A sampling procedure and public policy

This paper describes the background of the Office of Management Budget Circular A-21, “Principles for Determining Costs Applicable to Grants, Contracts, and Other Agreements with Educational Institutions,” that describes the requirement for effort reporting. A sampling procedure is proposed as an alternative to 100% reporting.     

An application of statistical techniques to estimate engineering man-hours on major aircraft programs

Data on 23 lots of various aircraft programs were gathered. Total engineering man-hours, and information on performance, weight, area, avionics systems, data, and schedule were subjected to least squares analysis. An equation is presented which indicates a relationship between total engineering manhours and a set of seven predictor variables. While the equation derived could only be used with confidence by the manufacturer whose data was analyzed, this article should be looked upon as demonstrating a method of data analysis which others may also find useful, not only for predicting engineering manhours in major aircraft programs, but also in other situations where there is an abundance of possible predictor variables, and the problem is to sort out a meaningful subset of these variables. In order to demonstrate the viability of the formula obtained, comparisons were made with various bid programs.     

Application of the GLM technique to a production planning problem

Generalized Lagrange Multipliers (GLM) are used to develop an algorithm for a type of multiproduct single period production planning problem which involves discontinuities of the fixed charge variety. Several properties of the GLM technique are developed for this class of problems and from these properties an algorithm is obtained. The problem of resolving the gaps which are exposed by the GLM procedure is considered, and an example involving a quadratic cost function is explored in detail.     

Locating facilities in three-dimensional space by convex programming

We consider the problem of simultaneously locating any number of facilities in three-dimensional Euclidean space. The criterion to be satisfied is that of minimizing the total cost of some activity between the facilities to be located and any number of fixed locations. Any amount of activity may be present between any pair of the facilities themselves. The total cost is assumed to be a linear function of the inter-facility and facility-to-fixed locations distances. Since the total cost function for this problem is convex, a unique optimal solution exists. Certain discontinuities are shown to exist in the derivatives of the total cost function which previously has prevented the successful use of gradient computing methods for locating optimal solutions. This article demonstrates the use of a created function which possesses all the necessary properties for ensuring the convergence of first order gradient techniques and is itself uniformly convergent to the actual objective function. Use of the fitted function and the dual problem in the case of constrained problems enables solutions to be determined within any predetermined degree of accuracy. Some computation results are given for both constrained and unconstrained problems.     

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.     

A queuing process with bilevel hysteretic service-rate control

The purpose of this paper is to analyze the effect of a particular control doctrine applied to the service mechanism of a queuing process. A bilevel hysteretic control based on queue length control levels is employed in an M/M/1 queuing system. Expressions are obtained for queue length probabilities, the first two factorial moments of queue length and two figures of merit for describing control performance under the assumption of statistical equilibrium. Computational examples illustrate the effects on queuing processes subject to this type of control. Several cost formulae are considered for comparison of costs when the queue control doctrine is varied. Situations in which hysteretic control is useful are discussed.     

Solutions for a class of n-person games in partition function form

A unique polyhedral solution is given for most n-person games in partition function form when only partitions into coalitions with 1, n-1, and n players have large payoffs.     

A (Q,R) inventory model with lost sales and erlang-distributed lead times

The exact expression is derived for the average stationary cost of a (Q,R) inventory system with lost sales, unit Poisson demands, Erlang-distributed lead times, fixed order cost, fixed cost per unit lost sale, linear holding cost per unit time, and a maximum of one order outstanding. Explicit expressions for the state probabilities and a fast method of calculating them are obtained for the case of Q greater than R. Exponential lead times are analyzed as a special case. A simple cyclic coordinate search procedure is used to locate the minimum cost policy. Examples of the effect of lead time variability on costs are given.     

Cyclic preference scheduling for nurses using branch and price

This paper presents a new methodology to solve the cyclic preference scheduling problem for hourly workers. The focus is on nurse rostering but is applicable to any organization in which the midterm scheduling decision must take into account a complex of legal, institutional, and preferential constraints. The objective is to strike a balance between satisfying individual preferences and minimizing personnel costs. The common practice is to consider each planning period independently and to generate new rosters at the beginning of each. To reduce some of the instability in the process, there is a growing trend toward cyclic schedules, which are easier to manage and are generally perceived to be more equitable. To address this problem, a new integer programming model is presented that combines the elements of both cyclic and preference scheduling. To find solutions, a branch‐and‐price algorithm is developed that makes use of several branching rules and an extremely effective rounding heuristic. A unique feature of the formulation is that the master problem contains integer rather than binary variables. Computational results are reported for problem instances with up to 200 nurses. Most were solved within 10 minutes and many within 3 minutes when a double aggregation approach was applicable. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007.