Managing Logistics in Regional Banknote Supply Chain Under Security Concerns

We study the logistics problem faced by Regional Branches (RBs) of a central bank in managing the currency supply under security concerns. While making banknote supply decisions to Sub‐Branches (SBs), the management of RB must achieve two goals simultaneously: (i) guarantee that each SB has sufficient inventories of all denominations of banknotes to satisfy the demands from all commercial banks within its service area, and (ii) control the annual spending on this banknote supply operation. Due to security concerns, the following methods are implemented in the process of transporting banknotes: (i) the capacity of a cash truck is limited by the total face value (instead of the physical space) of banknotes, and (ii) empty decoy trucks are deployed along with the trucks filled with banknotes. After deriving a polynomial‐time strategy to guarantee an optimal solution for the special Bin‐Packing Problem faced in this study, we provide an exact formulation for the RB's supply planning problem. We also propose several polynomial‐time algorithms for deriving either optimal or near‐optimal solutions for the problem under different settings. Using the weekly demand data obtained from the central bank, we verify the performance of our algorithms, and analyze the impacts of changes in these features and in the fleet capacity on the total cost incurred by an RB under various scenarios.     

Analysis of Revenue Maximization Under Two Movie‐Screening Policies

A few weeks before the start of a major season, movie distributors arrange a private screening of the movies to be released during that season for exhibitors and, subsequently, solicit bids for these movies (from exhibitors). Since the number of such solicitations far exceeds the number of movies that can be feasibly screened at a multiplex (i.e., a theater with multiple screens), the problem of interest for an exhibitor is that of choosing a subset of movies for which to submit bids to the distributors. We consider the problem of the selection and screening of movies for a multiplex to maximize the exhibitor's cumulative revenue over a fixed planning horizon. The release times of the movies that can potentially be selected during the planning horizon are known a priori. If selected for screening, a movie must be scheduled through its obligatory period, after which its run may or may not be extended. The problem involves two primary decisions: (i) the selection of a subset of movies for screening from those that can potentially be screened during the planning horizon and (ii) the determination of the duration of screening for the selected movies. We investigate two basic and popular screening policies: preempt‐resume and non‐preempt. In the preempt‐resume policy, the screening of a movie can be preempted and resumed in its post‐obligatory period. In the non‐preempt policy, a movie is screened continuously from its release time until the time it is permanently withdrawn from the multiplex. We show that optimizing under the preempt‐resume policy is strongly NP‐hard while the problem under the non‐preempt policy is polynomially solvable. We develop efficient algorithms for the problem under both screening policies and show that the revenue obtained from the preempt‐resume policy can be significantly higher as compared with that from the non‐preempt policy. Our work provides managers of multiplexes with valuable insights into the selection and screening of movies and offers an easy‐to‐use computational tool to compare the revenues obtainable from adopting these popular policies.     

Pool‐Point Distribution of Zero‐Inventory Products

We study zero‐inventory production‐distribution systems under pool‐point delivery. The zero‐inventory production and distribution paradigm is supported in a variety of industries in which a product cannot be inventoried because of its short shelf life. The advantages of pool‐point (or hub‐and‐spoke) distribution, explored extensively in the literature, include the efficient use of transportation resources and effective day‐to‐day management of operations. The setting of our analysis is as follows: A production facility (plant) with a finite production rate distributes its single product, which cannot be inventoried, to several pool points. Each pool point may require multiple truckloads to satisfy its customers' demand. A third‐party logistics provider then transports the product to individual customers surrounding each pool point. The production rate can be increased up to a certain limit by incurring additional cost. The delivery of the product is done by identical trucks, each having limited capacity and non‐negligible traveling time between the plant and the pool points. Our objective is to coordinate the production and transportation operations so that the total cost of production and distribution is minimized, while respecting the product lifetime and the delivery capacity constraints. This study attempts to develop intuition into zero‐inventory production‐distribution systems under pool‐point delivery by considering several variants of the above setting. These include multiple trucks, a modifiable production rate, and alternative objectives. Using a combination of theoretical analysis and computational experiments, we gain insights into optimizing the total cost of a production‐delivery plan by understanding the trade‐off between production and transportation.     

