Michael S. Pangburn

Stack Them High, Let 'em Fly: Lot-Sizing Policies When Inventories Stimulate Demand

In some retail contexts, stocking large quantities of inventory may not only improve service levels, but can also stimulate demand. For products having demand rates that increase with inventory levels, we analyze the effect of stocking decisions on firm profitability to develop managerial insights regarding the structure of the optimal inventory policy, and to understand how this policy differs from traditional approaches. When inventories stimulate demand, iteratively applying the standard economic order quantity (EOQ) model--by setting the demand rate parameter equal to the observed average demand rate in prior cycles--yields an equilibrium order quantity that is robust to demand parameter misestimation, but is suboptimal. The profit-maximizing policy orders larger quantities, and can replenish inventory even before on-hand stock fully depletes. Using an extension of a standard inventory-dependent demand model from the literature, we first provide a convenient characterization of products that require early replenishment. We demonstrate that the optimal cycle time is largely governed by the conventional trade-off between ordering and holding costs, whereas the reorder point relates to a promotions-oriented cost-benefit perspective. We show that the optimal policy yields significantly higher profits than cost-based inventory policies, underscoring the importance of profit-driven inventory management.

Capacity and price setting for dispersed, time-sensitive customer segments

Abstract We consider joint pricing and capacity decisions for a facility serving heterogeneous consumers that span a continuous range of locations, and are sensitive to time delays. Within this context, we analyze two contrasting service strategies: segmentation and pooling. Consumer segments differ with respect to their reservation prices and time sensitivities, and are dispersed over a single distance dimension. The firm serves these consumers using a process that we initially model as an M/M/1 queuing system. We analyze profit-maximizing price and capacity levels for a monopolist, and contrast the optimal segmentation and pooling policies. We find that when consumers are time sensitive, and can expect queuing delays at the firm’s facility (due to random arrival and service times), then scale economies from pooling can outweigh segmentation benefits. Yet, segmentation outperforms pooling when consumer segments differ substantively, in which case the firm can use capacity as a lever to price discriminate between the segments. Moreover, by contrasting a dedicated-services strategy, which directly targets specific segments and serves them separately, with the alternative of allowing consumers to self-select, we find that self-selection has a moderate negative influence on profits. We also examine the profit impact of employing alternative queuing systems, and find that a hybrid strategy based on a prioritized queuing discipline, that combines elements of segmentation (by offering different waiting times) and pooling (by sharing capacity across consumer segments), can outperform both the pure segmentation and pooling strategies.

Capacity decisions for high-tech products with obsolescence

Modern high-tech products experience rapid obsolescence. Capacity investments must be recouped during the brief product lifecycle, during which prices fall continuously. We employ a multiplicative demand model that incorporates price declines due to both market heterogeneity and product obsolescence, and study a monopolistic firms capacity decision. We investigate profit concavity, and characterize the structure of the optimal capacity solution. Moreover, for products with negligible variable costs, we identify two distinct strategies for capacity choice demarcated by an obsolescence rate threshold that relates both to market factors and capacity costs. Finally, we empirically test the demand model by analyzing shipping and pricing data from the PC microprocessor market.

Optimizing Delivery Fees for a Network of Distributors

The third-party logistics industry has grown rapidly in recent years, accounting for

Take back costs and product durability

46 billion of the total

Reducing Packaging Waste and Cost via Consumer Price Discounts

921 billion in logistics spending in the United States during 1999. This figure is expected to grow by 15 to 20% annually as manufacturing firms increasingly partner with third-party logistics providers to cost effectively distribute their products, while meeting increasingly stringent service expectations of customers. These logistics partnerships have introduced a new set of decision requirements to negotiate compensation for distribution services. Based on a collaborative project with a leading building products manufacturer, this paper describes the development and implementation of a novel linear programming model to decide the delivery fees paid to distributors. The model applies to manufacturer-distributor partnerships where distributors are compensated using fee values that depend on delivery weights and distances. It ensures that the expected compensation, considering stochastic demands, is adequate to cover the aggregate distribution costs for each distributor, and permits imposing various consistency conditions to ensure that fee values are credible. The model proved effective in helping the manufacturer develop a new fee table that generated considerable economic savings and provided more equitable compensation to distributors.

