Dynamic Pricing and Lead‐Time Policies for Make‐to‐Order Systems*

Make‐to‐order firms use different approaches for managing their lead‐times and pricing in the face of changing market conditions. A particular firm's approach may be largely dictated by environmental constraints. For example, it makes little sense to carefully manage lead‐time if its effect on demand is muted, as it can be in situations where leadtime is difficult for the market to gauge or requires investment to estimate. Similarly, it can be impractical to change capacity and price. However, environmental constraints are likely to become less of an issue in the future with the expanding e‐business infrastructure, and this trend raises questions into how to manage effectively the marketing mix of price and lead‐time in a more “friction‐free” setting. We study a simple model of a make‐to‐order firm, and we examine policies for adjusting price and capacity in response to periodic and unpredictable shifts in how the market values price and lead‐time. Our analysis suggests that maintaining a fixed capacity while using lead‐time and/or price to absorb changes in the market will be most attractive when stability in throughput and profit are highly valued, but in volatile markets, this stability comes at a cost of low profits. From a pure profit maximization perspective, it is best to strive for a short and consistent lead‐times by adjusting both capacity and price in response to market changes.     

Coordinating Supply Chains via Advance‐Order Discounts,Minimum Order Quantities,and Delegations

To avoid inventory risks, manufacturers often place rush orders with suppliers only after they receive firm orders from their customers (retailers). Rush orders are costly to both parties because the supplier incurs higher production costs. We consider a situation where the supplier's production cost is reduced if the manufacturer can place some of its order in advance. In addition to the rush order contract with a pre‐established price, we examine whether the supplier should offer advance‐order discounts to encourage the manufacturer to place a portion of its order in advance, even though the manufacturer incurs some inventory risk. While the advance‐order discount contract is Pareto‐improving, our analysis shows that the discount contract cannot coordinate the supply chain. However, if the supplier imposes a pre‐specified minimum order quantity requirement as a qualifier for the manufacturer to receive the advance‐order discount, then such a combined contract can coordinate the supply chain. Furthermore, the combined contract enables the supplier to attain the first‐best solution. We also explore a delegation contract that either party could propose. Under this contract, the manufacturer delegates the ordering and salvaging activities to the supplier in return for a discounted price on all units procured. We find the delegation contract coordinates the supply chain and is Pareto‐improving. We extend our analysis to a setting where the suppliers capacity is limited for advance production but unlimited for rush orders. Our structural results obtained for the one‐supplier‐one‐manufacturer case continue to hold when we have two manufacturers.     

Entry Deterrence of Capacitated Competition Using Price and Non‐Price Strategies

We analyze the role of pricing and branding in an incumbent firm's decision when facing competition from an entrant firm with limited capacity. We do so by studying two price competition models (Stackelberg and Nash), where we consider the incumbent's entry‐deterrence pricing strategy based on a potential entrant's capacity size. In an extension, we also study a branding model, where the incumbent firm, in addition to pricing, can also invest in influencing market preference for its product. With these models, we study conditions under which the incumbent firm may block the entrant (i.e., prevent entry without any market actions), deter the entrant (i.e., stop entry with suitable market actions) or accommodate the entrant (i.e., allow entry and compete), and how the entrant will allocate its limited capacity across its own and the new market, if entry occurs. We also study the timing difference between the two different dynamics of the price competition models and find that the incumbent's first‐mover advantage benefits both the incumbent and the entrant. Interestingly, the entrant firm's profits are not monotonically increasing in its capacity even when it is costless to build capacity. In the branding model, we show that in some cases, the incumbent may even increase its price and successfully deter entry by investing in consumer's preference for its product. Finally, we incorporate demand uncertainty into our model and show that the incumbent benefits from demand uncertainty while the entrant may be worse off depending on the magnitude of demand uncertainty and its capacity.     

