A branch-bound algorithm for the capacitated facilities location problem

This paper discusses a mixed integer programming method for solving the Facilities Location Problem with capacities on the facilities. The algorithm uses a Decomposition technique to solve the dual of the associated continuous problem in each branch-bound iteration. The method was designed to produce the global optimum solution for problems with up to 100 facilities and 1,000 customers. Computational experience and a complete example are also presented in the appendix.     

A test for the hypothesis that two extreme-value scale parameters are equal

A statistic is determined for testing the hypothesis of equality for scale parameters from two populations, each of which has the first asymptotic distribution of smallest (extreme) values. The probability distribution is derived for this statistic, and critical values are determined and given in tabular form for a one-sided or two-sided alternative, for censored samples of size n₁ and n₂, n₁ = 2, 3, …. 6, n₂ = 2, 3, …. 6. The power function of the test for certain alternatives is also calculated and listed in each case considered.     

Problems in life cycle support cost estimation

Although industry is expected to design hardware to fit into a general support system and to be capable of arguing life-cycle system costs, adequate information has not been available on the support system in terms of policies and operating decision rules. Policies and operating decisions by users dominate engineering design decisions in determining life-cycle support costs. The relative effect of each of these decision areas on support costs has yet to be resolved empirically. Without an understanding of the sensitivity of support costs to alternative designs, capability is limited in design improvement and support of end items. Life-cycle costing of analysis under cost-effectiveness and the maintainability of integrated logistics support is open to question.     

On a new approach to the analysis of stationary inventory problems

The intent of this paper is to demonstrate that the theory of stationary point processes is a useful tool for the analysis of stationary inventory systems. In conventional inventory theory, the equilibrium distributions for a specified inventory policy are obtained, whenever possible, by recursive or limiting procedures, or both. A different and more direct approach, based on stationary point processes, is proposed here. The time instants at which stock delivery is effected are viewed as points of the stationary point process, which possesses uniform statistical properties on the entire real axis; hence the equilibrium statistics of the inventory process can be calculated directly. In order to best illustrate this approach, various examples are given, including some that constitute new results.     

A note on cycling in the simplex method

Although cycling in the simplex method has long been known, a number of theoretical questions concerning cycling have not been fully answered. One of these, stated in [3], is to find the smallest example of cycling, and Beale's example with three equations and seven variables is conjectured to be the smallest one. The exact bounds on dimensions of cycling examples are established in this paper. We show that Beale's example is the smallest one which cycles at a non-optimal solution, that a smaller one can cycle at the optimum, and that, in general (including the completely degenerate case), a cycling example must have at least two equations, at least six variables, and at least three non-basic variables. Examples and geometries are given for the extreme cases, showing that the bounds are sharp.     

An evaluation of incentive contracting experience

Incentive contracts are intended to motivate defense contractors to perform more efficiently and control costs more closely. By increasing the total profit as actual costs are reduced below a predetermined cost target, they encourage contractors to achieve cost under runs. Consequently, the principal advantage claimed for these contracts is that they make the financial incentives to reduce costs more effective. This study examines the effectiveness of incentive contracts as a means for controlling defense procurement costs. The study considers the various effects that incentive contracts may have on both contractors' performance and contract costs, and presents empirical evidence suggesting that these contracts may not have accomplished their intended goal of increased efficiency and lower procurement costs.     

Vessel allocation by linear programming

This paper presents a linear programming model of a fleet of vessels which is required to transport quantities of cargo, such as coal, iron ore, limestone, and salt from certain producing ports to specific destination ports. This model has been implemented and is currently being used both for planning purposes and as an aid in scheduling the trips to be made by each vessel.