Inventory disclosure in online retailing

Extended Producer Responsibility (EPR) initiatives may require a manufacturer to be responsible in the future for taking back the products it produces today. A ramification of EPR is that take back costs may influence firms’ decisions regarding product durability. In the absence of EPR, prior literature has shown that a firm may intentionally lower durability, yielding planned obsolescence. We use a two period model to examine the impact of take back costs on a manufacturer’s product durability and pricing decisions, under both selling and leasing scenarios. We show that compared to selling, leasing provides a greater incentive to raise durability, thus extending a classic insight to a setting with product take backs. Interestingly, we also show that it is possible for the optimal product durability to decrease if the stipulated take back fraction increases. In such situations, were the take back fraction tied to durability rather than a fixed fraction, we demonstrate durability can increase. We explore the impact of take backs on profits and surplus by alternatively considering products for which take back costs are either increasing or decreasing functions of durability. When increasing durability implies higher take back costs, our results demonstrate that leasing can increase durability, profits, and surplus significantly compared to selling. In contrast, when increasing durability implies a lower take back cost, there is a built-in incentive for the firm to increase durability, which can make selling more efficient (i.e., surplus enhancing) than leasing.

Coordinating the Distribution Chain: New Models for New Challenges

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.

Mass Customization and Guardrails: 'You Can't Be All Things to All People'

Unlike in a traditional store environment where inventory is directly visible to customers, Internet retailers can selectively choose how to divulge inventory level information to customers. For example, when viewing a particular item page, online shoppers may either see merely “in stock” or a specific inventory level. By choosing the appropriate inventory-level cue to display, a retailer can selectively signal stock-out risk to customers. In this paper, we analyze the optimal structure of an online retailers inventory disclosure and pricing policy, in a two-period setting—a regular selling period followed by a clearance period. Consumers may potentially face uncertainty regarding the firms inventory level, as well as the overall market demand. We show that there exists an inventory level threshold below which a retailer should optimally disclose inventory, and above which masking (i.e., showing only “in stock”) is optimal.Even though the optimal price decreases in the stock level, we show that equilibrium full-price sales may increase or decrease, highlighting the non-intuitive consumer behavior implications of selective inventory disclosure. The optimal “threshold-type” inventory disclosure that we derive reflects the practice of several prominent online retailers selling fashion products, and is new to the literature as prior models of inventory sharing invoked assumptions that led to either consistent disclosure or consistent masking to be optimal. We also extend the model to consider a stochastic market size, and thus highlight that the threshold policy structure continues to hold with demand uncertainty.

An Empirical Analysis of How Inventory Disclosure Affects Online Retail Sales

Recent business and technological trends have transformed the structure and performance requirements for distribution channels in many industries. Higher service level expectations of retail customers, distribution outsourcing by manufacturers, and the proliferation of advanced information technologies drive these transformations, presenting new problems in supply chain management. Motivated by a project with a leading building-products manufacturer, this paper addresses some of these new issues. Over the past two decades, this manufacturer witnessed the migration of building-products sales from independent specialty retailers to largeretail chains, prompting it to create a new network of independent distributors to meet the service expectations of these ‘big-box’ retailers. This paper addresses three important challenges in managing the new distribution network. We first develop a fee-setting model to decide the manufacturer’s compensation scheme for the services provided by its in dependent distributors. Next, we address a tactical distribution planning problem, incorporating resource acquisition and deployment decisions, for scheduled deliveries when demand is highly variable. Lastly, we investigate possible mechanisms for limiting retail store-order variability, and analyze the system-wide cost benefits resulting from variability reduction. In addition to identifying new modeling opportunities and discussing their implications for the building-products manufacturer, this paper highlights new research opportunities resulting from the evolving dynamics of supply chain management.