On the expected number of assignments in reduced matrices for the linear assignment problem

A linear n × n assignment problem is considered for which the elements of the cost matrix are sampled from a continuous probability distribution. Based on the zero entries of the reduced matrix the expectation of the maximum number of initial assignments is determined for general n, as well as an asymptotic value for large n

The Evolution, Cost, and Operation of the Private Food Assistance Network

Delivery of assistance to the poor has changed drastically in the past 20 years. While the availability of cash assistance has decreased, the availability of food assistance has widened. The most substantial change in assistance available to the poor may have been the emergence of food pantries as a source of free food to prepare at home. Large numbers of Americans rely on food pantries, but many policymakers, academics, and participants in the private food assistance network have limited understanding of the network. This paper aims to fill that gap by examining how the network evolved, how much it costs, and how it operates. We provide a detailed review of domestic food policy since the 1930s, show how agricultural and welfare policies contributed to developing a supply of free food available to the needy, and explain how private efforts, such as the creation of Second Harvest, resulted in a rise in food pantries. Our research also highlights policy changes in the Food Stamp program that may have contributed to the tremendous demand for free food in the 1980s. Using secondary data, we estimate that the private food assistance network costs about $2.3 billion annually, making it about one-twelfth the size of the Food Stamp program. We show that the benefits available to the needy from the network differ among geographic areas. We highlight the heterogeneity of organizations in the network by examining two food banks, the Connecticut Food Bank and the Greater Pittsburgh Community Food Bank. We conclude that the private food assistance network provides the needy with valuable resources and offer recommendations for making the public food safety net more effective.

Application of a General Risk Management Model to Portfolio Optimization Problems with Elliptical Distributed Returns for Risk Neutral and Risk Averse Decision Makers

In this paper portfolio problems with linear loss functions and multivariate elliptical distributed returns are studied. We consider two risk measures, Value-at-Risk and Conditional-Value-at-Risk, and two types of decision makers, risk neutral and risk averse. For Value-at-Risk, we show that the optimal solution does not change with the type of decision maker. However, this observation is not true for Conditional-Value-at-Risk. We then show for Conditional-Value-at-Risk that the objective function can be approximated by Monte Carlo simulation using only a univariate distribution. To solve the equivalent Markowitz model, we modify and implement a finite step algorithm. Finally, a numerical study is conducted.Conditional value-at-risk;Disutility;Elliptical distributions;Linear loss functions;Portfolio optimization;Value-at-risk

Some conservative stopping rules for the operational testing of safety-critical software

Operational testing, which aims to generate sequences of test cases with the same statistical properties as those that would be experienced in real operational use, can be used to obtain quantitative measures of the reliability of software. In the case of safety critical software it is common to demand that all known faults are removed. This means that if there is a failure during the operational testing, the offending fault must be identified and removed. Thus an operational test for safety critical software takes the form of a specified number of test cases (or a specified period of working) that must be executed failure-free. This paper addresses the problem of specifying the numbers of test cases (or time periods) required for a test, when the previous test has terminated as a result of a failure. It has been proposed that, after the obligatory fix of the offending fault, the software should be treated as if it were completely novel, and be required to pass exactly the same test as originally specified. The reasoning here claims to be conservative, inasmuch as no credit is given for any previous failure-free operation prior to the failure that terminated the test. We show that, in fact, this is not a conservative approach in all cases, and propose instead some new Bayesian stopping rules. We show that the degree of conservatism in stopping rules depends upon the precise way in which the reliability requirement is expressed. We define a particular form of conservatism that seems desirable on intuitive grounds, and show that the stopping rules that exhibit this conservatism are also precisely the ones that seem preferable on other grounds