William P. Pierskalla

An efficient approach to solving the road network equilibrium traffic assignment problem

This paper presents a solution technique that requires only the solution of a sequence of shortest route problems, such as computing time for the one dimensional searches being insignificant. The computing time for finding an approximate solution to the equilibrium problem was less than that required by the simplex method by orders of magnitude even on a fairly small network. For larger problems the savings would be even greater, since for multi-commodity network problems the number of constraints grows as the square of the conservation of flow and non-negativity constraints used explicitly in this technique. Preliminary computational results indicate that the number of shortest route subproblems for a network equilibrium problem with several hundred nodes will not be excessive; thus the solution approach presented appears very promising for large network equilibrium problems.

Surrogate Mathematical Programming

This paper presents an approach, similar to penalty functions, for solving arbitrary mathematical programs. The surrogate mathematical program is a lesser constrained problem that, in some cases, may be solved with dynamic programming. The paper deals with the theoretical development of this surrogate approach.

Nurse Scheduling Using Mathematical Programming

This paper formulates the nurse-scheduling problem as one of selecting a configuration of nurse schedules that minimize an objective function that balances the trade-off between staffing coverage and schedule preferences of individual nurses, subject to certain feasibility constraints on the nurse schedules. The problem is solved by a cyclic coordinate descent algorithm. We present results pertaining to a six-month application to a particular hospital unit and draw comparisons between the algorithm and hospital-generated schedules.

Letter to the Editor—The Multidimensional Assignment Problem

The multidimensional assignment problem is a higher dimensional version of the standard (two-dimensional) assignment problem in the literature. The higher dimensions can be thought of as time or space dimensions or both. An algorithm is proposed for the solution of the multi-index assignment problem. The algorithm is based on a tree search technique of the branch-and-bound variety. It uses dual subproblems to provide easily computed bounds for the primal assignment problem.

A Transportation Location-Allocation Model for Regional Blood Banking

Abstract In recent years, there has been much discussion about the issue of regionalization of blood banking systems. In this work we focus on the transportation location-allocation aspects of regionalization. We are given the locations and expected blood requirements of a set of N hospitals. Each hospital is to be assigned to a regional blood bank which will periodically supply the hospitals expected blood requirement for the period, as well as supply its emergency blood demands at the time of the emergency. The blood shipments are to be made by special delivery vehicles which have given capacities and given limits on the number of deliveries they can make per day. We present algorithms to decide how many blood banks to set up, where to locate them, how to allocate the hospitals to the banks, and how to route the periodic supply operation, so that the total of transportation costs (periodic and emergency supply costs) and the system costs are minimum. The algorithms are tested on data from the Chicago a...

A Review of Quasi-Convex Functions

Many theorems involving convex functions have appeared in the literature since the pioneering work of Jensen. Recently some results have been obtained for a larger class of functions: quasi-convex. This review summarizes in condensed form results known to date, providing some refinements to gain further generality. An additional objective of this review is to clarify the structure underlying quasi-convex functions by presenting analogues to properties of convex functions, and by illustrating where analogues do not exist.

Target Inventory Levels for a Hospital Blood Bank or a Decentralized Regional Blood Banking System

For any blood type, there is a complex interaction among the optimal inventory level, daily demand level, the transfusion to crossmatch ratio, the crossmatch release period and the age of arriving units that determine the shortage and outdate rate. The blood bank administrator should establish optimal target inventory levels based on a simple equation (decision rule) relating these factors. Evaluation of this rule indicates that its implementation can lead to a very low shortage rate and a reasonable low outdate rate if the blood bank administrator makes efforts to control the crossmatch release period and the average transfusion to crossmatch ratio.

Management Policies for a Regional Blood Bank

This paper considers management strategies for the administration of a regional blood bank. The techniques of management science and mathematical inventory theory are applied to construct a model for the system, identify policy areas, and formulate management objectives. Two simulation models and data collected from both a regional and single hospital blood bank are used in the analysis. The results presented examine the interactions and savings associated with following optimal ordering, crossmatch, and issuing policies. Since each of these policies have an important effect on the number of shortages and outdates, they therefore influence optimal blood bank management. In addition, the question of centralized versus decentralized control is examined.

A Two-Product Perishable/Nonperishable Inventory Problem

We consider a situation in which two types of inventories are available to satisfy demands, one having finite lifetime and one an infinite lifetime. It is assumed that demands form a sequence of independent random variables which first deplete from the perishable inventory and then the non-perishable. We show that there are exactly three ordering regions in each period which correspond to the three alternatives: ordering in both periods, ordering only perishable inventory or not ordering. The region boundaries and the optimal policies are characterized for both the single period and dynamic problems. A unique property of the model is that even with inclusion of salvage values at the end of the horizon, the region boundaries remain nonstationary.

Extensions of the Evans-Gould Stability Theorems for Mathematical Programs

This paper extends the results of Evans and Gould for stability in mathematical programming. In particular, it shows that their conditions apply to functional perturbation, to equality constraints, and to policy stability under certain conditions. Further, it shows that strictly monotonic programs and positively homogeneous programs possess the closure property needed for stability. Finally, some necessary and sufficient conditions are presented for lower and upper semicontinuity of certain point-to-set mappings.