The Affiliation Effect in First‐Price Auctions

We study the monotonicity of the equilibrium bid with respect to the number of bidders n in affiliated private‐value models of first‐price sealed‐bid auctions and prove the existence of a large class of such models in which the equilibrium bid function is not increasing in n. We moreover decompose the effect of a change in n on the bid level into a competition effect and an affiliation effect. The latter suggests to the winner of the auction that competition is less intense than she had thought before the auction. Since the affiliation effect can occur in both private‐ and common‐value models, a negative relationship between the bid level and n does not allow one to distinguish between the two models and is also not necessarily (only) due to bidders taking account of the winner's curse.     

Distressed Selling by Farmers: Model,Analysis, and Use in Policy‐Making

Among the various governmental schemes that support agriculture, support prices have been adopted by many developing countries. A support price for an agricultural crop is a guaranteed price at which a governmental entity agrees to purchase that crop from farmers. Despite this surety, a surprising practice of “distressed” selling 1 1 A 1‐minute news clip on distressed selling is available at: https://www.youtube.com/watch?v=U2lr5rBTpaU
has been widely observed in practice: Farmers sell a significant portion of their crops to outside agents at prices much lower than the support price. We build a tractable stochastic dynamic programming model that captures the salient features of the ground realities—limited as well as uncertain procurement capacity, high holding costs for the farmers, and lack of affordable credit—that conspire to induce distressed selling and, consequently, a significant loss of welfare of the farmers. Using real data on procurement under a support‐price program, we establish the accuracy of our model's prediction on the volume of distressed sales. Finally, we show how our model and its solution can serve as a simple and useful tool for policy‐makers to assess the relative impact of the improvements in the main determinants of distressed sales.     

Coordinating Service‐Sensitive Demand and Capacity by Adaptive Decision Making: An Application of Case‐Based Decision Theory*

The subject of this article is the simultaneous choice of product price and manufacturing capacity if demand is stochastic and service‐level sensitive. In this setting, capacity as well as price have an impact on demand because several aspects of service level depend on capacity. For example, delivery time will be reduced if capacity is increased given a constant demand rate. We illustrate the relationship between service level, capacity, and demand reaction by a stylized application problem from the after‐sales services industry. The reaction of customers to variations in service level and price is represented by a kinked price‐demand‐rate function. We first derive the optimal price‐capacity combination for the resulting decision problem under full information. Subsequently, we focus on a decision maker (DM) who lacks complete knowledge of the demand function. Hence the DM is unable to anticipate the service level and consequently cannot identify the optimal solution. However, the DM will acquire additional information during the sales process and use it in subsequent revisions of the price‐capacity decision. Thus, this decision making is adaptive and based on experience. In contrast to the literature, which assumes certain repetitive procedures somewhat ad hoc, we develop an adaptive decision process based on case‐based decision theory (CBDT) for the price‐capacity problem. Finally, we show that a CBDT DM in our setting eventually finds the optimal solution, if the DM sets the price based on absorption costs and adequately adjusts the capacity with respect to the observed demand.     

Up Then Down: Bid‐Price Trends in Revenue Management

In the classic revenue management (RM) problem of selling a fixed quantity of perishable inventories to price‐sensitive non‐strategic consumers over a finite horizon, the optimal pricing decision at any time depends on two important factors: consumer valuation and bid price. The former is determined exogenously by the demand side, while the latter is determined jointly by the inventory level on the supply side and the consumer valuations in the time remaining within the selling horizon. Because of the importance of bid prices in theory and practice of RM, this study aims to enhance the understanding of the intertemporal behavior of bid prices in dynamic RM environments. We provide a probabilistic characterization of the optimal policies from the perspective of bid‐price processes. We show that an optimal bid‐price process has an upward trend over time before the inventory level falls to one and then has a downward trend. This intertemporal up‐then‐down pattern of bid‐price processes is related to two fundamental static properties of the optimal bid prices: (i) At any given time, a lower inventory level yields a higher optimal bid price, which is referred to as the resource scarcity effect; (ii) Given any inventory level, the optimal bid price decreases with time; that is referred to as the resource perishability effect. The demonstrated upward trend implies that the optimal bid‐price process is mainly driven by the resource scarcity effect, while the downward trend implies that the bid‐price process is mainly driven by the resource perishability effect. We also demonstrate how optimal bid price and consumer valuation, as two competing forces, interact over time to drive the optimal‐price process. The results are also extended to the network RM problems.     

