Hasan Pirkul

Theory and methodology

Abstract The hierarchial network design problem with transshipment facilites was first formulated in Current, J. (1988), “The design of a hierarchical transportation network with transshipment facilities”, Transportation Science 22, 270–277. The objective of the FC-HNDP is to identify a least cost, two-level network. The network must include a primary path from a prespecified origin node to a prespecified terminus node. All nodes not on the primary path must be connected to that path via secondary arcs. In addition, transshipment facilities are required at the intersections of the two network levels. In this paper we present two efficient heuristics for solving the FC-HNDP. These heuristics were based upon a Lagrangian relaxation of the problem. To facilitate this relaxation, we have reformulated the original problem. Results for 240 randomly generated problems are summarized. The heuristics yielded the optimal solution in 72% of these problems. The mean gap between the Lagrangian lower bound and the feasible solution value was 0.38% and the maximum gap was 4.33% of the lower bound.

A multi-commodity, multi-plant, capacitated facility location problem: formulation and efficient heuristic solution

Abstract The PLANWAR model is a new formulation to the multi-commodity, multi-plant, capacitated facility location problem that seeks to locate a number of production plants and distribution centers so that total operating costs for the distribution network are minimized. An important component of a firms physical distribution strategy is its network strategy, which defines the physical flow of commodities (products) from production plants to warehouses and from warehouses to customer zones. A frequent objective when designing a network strategy is to determine the least total cost system design such that all customer demand is satisfied subject to limitations imposed by production capacities for plants and storage capacities for warehouses. We present a mixed integer programming model, PLANWAR, and provide an efficient heuristic solution procedure for this supply chain management problem. Distribution system design problems commonly occurs in the following form: A number of production plants supply warehouses with multiple products which in turn distribute these products to customer outlets based on their specified demand quantities of the different products. It is required to select the optimum set of plants and warehouses from a potential set and plan production capacities, warehouse capacities and quantities shipped so that the total operating costs of the distribution network are minimized. This paper is a computational study to investigate the value of coordinating production and distribution planning. We present a mixed integer programming formulation for the capacitated plant and warehouse supply chain management problem and propose an efficient heuristic based on Lagrangian relaxation of the problem.

Efficient algorithms for solving multiconstraint zero-one knapsack problems to optimality

The multiconstraint 0–1 knapsack problem is encountered when one has to decide how to use a knapsack with multiple resource constraints. Even though the single constraint version of this problem has received a lot of attention, the multiconstraint knapsack problem has been seldom addressed.This paper deals with developing an effective solution procedure for the multiconstraint knapsack problem. Various relaxation of the problem are suggested and theoretical relations between these relaxations are pointed out. Detailed computational experiments are carried out to compare bounds produced by these relaxations. New algorithms for obtaining surrogate bounds are developed and tested. Rules for reducing problem size are suggested and shown to be effective through computational tests. Different separation, branching and bounding rules are compared using an experimental branch and bound code. An efficient branch and bound procedure is developed, tested and compared with two previously developed optimal algorithms. Solution times with the new procedure are found to be considerably lower. This procedure can also be used as a heuristic for large problems by early termination of the search tree. This scheme was tested and found to be very effective.

Efficient algorithms for the capacitated concentrator location problem

Abstract Topological design of computer communication networks is a very difficult problem. This problem is generally disaggregated into a number of “simpler” problems. One of these “simpler” problems is the capacitated concentrator location problem. The paper makes use of the Lagrangian relaxation approach to develop optimal and heuristic solution procedures for this problem. Computational experiments show these procedures to be both efficient and effective. The heuristic solution procedure is compared to previously developed algorithms and found to generate significantly better results.

A heuristic solution procedure for the multiconstraint zero-one knapsack problem

In this article a new heuristic procedure is proposed. This procedure makes use of surrogate duality in solving multiconstraint knapsack problems. Computational effort involved in the procedure is bounded by a polynomial in the number of variables. Extensive computational testing indicates that the procedure generates good feasible solutions regardless of the problem structure. In 98% of the problems solved, the solution generated by the heuristic was within 1% of the optimal solution. This procedure was also tested against other heuristics and was found to compare favorably.

An integer programming model for the allocation of databases in a distributed computer system

Abstract Designers of distributed computer systems have to resolve issues like allocation of user nodes among processors, partitioning the central database and allocation of these partitions among processors. In this paper, we identify systems where decisions regarding the database partitioning and the allocation of these partitions among processors can be effectively merged with decisions regarding the assignment of user nodes to processors. An integer programming model that can be used in designing these systems is formulated. Heuristic and optimal solution procedures are developed. These procedures are tested and found to be effective on a wide range of problem structures.

Capacitated Multiple Item Ordering Problem with Quantity Discounts

Abstract Purchasing managers face a complex problem when determining order quantities for multiple items in the presence of quantity discounts and resource limitations. In this paper, the problem is formulated as a mathematical programming model. An efficient solution algorithm is developed utilizing the Lagrangian relaxation approach. Extensive computational experiments are performed and the results are presented.

Tabu search for graph partitioning

In this paper, we develop a tabu search procedure for solving the uniform graph partitioning problem. Tabu search, an abstract heuristic search method, has been shown to have promise in solving several NP-hard problems, such as job shop and flow shop scheduling, vehicle routing, quadratic assignment, and maximum satisfiability. We compare tabu search to other heuristic procedures for graph partitioning, and demonstrate that tabu search is superior to other solution approaches for the uniform graph partitioning problem both with respect to solution quality and computational requirements.

Organizational decision support systems

Abstract Decision support systems have traditionally been discussed within the context of individual or group decision making. In this paper we study decision support systems from an organizational perspective. We propose a framework for designing an organizational decision support system that is based on a network of knowledgebased systems. Nodes of this network interact with each other, as well as various other organizational systems, to provide comprehensive decision support. This network is also utilized to provide effective support for formal multi-participant decision making.

Locating concentrators for primary and secondary coverage in a computer communications network

A model is developed that assigns primary and secondary (backup) concentrator coverage to each terminal site. The objective is to minimize communications costs as well as costs for setting up and operating the concentrators subject to capacity constraints. A relaxation of the problem is studied, and an effective solution procedure that makes the use of this relaxation is developed. Experimental results over a wide range of problem structures show that this solution procedure is very effective. It is also found to be significantly faster than a state-of-the-art commercial integer programming package. >