T he necessity of surface water for irrigation and its increasing scarcity in developing economies motivate the need for its efficient distribution. The inequity in the distribution of surface water arises because of the relative physical locations of the farms. Head-reach (primary) farms are close to the source, whereas tail-end (secondary) farms are relatively farther. The lack of physical infrastructure implies that water allocated to secondary farms must pass through primary farms. Left to their individual incentives, primary farmers use more than their fair share of water by denying its release to secondary farmers. Such an inequitable sharing results in significantly suboptimal productivity of the farming community as a whole. We propose decentralized, individually rational mechanisms to achieve socially optimal distribution of surface water for a farming community under uncertainty in rainfall, choice of multiple crops, and differing risk-bearing abilities of primary and secondary farmers. We show that the mechanisms can be efficiently computed and highlight the impact of the improved sharing of surface water. We also study the movement of the price of water with its scarcity. Ideas that can help administer the mechanisms in practice are briefly discussed.

The overuse of its currency processing facilities by depository institutions (DIs) has motivated the Federal Reserve (Fed) to impose its new cash recirculation policy. This overuse is characterized by the practice of cross-shipping, where a DI both deposits and withdraws cash of the same denomination in the same business week in the same geographical area. Under the new policy, which came into effect July 2007, the Fed has imposed a recirculation fee on cross-shipped cash. The Fed intends to use this fee to induce DIs to effectively recirculate cash so that the societal cost of providing cash to the public is lowered. To examine the efficacy of this mechanism, we first characterize the social optimum and then analyze the response of DIs under a recirculation fee levied on cross-shipped cash. We show that neither a linear recirculation fee, which is the Fed's current practice, nor a more sophisticated nonlinear fee is sufficient to guarantee a socially optimal response from DIs. We then derive a fundamentally different mechanism that induces DIs to self-select the social optimum. Our mechanism incorporates a fairness adjustment that avoids penalizing DIs that recirculate their fair share of cash and rewards DIs that recirculate more than this amount. We demonstrate that the mechanism is easy to implement and tolerates a reasonable amount of imprecision in the problem parameters. We also discuss a concept of welfare-preserving redistribution wherein the Fed allows a group of DIs to reallocate (amongst themselves) their deposits and demand if such a possibility does not increase societal cost. Finally, we analyze the impact of incorporating the custodial inventory program, another component of the Fed's new policy.cash supply chain, coordination, fit sorting, cross shipping

Based on our work with ConAgra Foods (http://www.conagrafoods.com), a leading U.S. food manufacturer, we study a large-scale production-planning problem. The problem incorporates several distinguishing characteristics of production in the processed-food industry, including (i) production patterns that define specific combinations of weeks in which products can be produced, (ii) food groups that classify products based on the allergens they contain, (iii) sequence-dependent setup times, and (iv) manufacture of a large number of products (typically, around 200–250) on multiple production lines (typically, around 15–20) in the presence of significant inventory holding costs and production setup costs. The objective is to obtain a minimum-cost four-week cyclic schedule to resolve three basic decisions: (a) the assignment of products to each line, (b) the partitioning of the demand of each product over the lines to which it is assigned, and (c) the sequence of production on each line. We show that the general problem is strongly NP-hard. To develop intuition via theoretical analysis, we first obtain a polynomially solvable special case by sacrificing as little of its structure as possible and then analyzing the impact of imposing production patterns. A mixed-integer programming model of the general problem allows us to assess the average impact of production patterns and production capacities on the cost of an optimal schedule. Next, to solve practical instances of the problem, we develop an easy-to-implement heuristic. We first demonstrate the effectiveness of the heuristic on a comprehensive test bed of instances; the average percentage gap of the heuristic solution from the optimum is about 3%. Then, we show savings of about 28% on a real-world instance (283 products, 17 production lines) by comparing the schedule obtained from the heuristic to one that was in use (at ConAgra) based on an earlier consultant's work. Finally, we discuss the IT infrastructure implemented to enable the incorporation of optimized (or near-optimized) solutions for ongoing use.

The Centers for Medicare and Medicaid Services (CMS) has introduced a "bundled payments for care improvement" (BPCI) initiative. Each bundle pertains to a specific medical condition, a set of linked services, and a length of time referred to as an episode of care. Proposers choose bundles, design service chains, and propose target values of quality metrics and payments per episode. Expert panels evaluate proposals based on CMS-announced relative weights, but there is no limit on the number of proposers that may be selected. Moreover, there is no minimum score that will guarantee selection, which makes selection uncertain for proposers. We develop normative models for the parameter selection problems faced by potential proposers within the CMS' proposal selection process. Proposers have private information about their costs of achieving different quality targets, which determine their equilibrium responses. We show that an optimal strategy for CMS, under its current approach, may be to either announce a fixed threshold or keep the selection process uncertain, depending on market characteristics. We also formulate and solve the proposer selection problem as a constrained mechanism design problem, which reveals that CMS' current approach is not optimal. We present policy guidelines for government agencies pursuing bundled payment innovations.

We study a problem faced by a secure‐logistics provider (SLP) of maximizing profit by jointly pricing the services of fit‐sorting and transporting cash along with the design of the supporting logistics network, in a market consisting of a population of Depository Institutions (DIs). The need to jointly price the services assumes significance because they are partial substitutes of one another. Our study finds that the influence of the logistics network on prices is especially strong when there are non‐linearities in the cost of provisioning the logistics services. Furthermore, the impact of logistics decisions on different types of pricing schemes (e.g., volume discount, bundled pricing) is different, both in its structure and extent. In present times, when the market for the fit‐sorting service is relatively immature, our findings have major implications to the way an SLP's business is managed.