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AbstractThis paper concerns the approximation of optimal allocations by δ allocations. δ allocations are obtained by fixing an increment δ of effort and deciding at each step upon a single cell in which to allocate the entire increment. It is shown that δ allocations may be used as a simple method of approximating optimal allocations of effort resulting from constrained separable optimization problems involving a finite number of cells. The results are applied to find δ allocations (called δ plans) which approximate optimal search plans. δ plans have the property that as δ → 0, the mean time to find the target using a δ plan approaches the mean time when using the optimal plan. δ plans have the advantage that. they are easily computed and more easily realized in practice than optimal plans which tend to be difficult to calculate and to call for spreading impractically small amounts of effort over large areas.

"Countries differ in their governmental architectures and in the rules that describe the allocation of tasks, rights and duties across the various levels of government. In this paper, we present a short and selective survey of the development of the theory of optimal allocation of rights and duties along the vertical dimension in federations. We thereby first discuss the multiple trade-offs brought forward in the literature; these make that an ideal allocation of actual tasks across levels of government may be difficult, if not impossible, to attain. Then we turn to the consequences of a sub-optimal allocation of tasks and discuss spillover effects, strategic interactions between jurisdictions and intergovernmental competition. Throughout the review, we highlight paths in need of further research such that, in time, we will have a more solid ground for policy advice." (author's abstract)

Abstract
Survey response rates have declined dramatically in recent years, increasing the costs of data collection. Despite this, there is little existing research on how to most efficiently allocate samples in a manner that incorporates response rate information. Existing mathematical theory on allocation for single-stage stratified sample designs generally assumes complete response. A common practice is to allocate sample under complete response, then to inflate the sample sizes by the inverse of the anticipated response rates. However, we show that this method can fail to improve upon an unadjusted allocation, due to ignoring the associated increase in the cost per interview. We provide mathematical theory on how to allocate single-stage designs in a manner that incorporates the effects of nonresponse on cost efficiency. We derive the optimal allocation for the poststratified estimator under nonresponse, which minimizes either the unconditional variance of our estimator or the expected costs, holding the other constant, and taking into account uncertainty in the number of respondents. We assume a cost model that incorporates effects of nonresponse. We provide theoretical comparisons between our allocation and common alternatives, which illustrate how response rates, population characteristics, and cost structure can affect the methods' relative efficiency. In an application to a self-administered survey of US military personnel, the proposed allocation increases the effective sample size by 25 percent, compared with common practice.

ABSTRACTAllocation of at most n recoverable items among m demand locations is considered. Items are assumed to be demanded singly and independently and are eventually returned to the demand location. If a stockout occurs, the demand is lost and a penalty corresponding to lost profit is assessed. The allocation that minimizes the sum of expected stockout costs plus holding costs is readily obtained. An example involving allocation of rental cars among outlets is solved in detail.

Any system of ideas which underlies economic policy
recommendations needs to be made explicit so that its doctrinal premise
may be examined and debated. Section I of this paper, therefore,
explicitly states the philosophical under -pinning of this study.
Section 2 presents the central energy problem in a general mathematical
form whereas the solution of the specific energy problem for the
Pakistani economy is presented in Section 3, in which policy guidelines
for obtaining the desired solution have also been discussed. Finally,
Section 4 briefly presents our concluding remarks.

A principal allocates an object to one of I agents. Each agent values receiving the object and has private information regarding the value to the principal of giving it to him. There are no monetary transfers, but the principal can check an agent's information at a cost. A favored-agent mechanism specifies a value v* and an agent i*. If all agents other than i* report values below v*, then i* receives the good and no one is checked. Otherwise, whoever reports the highest value is checked and receives the good if and only if her report is confirmed. All optimal mechanisms are essentially randomizations over optimal favored-agent mechanisms. (JEL D82)

AbstractThis paper considers the problem of finding optimal solutions to a class of separable constrained extremal problems involving nonlinear functionals. The results are proved for rather general situations, but they may be easily stated for the case of search for a stationary object whose a priori location distribution is given by a density function on R, a subset of Euclidean n‐space. The functional to be optimized in this case is the probability of detection and the constraint is on the amount of effort to be usedSuppose that a search of the above type is conducted in such a manner as to produce the maximum increase in probability of detection for each increment of effort added to the search. Then under very weak assumptions, it is proven that this search will produce an optimal allocation of the total effort involved. Under some additional assumptions, it is shown that any amount of search effort may be allocated in an optimal fashion.

AbstractThis paper provides an overview of approaches to the allocation of scarce vaccine doses during a pandemic. Price and non-price methods are outlined to determine whom to prioritize. It is argued that depending on viral and vaccine properties, it may be superior to use epidemiological criteria than health risk criteria for prioritization. The paper concludes by noting that the key trade-offs between health risk and epidemiological properties have received too little study to systematically inform allocation during a public health emergency. Moreover, the evaluation criteria for vaccines themselves need to be adjusted to take potential short-term scarcity into account.

We study a contest with multiple, nonidentical prizes. Participants are privately informed about a parameter (ability) affecting their costs of effort. The contestant with the highest effort wins the first prize, the contestant with the second-highest effort wins the second prize, and so on until all the prizes are allocated. The contest's designer maximizes expected effort. When cost functions are linear or concave in effort, it is optimal to allocate the entire prize sum to a single "first" prize. When cost functions are convex, several positive prizes may be optimal. (JEL D44, J31, D72, D82)