Decisions, Operations, and Technology Management

We consider the Retail Planning Problem in which the retailer chooses suppliers, and determines the production, distribution and inventory planning for products with uncertain demand in order to minimize total expected costs. This problem is often faced by large retail chains that carry private label products. We formulate this problem as a convex mixed integer program and show that it is strongly NP-hard. We determine a lower bound by applying a Lagrangean relaxation and show that this bound out- performs the standard convex programming relaxation, while being computationally efficient. We also establish a worst-case error bound for the Lagrangean relaxation. We then develop heuristics to generate feasible solutions. Our computational results indicate that our convex programming heuristic yields feasible solutions that are close to optimal with an average suboptimality gap at 3.4%. We also develop managerial insights for practitioners who choose suppliers, and make production, distribution and inventory decisions in the supply chain.

Motivated by retailers' frequent introduction of new items to refresh product lines and maintain their market share, we present the assortment packing problem in which a firm must decide, in advance, the release date of each product in a given collection over a selling season. Our formulation models the trade-offs among profit margins, preference weights, and limited life cycles. A key aspect of the problem is that each product is short-lived in the sense that, once introduced, its attractiveness lasts only a few periods and vanishes over time. The objective is to determine when to introduce each product to maximize the total profit over the selling season. Even for two periods, the corresponding optimization problem is shown to be NP-complete. As a result, we study a continuous relaxation of the problem that approximates the problem well when the number of products is large. When margins are identical and product preferences decay exponentially, its solution can be characterized: it is optimal to introduce products with slower decays earlier. The relaxation also helps us to develop several heuristics, for which we establish performance guarantees. Numerical experiments show that these heuristics perform very well, yielding profits within 1% of the optimal in most cases.

In this paper we apply emerging theories in probability and statistics to examine the value of pooling of inventories under arbitrary non-normal dependent demand structures. Eppen (1979) showed that inventory costs in a centralized system increase with the correlation between multivariate normal product demands; using multivariate stochastic orders, we generalize this statement to arbitrary distributions. We then describe methods to construct models with arbitrary dependence structure, using the copula of a multivariate distribution to capture the dependence between the components of a random vector. For broad classes of distributions with arbitrary marginals, we confirm that pooling of inventories is more valuable when demands are less positively dependent.

Diverting large quantities of goods from authorized distribution channels to unauthorized or �gray market� channels, albeit legal, significantly affects both firms and consumers due to effects on price, revenue, service and warranty availability, and product availability. In this paper we consider mechanisms by which the uncertainty surrounding inventory ordering decisions drives gray markets. We start with a minimal stochastic supply chain model composed of a producer and a retailer; then we restructure the model to add a distributor whereby the distributor and authorized retailer have the option of diverting inventory to a gray market. Our analysis sheds light on three issues: impacts of diversion on the various supply chain participants, strategies producers could use to combat or exploit gray markets, and important considerations for authorized retailers trying to set optimal order quantities in the presence of a gray market. Our analysis yields new insights into the behavior and impact of gray markets, which can inform management strategies and policies for confronting them.

This paper introduces a new generalized version of the Traveling Salesman Problem (TSP) in which nodes belong to various color classes and each color class must be visited as an entity. We distinguish the cases of the problem for which the colors are either pre-assigned or can be selected from a given subset of colors. We establish computational complexity and provide concise formulations for the problems that lend themselves to derive tight lower bounds. Exact solutions for special cases and a two-phase heuristic for the general case are provided. Worst case performance and asymptotic performance of the heuristic are analyzed and the effectiveness of the proposed heuristic in solving large industrial size problems is empirically demonstrated.

Gray markets, also known as parallel imports, are marketplaces for trading genuine products that are diverted from authorized distribution channels. They have created fierce competition for manufacturers in many industries and each year billions of dollars worth of products are traded in these markets. Using a game-theoretic model, we analyze the impact of parallel importation on a price-setting manufacturer that serves two markets with uncertain demand. We characterize the optimal joint price and quantity decisions of the manufacturer which determine whether the manufacturer should ignore, block, or allow parallel importation. We also show that parallel importation forces the manufacturer to reduce her price gap while demand uncertainty forces her to lower prices in both markets. Moreover, we observe that parallel importation may force the manufacturer to exit the low-profit market. Through extensive numerical experiments, we explore the impact of market conditions (size and price elasticity) and product characteristics (a fashion item or a commodity) on the manufacturer's reaction to parallel importation. In addition, we provide interesting insights about the value of strategic pricing for coping with gray markets versus the uniform pricing policy that has been adopted by some companies to eliminate gray markets.