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.     

Centralized versus Decentralized Competition for Price and Lead‐Time Sensitive Demand

We study two firms that compete on price and lead‐time decisions in a common market. We explore the impact of decentralizing these decisions, as made by the marketing and production departments, respectively, with either marketing or production as the leader. We compare scenarios in which none, one, or both of the firms are decentralized to see whether decentralization can be the equilibrium strategy. We find that under intense price competition, with intensity characterized by the underlying parameters of market demand, firms may suffer from a decentralized structure, particularly under high flexibility induced by high capacity, where revenue‐based sales incentives motivate sales/marketing to make aggressive price cuts that often erode profit margins. In contrast, under intense lead‐time competition, a decentralized strategy with marketing as the leader can not only result in significantly higher profits, but also be the equilibrium strategy. Moreover, decentralization may no longer lead to lower prices or longer lead‐times if the production department chooses capacity along with lead‐time.      

Training,Production, and Channel Separation in ITC's E‐Choupal Network

In recent years, I.T.C. Limited (hereafter ITC) developed the “e‐Choupals” for the rural areas of India. In this new business model, ITC reaches implicit agreements with some farmers (inside the network) that they can sell the products directly to ITC at the market price in the local market, but allow the farmers, both inside and outside the network, to access valuable information through the e‐Choupals. In this study, we investigate ITC's incentive of offering such opportunities, especially to those farmers outside the network, and analyze the farmers’ strategic quantity decisions. We show that the implicit agreement behaves as a formal contract, regardless of the price elasticity of the local market: Once reaching an agreement with ITC, the farmers always give priority to delivering directly to ITC. The e‐Choupal network leads naturally to the complete separation of selling channels, provided that ITC's capacity constraint is not tight. Surprisingly, in a variety of scenarios, ITC finds it optimal to provide the best available training to the farmers outside the network. We further show that our results are not prone to potential cheating in the mandi system, the possible exploitation via postponed payments, and the stochastic effects on the market‐clearing price.     

The Impact of Capacity Costs on Product Differentiation in Delivery Time,Delivery Reliability,and Price

We develop an analytical framework for studying the role capacity costs play in shaping the optimal differentiation strategy in terms of prices, delivery times, and delivery reliabilities of a profit‐maximizing firm selling two variants (express and regular) of a product in a capacitated environment. We first investigate three special cases. The first is an existing model of price and delivery time differentiation with exogenous reliabilities, which we only review. The second focuses on time‐based (i.e., length and reliability) differentiation with exogenous prices. The third deals with deciding on all features for an express variant when a regular product already exists in the marketplace. We subsequently address the integrative framework of time‐and‐price‐based differentiation for both products in a numerical study. Our results shed light on the role that customer preferences towards delivery times, reliabilities and prices, and the capacity costs (absolute and relative) have on the firm's optimal product positioning policy.     

Sourcing from Multiple Suppliers for Price‐Dependent Demands

We analyze a model that integrates demand shaping via dynamic pricing and risk mitigation via supply diversification. The firm under consideration replenishes a certain product from a set of capacitated suppliers for a price‐dependent demand in each period. Under deterministic capacities, we derive a multilevel base stock list price policy and establish the optimality of cost‐based supplier selection, that is, ordering from a cheaper source before more expensive ones. With general random capacities, however, neither result holds. While it is optimal to price low for a high inventory level, the optimal order quantities are not monotone with respect to the inventory level. In general, a near reorder‐point policy should be followed. Specifically, there is a reorder point for each supplier such that no order is issued to him when the inventory level is above this point and a positive order is placed almost everywhere when the inventory level is below this point. Under this policy, it may be profitable to order exclusively from the most expensive source. We characterize conditions under which a strict reorder‐point policy and a cost‐based supplier‐selection criterion become optimal. Moreover, we quantify the benefit from dynamic pricing, as opposed to static pricing, and the benefit from multiple sourcing, as opposed to single sourcing. We show that these two strategies exhibit a substitutable relationship. Dynamic pricing is less effective under multiple sourcing than under single sourcing, and supplier diversification is less valuable with price adjustments than without. Under limited supply, dynamic pricing yields a robust, long‐term profit improvement. The value of supply diversification, in contrast, mainly comes from added capacities and is most significant in the short run.     

