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.     

Optimal Descending Mechanisms for Constrained Procurement

Descending mechanisms for procurement (or, ascending mechanisms for selling) have been well‐recognized for their simplicity from the viewpoint of bidders—they require less bidder sophistication as compared to sealed‐bid mechanisms. In this study, we consider procurement under each of two types of constraints: (1) Individual/Group Capacities: limitations on the amounts that can be sourced from individual and/or subsets of suppliers, and (2) Business Rules: lower and upper bounds on the number of suppliers to source from, and on the amount that can be sourced from any single supplier. We analyze two procurement problems, one that incorporates individual/group capacities and another that incorporates business rules. In each problem, we consider a buyer who wants to procure a fixed quantity of a product from a set of suppliers, where each supplier is endowed with a privately known constant marginal cost. The buyer's objective is to minimize her total expected procurement cost. For both problems, we present descending auction mechanisms that are optimal mechanisms. We then show that these two problems belong to a larger class of mechanism design problems with constraints specified by polymatroids, for which we prove that optimal mechanisms can be implemented as descending mechanisms.     

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.     

Threshold Incentives and Sales Variance

In this paper, we analyze the impact of two forms of commonly used threshold‐based incentive schemes on the observed sales variability. The first form of the incentive comprises an additional marginal payment on crossing a specified sales threshold and the second form of the incentive scheme comprises a lumpsum bonus payment on crossing the predetermined sales threshold. We model the effect of such incentives under two specific scenarios: an exclusive dealership selling a single product and a non‐exclusive dealer selling two competing products. For an exclusive dealer, we show that a bonus contract not only increases the expected sales, but, more importantly, decreases the sales (order) variance. Consequently, the bonus‐based scheme allows the manufacturer to regulate sales variance better. With a non‐exclusive dealer, the sales variance increases substantially with an additional marginal payment contract. However, our analysis suggests that the bonus contract continues to perform better in this case, too, if the threshold level is set appropriately using the underlying demand distribution.     

Maximizing Revenue Through Two‐Dimensional Shelf‐Space Allocation

We consider the problem of optimally allocating contiguous rectangular presentation spaces in order to maximize revenues. Such problems are encountered in the arrangement of products in retail shelf‐space and in the design of feature advertising displays or webpages. Specifically, we allow (i) the shape of a product's presentation to have a vertical as well as a horizontal component and (ii) displays to extend across multiple shelves for in‐store presentations. Since the vertical location of the shelf on which a product is displayed affects its sales, each vertical location is assigned its own effectiveness with regard to revenue generation. The problem of maximizing the total weighted revenue of a display is strongly NP‐hard. Therefore, we decompose it into two subproblems. The first consists of allocating products to different cabinets. In the second, within each cabinet, each product's units are arranged in a contiguous rectangle and assigned a location. These subproblems are solved using an innovative approach that uses a combination of integer programming and an algorithm for the maximum‐weight independent set problem. Based on computational studies on both real‐world and simulated data, we demonstrate the efficiency and effectiveness of our approach. Specifically, the revenue generated by this scheme is within 1% of the optimum for actual data and within 5% for simulated data.     

On the transfer and advantageous reallocation paradoxes

It is well known that the transfer and advantageous reallocation paradoxes cannot occur at a Walrasian stable equilibrium in a two agent economy. In an influential recent paper Chichilnisky provided an example of the transfer paradox in the context of a globally Walrasian stable three agent economy. It is evident, though, that the paradoxes depend on the underlying data-tastes, preferences and net export positions-of the economy. This paper characterizes and generalizes the transfer and advantageous reallocation paradoxes: necessary and sufficient conditions on the underlying data of a globally Walrasian stable economy for the occurence of each of these paradoxes are established; the key role of the third agent in generating these paradoxes is clarified.I would like to thank John Donaldson, Duncan Foley and two anonymous referees of this journal for helpful comments. The usual disclaimers apply.     

Improving the Milk Supply Chain in Developing Countries: Analysis,Insights, and Recommendations

Quality issues in milk—arising primarily from deliberate adulteration by producers—have been reported in several developing countries. In the milk supply chain, a station buys raw milk from a number of producers, mixes the milk and sells it to a firm (that then sells the processed milk to end consumers). We study a non‐cooperative game between a station and a population of producers. Apart from penalties on proven low‐quality producers, two types of incentives are analyzed: confessor rewards for low‐quality producers who confess and quality rewards for producers of high‐quality milk. Contrary to our expectations, whereas (small) confessor rewards can help increase both the quality of milk and the station's profit, quality rewards can be detrimental. We examine two structures based on the ordering of individual and mixed testing of milk: pre‐mixed individual testing (first test a fraction of producers individually and then [possibly] perform a mixed test on the remaining producers) and post‐mixed individual testing (first test the mixed milk from all producers and then test a fraction of producers individually). Whereas pre‐mixed individual testing can be socially harmful, a combination of post‐mixed individual testing and other incentives achieves a desirable outcome: all producers supply high‐quality milk with only one mixed test and no further testing by the station.     

Dedicated Transportation Subnetworks: Design,Analysis, and Insights

A dedicated subnetwork (DSN) refers to a subset of lanes, with associated loads, in a shipper's transportation network, for which resources—trucks, drivers, and other equipment—are exclusively assigned to accomplish shipping requirements. The resources assigned to a DSN are not shared with the rest of the shipper's network. Thus, a DSN is an autonomously operated subnetwork and, hence, can be subcontracted. We address a novel problem of extracting a DSN for outsourcing to one or more subcontractors, with the objective of maximizing the shipper's savings. In their pure form, the defining conditions of a DSN are often too restrictive to enable the extraction of a sizable subnetwork. We consider two notions—deadheading and lane‐sharing—that aid in improving the size of the DSN. We show that all the optimization problems involved are both strongly NP‐hard and APX‐hard, and demonstrate several polynomially solvable special cases arising from topological properties of the network and parametric relationships. Next, we develop a network‐flow‐based heuristic that provides near‐optimal solutions to practical instances in reasonable time. Finally, using a test bed based on data obtained from a national 3PL company, we demonstrate the substantial monetary impact of subcontracting a DSN and offer useful managerial insights.     

Integrality in Stochastic Inventory Models

We study several finite‐horizon, discrete‐time, dynamic, stochastic inventory control models with integer demands: the newsvendor model, its multi‐period extension, and a single‐product, multi‐echelon assembly model. Equivalent linear programs are formulated for the corresponding stochastic dynamic programs, and integrality results are derived based on the total unimodularity of the constraint matrices. Specifically, for all these models, starting with integer inventory levels, we show that there exist optimal policies that are integral. For the most general single‐product, multi‐echelon assembly system model, integrality results are also derived for a practical alternative to stochastic dynamic programming, namely, rolling‐horizon optimization by a similar argument. We also present a different approach to prove integrality results for stochastic inventory models. This new approach is based on a generalization we propose for the one‐dimensional notion of piecewise linearity with integer breakpoints to higher dimensions. The usefulness of this new approach is illustrated by establishing the integrality of both the dynamic programming and rolling‐horizon optimization models of a two‐product capacitated stochastic inventory control system.