Carbon footprinting is a tool for firms to determine the total greenhouse gas (GHG) emissions associated with their supply chain or with a unit of final product or service. Carbon footprinting efforts typically aim to identify where best to invest in emission reduction efforts, and/or to determine the proportion of total emissions that an individual firm is accountable for, whether financially and/or operationally. A major and under-recognized challenge in determining the appropriate allocation stems from the high degree to which GHG emissions (or emissions reductions) are the result of joint efforts by multiple firms.In this paper we introduce a simple but effective model of joint production of GHG emissions in general supply chains, decomposing the total footprint into processes, each of which can be influenced by any combination of firms. A supply chain in which all firms exert their first-best emissions reduction effort levels is �carbon optimal�, while a supply chain which offsets all emissions is �carbon neutral�. With this structure, we examine conditions under which the supply chain can be carbon-neutral and/or carbon-optimal. We find that, in order to induce the carbon-optimal effort levels, the emissions need to be over-allocated. This means that the focus in the life-cycle assessment (LCA) and carbon footprinting literature on avoiding double-counting is, in the context of setting incentives, misguided. We also compare the situation where a single firm offsets all supply chain emissions with that where one powerful firm can enforce an emissions reduction target across all firms in the supply chain, and find that neither scenario is always preferred over the other. Our work aims to lay the foundation for a framework to integrate the economics- and LCA-based perspectives on supply chain carbon footprinting.

Every year, companies that produce consumer tax preparation software struggle with a massive amount of work imposed by thousands of state and federal changes to tax laws and forms. With their release not even beginning before August, these changes still must be processed and incorporated into the application by mid- December. Three companies dominate this competitive market with its short selling season so that release delays create significant losses. Though systematic resource allocation and process management are crucial, the volume and complexity of the changes, the brief timeframe to implement them, and feedback loops built into the system for error resolution make it extremely difficult to analyze the process. One of the leading tax software providers tasked us with developing systematic approaches for managing the process flow and staffing each stage so that the company met the deadline at the lowest cost. Based on the characteristics of the process, we develop deterministic models that partition tax forms into groups and determine the staffing levels for each group. Partitioning the development process into groups has the benefit of simplifying workflow management and making it easier to find staffing levels. To provide the company with a range of resource configurations, we use two modeling approaches to obtain lower and upper bounds on the number of resources at each stage. Numerical experiments indicate that the models successfully capture the features of the process and the heuristics perform well. Implementing our models at the company has resulted in 31% reduction in overtime and 13% reduction in total resource costs.

We investigate the adoption of energy efficiency initiatives using information on over 100,000 recommendations provided to more than 13,000 small and medium sized firms under the Industrial Assessment Centers (IAC) program of the US Department of Energy (DOE). We build on an earlier study by Anderson and Newell (2004) that explored the impact of economic factors on the adoption of energy efficiency initiatives, by investigating the role of behavioral factors on the adoption of energy efficiency initiatives. Using a probit instrumental variable model, we investigate three behavioral factors that could affect investment in energy efficiency. First, we find that adoption of a recommendation depends not only on its characteristics but also on the order in which the recommendations are presented. Adoption rates are higher for initiatives appearing early in a list of recommendations. We find evidence that this may in part be due to anchoring effects. Second, we find that adoption is not influenced by the number of options provided to decision makers. Third, we find that adoption is higher for recommendations that need lower managerial effort. Additionally, we identify conditions under which these behavioral factors are mitigated. We draw implications for enhancing adoption of energy efficiency initiatives and for other decision contexts where a collection of process improvement recommendations are made to firms.

We investigate a model in which one seller and one buyer trade in each of two periods. The buyer has demand for one unit of a non-durable object per period. The buyer's reservation value for the good is private information and is the same in both periods. The seller commits to prices in each of two periods. Prices in the second period may depend on the buyer's first-period behavior. Unlike the equal discount factor case studied in earlier papers, we show that when the seller is more patient than the buyer, second-period prices increase after a purchase. In particular, the optimal dynamic pricing scheme is not a repetition of the optimal static pricing scheme.