Zvi Drezner

An Efficient Genetic Algorithm for the p-Median Problem

We propose a new genetic algorithm for a well-known facility location problem. The algorithm is relatively simple and it generates good solutions quickly. Evolution is facilitated by a greedy heuristic. Computational tests with a total of 80 problems from four different sources with 100 to 1,000 nodes indicate that the best solution generated by the algorithm is within 0.1% of the optimum for 85% of the problems. The coding effort and the computational effort required are minimal, making the algorithm a good choice for practical applications requiring quick solutions, or for upper-bound generation to speed up optimal algorithms.

On the computation of the bivariate normal integral

We propose a simple and efficient way to calculate bivariate normal probabilities. The algorithm is based on a formula for the partial derivative of the bivariate probability with respect to the correlation coefficient.

A New Genetic Algorithm for the Quadratic Assignment Problem

In this paper we propose several variants of a new genetic algorithm for the solution of the quadratic assignment problem. We designed a special merging rule for creating an offspring that exploits the special structure of the problem. We also designed a new type of a tabu search, which we term aconcentric tabu search. This tabu search is applied on the offspring before consideration for inclusion in the population. The algorithm provided excellent results for a set of 29 test problems having between 30 and 100 facilities.

Optimal inventory policies for substitutable commodities with stochastic demand

In this article we consider a stochastic model for two products which have a single‐period inventory structure and which can be used as substitutes for each other should the need arise. Substitution will occur with probability one, but at perhaps a different revenue level. We prove that the expected profit function is concave, allowing us to find optimal stocking levels for the two products. We compare optimum inventory levels for the case of single substitution with that where there is no substitution. It is demonstrated for the case of single substitution that total optimum order quantities can actually increase or decrease with the substitution revenue.

Competitive location strategies for two facilities

Abstract In this paper we present the problem of locating a facility when competition from another facility is taken into consideration. Two problems are addressed here. One is the location of a new facility that will attract the most buying power from an existing facility. The other is the location of a facility that will secure the most buying power againts the best location of competing facility to be set up in the future.

The gradual covering decay location problem on a network

Abstract In covering problems it is assumed that there is a critical distance within which the demand point is fully covered, while beyond this distance it is not covered at all. In this paper we define two distances. Within the lower distance a demand point is fully covered and beyond the larger distance it is not covered at all. For a distance between these two values we assume a gradual coverage decreasing from full coverage at the lower distance to no coverage at the larger distance.

NETWORK DESIGN: SELECTION AND DESIGN OF LINKS AND FACILITY LOCATION

In this paper we introduce new network design problems. A network of potential links is given. Each link can be either constructed or not at a given cost. Also, each constructed link can be constructed either as a one-way or two-way link. The objective is to minimize the total construction and transportation costs. Two different transportation costs are considered: (i) traffic is generated between any pair of nodes and the transportation cost is the total cost for the users and (ii) demand for service is generated at each node and a facility is to be located on a node to satisfy the demand. The transportation cost in this case is the total cost for a round trip from the facility to each node and back. We will consider two options in regard to the links between nodes. They can either be two-way only, or mixed, with both two-way and one-way (in either direction) allowed. When these options are combined with the two objective functions, four basic problems are created. These problems are solved by a descent algorithm, simulated annealing, tabu search, and a genetic algorithm. Extensive computational results are presented.

The Bullwhip Effect: Managerial Insights on the Impact of Forecasting and Information on Variability in a Supply Chain

An important observation in supply chain management, popularly known as the bull-whip effect, suggests that demand variability increases as one moves up a supply chain. For example, empirical evidence suggests that the orders placed by a retailer tend to be much more variable than the customer demand seen by that retailer. This increase in variability propagates up the supply chain, distorting the pattern of orders received by distributors, manufacturers and suppliers.

On Optimizing Bin Picking and Insertion Plans for Assembly Robots

Abstract In robotic assembly stations robots pick a series of component parts from bins and then insert and assemble them. Several approaches are described and formulated for optimizing bin organization, picking, and insertion sequence and route. Solution procedures are developed for several modes of assembly tasks. The Simple Assembly Plan problem (SAP) is defined and solved. Extensions to this problem are heuristically solved by separating the SAP problem into the Bin Assignment Problem (BAP) and the Pick-Insert Sequencing (PIS) problem. We then define and formulate a new version of the assignment problem which is termed the Minimax Assignment Problem (MAP). An algorithm for the solution of this problem is developed and tested.

The Planar Two-Center and Two-Median Problems

We present algorithms for the solution of planar location-allocation problems with two new facilities. Euclidean distances are assumed. We address both the minimax or “two-center”, and minisum or “two-median” problems. Computational results are presented.