In‐Store Experiments to Determine the Impact of Price on Sales

This paper describes an experimentation methodology to measure how demand varies with price and the results of its application at a toy retailer. The same product is assigned different price‐points in different store panels and the resulting sales are used to estimate a demand curve. We use a variant of the k‐median problem to form store panels that control for differences between stores and produce results that are representative of the entire chain. We use the estimated demand curve to find a price that maximizes profit. Our experiment yielded the unexpected result that demand increases with price in some cases. We present likely reasons for this finding from our discussions with retail managers. Our methodology can be used to analyze the effect of several marketing and promotional levers employed in a retail store besides pricing.     

The Use of Switching Point and Protection Levels to Improve Revenue Performance in Order‐Driven Production Systems

In a multiproduct order‐driven production system, an organization has to decide how to selectively accept orders and allocate capacity to these orders so as to maximize total profit (TP). In this article, we incorporate the novel concept of switching point in developing three capacity‐allocation with switching point heuristics (CASP_a‐c). Our analysis indicates that all three CASP heuristics outperform the first‐come‐first‐served model and Barut and Sridharan's dynamic capacity‐allocation process (DCAP) model. The best model, CASP_b, has an 8% and 6% average TP improvement over DCAP using the split lot and whole lot policies, respectively. In addition, CASP_b performs particularly well under operating conditions of tight capacity and large price differences between product classes. The introduction of a switching point, which has not been found in previous capacity‐allocation heuristics, provides for a better balance between forward and backward allocation of available capacity and plays a significant role in improving TP.     

Efficient Multi‐Attribute Multi‐Unit Auctions for B2B E‐Commerce Logistics

This study is the first proposing allocatively efficient multi‐attribute auctions for the procurement of multiple items. In the B2B e‐commerce logistics problem (ELP), the e‐commerce platform is the shipper generating a large number of online orders between product sellers and buyers, and third‐party logistics (3PL) providers are carriers that can deliver these online orders. This study focuses on the ELP with multiple attributes (ELP‐MA), which is generally the problem of matching the shipper's online orders and 3PL providers given that price and other attributes are jointly evaluated. We develop a one‐sided Vickrey–Clarke–Groves (O‐VCG) auction for the ELP‐MA. The O‐VCG auction leads to incentive compatibility (on the sell side), allocative efficiency, budget balance, and individual rationality. We next introduce the concept of universally unsatisfied set to construct a primal‐dual algorithm, also called the primal‐dual Vickrey (PDV) auction. We prove that the O‐VCG auction can be viewed as a single‐attribute multi‐unit forward Vickrey (SA‐MFV) auction. Both PDV and SA‐MFV auctions realize VCG payments and truthful bidding for general valuations. This result reveals the underlying link not only between single‐attribute and multi‐attribute auctions, but between static and dynamic auctions in a multi‐attribute setting.     

