‐price period. However, in a mark‐up scenario, whether it is beneficial for the firm to induce disappointment aversion behavior depends on how customers frame payoffs in different periods when forming utilities. Particularly, when customers compartmentalize payoffs in different periods to form utilities, the firm should not induce disappointment aversion behavior.     

INVENTORY RATIONING AND SHIPMENT FLEXIBILITY ALTERNATIVES FOR DIRECT MARKET FIRMS

This paper investigates inventory‐rationing policies of interest to firms operating in a direct market channel. We model a single product with two demand classes, where one class requests a lower order fulfillment lead time but pays a higher price. Demand for each class follows a Poisson process. Inventory is fed by a production system with exponentially distributed build times. We study rationing policies in which the firm either blocks or backlogs orders for the lower priority customers when inventory drops below a certain level. We compare the performance of these rationing policies with a pure first‐come, first‐serve policy under various scenarios for customer response to delay: lost sales, backlog, and a combination of lost sales and backlog.     

Electricity Time‐of‐Use Tariff with Stochastic Demand

In this article, we study the electricity time‐of‐use (TOU) tariff for an electricity company with stochastic demand. The electricity company offers the flat rate (FR) and TOU tariffs to customers. Under the FR tariff, the customer pays a flat price for electricity consumption in both the peak and non‐peak periods. Under the TOU tariff, the customer pays a high price for electricity consumption in the peak period and a low price for electricity consumption in the non‐peak period. The electricity company uses two technologies, namely the base‐load and peak‐load technologies, to generate electricity. We derive the optimal capacity investment and pricing decisions for the electricity company. Furthermore, we use real data from a case study to validate the results and derive insights for implementing the TOU tariff. We show that in almost all the cases, the electricity company needs less capacity for both technologies under the TOU tariff than under the FR tariff, even though the expected demand in the non‐peak period increases. In addition, except for some extreme cases, there is essentially no signicant reduction in the total demand of the two periods, although the TOU tariff can reduce the demand in the peak period. Under the price‐cap regulation, the customer may pay a lower price on average under the TOU tariff than under the FR tariff. We conduct an extensive numerical study to assess the impacts of the model parameters on the optimal solutions and the robustness of the analytical results, and generate managerial implications of the research findings.     

Reducing Packaging Waste and Cost via Consumer Price Discounts

Low‐waste packaging may imply an inconvenience to consumers and cause firms to offer a compensating price discount. For example, Starbucks’ “Take the Mug Pledge” campaign provides a 10‐cent discount for customers who purchase coffee without a standard cup (i.e., customers provide their own cup). Understanding how such a discount drives demand and profit is the focus of this article. We consider a monopolist that can offer a reduced‐packaging option for its product at a variable cost savings. That option implies a transactional “inconvenience” cost for consumers. While that transactional cost is generally positive, our model also permits some consumers to associate convenience with reduced packaging. We derive the optimal price and discount that maximize profits. We show the optimal discount is bounded by the magnitude of the variable cost savings associated with the packaging reduction. We explore when the optimal discount is negative (a price premium), which requires a specific proportion of consumers to associate convenience with reduced packaging. We also derive conditions under which the firm should price to eliminate demand for the standard product, rather than segment the market, to leverage the variable cost savings of reduced packaging. When the variable cost savings are low (e.g., as is true for Starbucks), we show the profit curve for the segmenting policy is relatively flat for a discount up to several multiples of the cost differential. Finally, we demonstrate the potential for the reduced packaging option, with optimal discounting, to simultaneously increase profit and consumer surplus while reducing waste.     

Vendor managed inventory in tramp shipping

This paper introduces a new problem to the OR community that combines traditional tramp shipping with a vendor managed inventory (VMI) service. Such a service may replace the more traditional contract of affreightment (COA) which for decades has been the standard agreement between a tramp shipping company and a charterer. We present a mathematical formulation describing the routing and scheduling problem faced by a tramp shipping company that offers a VMI service to its customers. The problem is formulated as an arc-flow model, and is then reformulated as a path-flow model which is solved using a hybrid approach that combines branch-and-price with a priori path-generation. To solve larger, and more realistic, instances we present a heuristic path-generation algorithm. Computational experiments show that the heuristic approach is much faster than the exact method, with insignificant reductions in solution quality. Further, we investigate the economic impact of introducing a VMI service, by comparing the results obtained with the new model with results obtained by solving the traditional routing and scheduling problem faced by tramp shipping companies using COA. The computational results show that it is possible to substantially increase supply chain profit and efficiency by replacing the traditional COAs with VMI services.     

Distribution planning of bulk lubricants at BP Turkey

We address the distribution planning problem of bulk lubricants at BP Turkey. The problem involves the distribution of different lube products from a single production plant to industrial customers using a heterogeneous fleet. The fleet consists of tank trucks where each tank can only be assigned to a single lube. The objective is to minimize total transportation related costs. The problem basically consists of assigning customer orders to the tanks of the trucks and determining the routes of the tank trucks simultaneously. We model this problem as a 0–1 mixed integer linear program. Since the model is intractable for real-life industrial environment we propose two heuristic approaches and investigate their performances. The first approach is a linear programming relaxation-based algorithm while the second is a rolling-horizon threshold heuristic. We propose two variants of the latter heuristic: the first uses a distance priority whereas the second has a due date priority. Our numerical analysis using company data shows that both variants of the rolling horizon threshold heuristic are able to provide good results fast.     

A flexible model for the pricing of perishable assets

We present a flexible and versatile model which addresses the problem of assigning optimal prices to assets whose value becomes zero after a fixed expiry date. (Such assets include the important example of seats on airline flights.) Our model is broad in scope, in particular encompassing the ability to deal with arrivals of customers in groups. It is highly adaptable and can be adjusted to deal with a very extensive set of circumstances.Our approach to the problem is based on elementary and intuitively appealing ideas. We model the arrival of customers (or groups of customers) according to an inhomogeneous Poisson process. We incorporate into the model time dependent price sensitivity (which may also be described as “time dependent elasticity of demand”). In this setting the solution to the asset pricing problem is achieved by setting up coupled systems of differential equations which are readily amenable to numerical solution via (for instance) a vectorised Runge-Kutta procedure. An attractive feature of our approach is that it unifies the treatment of discrete and continuous prices for the assets.