A Sales Forecast Model for Short‐Life‐Cycle Products: New Releases at Blockbuster

We develop, in this article, a sales model for movie and game products at Blockbuster. The model assumes that there are three sales components: the first is from consumers who have already committed to purchasing (or renting) a product (e.g., based on promotion of, or exposure to, the product prior to its launch); the second comes from consumers who are potential buyers of the product; and the third comes from either a networking effect on closely tied (as in a social group) potential buyers from previous buyers (in the case of movie rental and all retail products) or re‐rents (in the case of game rental). In addition, we explicitly formulate into our model dynamic interactions between these sales components, both within and across sales periods. This important feature is motivated by realism, and it significantly contributes to the accuracy of our model. The model is thoroughly tested against sales data for rental and retail products from Blockbuster. Our empirical results show that the model offers excellent fit to actual sales activity. We also demonstrate that the model is capable of delivering reasonable sales forecasts based solely on environmental data (e.g., theatrical sales, studio, genre, MPAA ratings, etc.) and actual first‐period sales. Accurate sales forecasts can lead to significant cost savings. In particular, it can improve the retail operations at Blockbuster by determining appropriate order quantities of products, which is critical in effective inventory management (i.e., it can reduce the extent of over‐stocking and under‐stocking). While our model is developed specifically for product sales at Blockbuster, we believe that with context‐dependent modifications, our modeling approach could also provide a reasonable basis for the study of sales for other short‐Life‐Cycle products.     

Managing Retail Budget Allocation between Store Labor and Marketing Activities

The performance of a retail store depends on its ability to attract customer traffic, match labor with incoming traffic, and convert the incoming traffic into sales. Retailers make significant investments in marketing activities (such as advertising) to bring customers into their stores and in‐store labor to convert that traffic into sales. Thus, a common trade‐off that retail store managers face concerns the allocation of a store's limited budget between advertising and labor to enhance store‐level sales. To explore that trade‐off, we develop a centralized model to allocate limited store budget between store labor and advertising with the objective of maximizing store sales. We find that a store's inherent potential to drive traffic plays an important role, among other factors, in the relative allocation between advertising and store labor. We also find that as advertising instruments become more effective in bringing traffic to stores, managers should not always capitalize this effectiveness by increasing their existing allocations to advertising. In addition, we discuss a decentralized setting where budget allocation decisions cannot be enforced by a store manager and present a simple mechanism that can achieve the centralized solution. In an extension, we address the budget allocation problem in the presence of marketing efforts to shift store traffic from peak to off peak hours and show that our initial findings are robust. Further, we illustrate how the solution from the budget allocation model can be used to facilitate store level sales force planning/scheduling decisions. Based on the results of our model, we present several insights that can help managers in budget allocation and sales force planning.     

A Depository Institution's Optimal Currency Supply Network Under the Fed's New Guidelines: Operating Policies,Logistics, and Impact