TIME‐BASED PRICING AND LEADTIME POLICIES FOR A BUILD‐TO‐ORDER MANUFACTURER

We studied time‐based policies on pricing and leadtime for a build‐to‐order and direct sales manufacturer. It is assumed that the utility of the product varies among potential customers and decreases over time, and that a potential customer will place an order if his or her utility is higher than the manufacturer's posted price. Once an order is placed, it will be delivered to the customer after a length of time called “leadtime.” Because of the decrease in a customer's utility during leadtime, a customer will cancel the order if the utility falls below the ordering price before the order is received. The manufacturer may choose to offer discounted prices to customers who would otherwise cancel their orders. We discuss two price policies: common discounted price and customized discounted price. In the common discounted price policy, the manufacturer offers a single lower price to the customers; in the customized discounted price policy, the manufacturer offers the customers separately for individual new prices. Our analytical and numerical studies show that the discounted price policies results in higher revenue and that the customized discounted price policy significantly outperforms the common discounted price policy when product utility decreases rapidly. We also study two leadtime policies when production cost decreases over time. The first uses a fixed leadtime, and the second allows the leadtime to vary dynamically over time. We find that the dynamic leadtime policy significantly outperforms the fixed leadtime policy when the product cost decreases rapidly.     

Browse‐and‐Switch: Retail‐Online Competition under Value Uncertainty

Although online shopping is becoming popular, consumers who are unsure about whether to buy a product may find it advantageous to visit a brick‐and‐mortar retail store to first examine the product before purchasing it. But, after browsing at the store, consumers have the option of switching to an e‐tailer to purchase the item at a cheaper price rather than buying at the store. Recent business press refers to this browse‐and‐switch behavior as “showrooming,” and attributes to it the declining profits of brick‐and‐mortar retailers. To study the effect of the browse‐and‐switch option on retail and online pricing strategies and profits, we analyze a stylized economic model that incorporates uncertainty in consumers' valuation of the product, captures the heterogeneity among consumers in their inclination to purchase online, and permits product returns. We consider various equilibrium scenarios for different combinations of consumer shopping behaviors, characterize the parameter ranges for each scenario, and demonstrate that browse‐and‐switch behavior can indeed occur under equilibrium. Our analysis further shows that the option for consumers to browse‐and‐switch intensifies competition, reducing the profits for both firms.     

Competitive Pricing in a Multi‐Product Multi‐Attribute Environment

We address the problem of simultaneous pricing of a line of several products, both complementary products and substitutes, with a number of distinct price differentiation classes for each product (e.g., volume discounts, different distribution channels, and customer segments) in both monopolistic and oligopolistic settings. We provide a generic framework to tackle this problem, consider several families of demand models, and focus on a real‐world case‐study example. We propose an iterative relaxation algorithm, and state sufficient conditions for convergence of the algorithm. Using historical sales and price data from a retailer, we apply our solution algorithm to suggest optimal pricing, and report on numerical results.     

Capacity Allocation among Multiple Suppliers in an Electronic Market

An electronic marketplace typically provides industrial suppliers an alternative option for selling their capacity in addition to the traditional open market. However, suppliers face different sets of costs and risks in open market and in electronic market. Consequently, suppliers participating in an electronic market are likely to offer their capacity at a different price compared with traditional open market. We analyze this problem and derive the price‐capacity function for the supplier. We also derive a basis for allocating buyer's requirements among multiple suppliers so as to minimize his cost. Our model shows that suppliers with large capacities would quote a lower price in the electronic market. It also predicts that the unit bid price increases with bid quantity in the electronic market. Based on the price‐capacity curve, we model a scenario where the buyer announces, a priori, the number of suppliers to be selected for award of a contract that will minimize its costs.     

An Analysis of Scoring and Buyer‐Determined Procurement Auctions

In procurement auctions, the object for sale is a contract, bidders are suppliers, and the bid taker is a buyer. The suppliers bidding for the contract are usually the current supplier (the incumbent) and a group of potential new suppliers (the entrants). As the buyer has an ongoing relationship with the incumbent, he needs to adjust the bids of the entrants to include non‐price attributes, such as the switching costs. The buyer can run a scoring auction, in which suppliers compete on the adjusted bids or scores, or, he can run a buyer‐determined auction, in which suppliers compete on the price, and the buyer adjusts a certain number of the bids with the non‐price attributes after the auction to determine the winner. Unless the incumbent has a significant cost advantage over the entrants, I find that the scoring auction yields a lower average cost for the buyer, if the non‐price attributes are available. If the non‐price attributes are difficult or expensive to obtain, the buyer could run a buyer‐determined auction adjusting only the lowest price bid.