The overuse of its currency processing operations by depository institutions (DIs) has motivated the Federal Reserve (Fed) to propose new currency recirculation guidelines. The Fed believes that DIs should play a more active role in recirculating fit (i.e., usable) currency so that the societal cost of providing currency to the public is minimized. The Fed characterizes the overuse by the extent of cross shipping, a practice in which the same DI deposits and withdraws currency of the same denomination within five business days in the same geographic region. The Fed's proposal encourages DIs to fit sort and reuse deposited currency through two components: a custodial inventory program and a recirculation fee that would be charged on withdrawals of cross‐shipped currency. Given the geographical network of the various branches of a DI, the extent of its participation in the proposed programs depends on a variety of factors: the nature of demand and supply of currency, number and locations of the processing centers, and the resulting fit‐sorting, holding, and transportation costs. The interrelated nature of these decisions motivates the need for an integrated model that captures the flow of currency in the entire network of the DI. Based on our work with Brink's Inc., a leading secure‐logistics provider, we develop a mixed‐integer linear programming (MILP) model to provide managers of DIs with a decision‐making tool under the Fed's new guidelines. Broadly, we analyze the following questions: (i) Over all typical practical realizations of the demand for currency that a DI may face, and over all reasonable cost implications, is there a menu of “good” operating policies? (ii) What is the monetary impact of fit‐sorting and custodial inventories on a DI? and (iii) To what extent will the Fed's new guidelines address its main goal, namely, a reduction in the practice of cross shipping by encouraging DIs to recirculate currency?     

Supply Chain Scheduling: Distribution Systems

We study conflict and cooperation issues arising in a supply chain where a manufacturer makes products which are shipped to customers by a distributor. The manufacturer and the distributor each has an ideal schedule, determined by cost and capacity considerations. However, these two schedules are in general not well coordinated, which leads to poor overall performance. In this context, we study two practical problems. In both problems, the manufacturer focuses on minimizing unproductive time. The distributor minimizes customer cost measures in the first problem and minimizes inventory holding cost in the second problem. We first evaluate each party's conflict, which is the relative increase in cost that results from using the other party's optimal schedule. Since this conflict is often significant, we consider several practical scenarios about the level of cooperation between the manufacturer and the distributor. These scenarios define various scheduling problems for the manufacturer, the distributor, and the overall system. For each of these scheduling problems, we provide an algorithm. We demonstrate that the cost saving provided by cooperation between the decision makers is usually significant. Finally, we discuss the implications of our work for how manufacturers and distributors negotiate, coordinate, and implement their supply chain schedules in practice.     

A Framework to Analyze Cash Supply Chains

The Federal Reserve System of the United States is making changes to its cash recirculation policy to reduce depository institutions' (banks') overuse of its cash processing services. These changes will affect operating policies and costs at many institutions having large cash businesses and, in turn, impact cash transportation and logistics providers. This study provides the framework to study the cash supply chain structure and analyzes it as a closed‐loop supply chain. Additionally, it describes the cash flow management system used by banks in the U.S.     

Scheduling Support Times for Satellites with Overlapping Visibilities

We consider the scheduling of ground station support times to low Earth orbit (LEO) satellites with overlapping visibilities. LEO satellites typically complete a revolution around the Earth in less than four hours at an altitude of a few hundred miles and are part of the critical infrastructure for natural resource management, crop yield estimation, meteorology, flood control, communication, and space research. Because these satellites are quite expensive to launch and operate, utilizing them in the best possible manner is of paramount importance for the agencies that own them. A ground station provides support time to a satellite to perform a variety of tasks when the satellite is visible to the station over a prespecified planning horizon; the payoff from providing such support is a function of the support time. When two or more satellites pass over the ground station, their visibility time windows may overlap. Thus, under overlapping visibilities, a relevant problem is that of scheduling ground station support time for each satellite with the objective of maximizing the total utility generated from supporting the satellites. We propose four basic scheduling models to address a variety of scenarios and investigate their computational complexities. For each model, we also identify special cases that are polynomially solvable.     

Estimated Generalized Least Squares for Random Coefficient Regression Models

ABSTRACT. This paper considers a general class of random coefficient regression (RCR) models to represent pooled cross-sectional and time series data. A new method is given to estimate the covariance matrix of the error component in these RCR models. Also, the asymptotic and small sample properties of the estimated generalized least squares estimator of the regression coefficient vector are established. Procedures for testing a linear restriction on the mean vector of the random coefficients are derived. Finally, a test for non-randomness in the RCR model is devised, and the asymptotic distribution of the test statistic is obtained.