Timothy J. Lowe

The stochastic p-hub center problem with service-level constraints

Small package delivery companies offer services where packages are guaranteed to be delivered within a given time-frame. With variability in travel time, the configuration on the hub-and-spoke delivery network is vital in ensuring a high probability of meeting the service-level guarantee. We present the stochastic p-hub center problem with chance constraints, which we use to model the service-level guarantees. We discuss analytical results, propose solution heuristics, and present the results from computational experiments.

Convex Location Problems on Tree Networks

This paper studies problems of finding optimal facility locations on an imbedding of a finite, undirected network having positive arc lengths. We establish that a large class of such problems is convex, in a well defined sense, for all choices of the data if and only if the network is a tree. A number of useful properties of related convex functions end convex sets are identified.

Decision Technologies for Agribusiness Problems: A Brief Review of Selected Literature and a Call for Research

The supply chain in the food and agribusiness sector is characterized by long supply lead times combined with significant supply and demand uncertainties, and relatively thin margins. These challenges generate a need for management efficiency and the use of modern decision technology tools. We review some of the literature on applications of decision technology tools for a selected set of agribusiness problems and conclude by outlining what we see as some of the significant new problems facing the industry. It is our hope that we will stimulate interest in these problems and encourage researchers to work on solving them.

Aggregation error for location models: survey and analysis

Location problems occurring in urban or regional settings may involve many tens of thousands of “demand points,” usually individual private residences. In modeling such problems it is common to aggregate demand points to obtain tractable models. We survey aggregation approaches to a large class of location models, consider and compare various aggregation error measures, identify some effective (and ineffective) aggregation error measures, and discuss some open research areas.

Efficient Points in Location Problems.

Abstract Much of the literature involving the location of one or more new facilities in the plane is concerned with minimizing a single objective function. In this paper we consider the problem of generating the efficient set of locations for a single facility where it is important that the facility be located as close as possible to each of a number of existing facilities whose locations are known. We concentrate on the notion of distance commonly referred to as the l1 norm, the Manhattan norm, or the city-block norm but results for other norms are given also. We develop properties of the efficient set and present two separate procedures for generating the efficient set.

Screening location strategies to reduce exchange rate risk

Abstract A firm that markets its products and services world-wide may face significant financial risk due to exchange rate fluctuations unless it maintains an international sourcing/production network. Thus, the firm must evaluate various sourcing/production network designs. The selection of the appropriate design is not straight-forward since decisions are made in an environment of uncertainty and involve multiple time periods. We propose a two-phase approach to screen various alternative designs (configurations) utilizing a number of criteria, and illustrate it using a popular Harvard Business School case. As by-products, we introduce a new criterion for making a pairwise stochastic comparison of alternatives and demonstrate the value of maintaining excess geographically-dispersed production capacity.

Aggregation Error Bounds for a Class of Location Models

Many location models involve distances and demand points in their objective function. In urban contexts, there can be millions of demand points. This leads to demand point aggregation, which produces error. We identify a general model structure that includes most such location models, and present a means of obtaining error bounds for all models with this structure. The error bounds suggest how to do the demand point aggregation so as to keep the error small.

Matching Supply and Demand: The Value of a Second Chance in Producing Hybrid Seed Corn

This paper considers a production-scheduling problem arising when there are random yields and demands as well as two sequential production periods before demand occurs. A typical instance is the production of seed corn. The paper makes three contributions. First, we verify that the objective function for the problem is smooth and concave so that optimal solutions are easily computed. Second, by examining data that represents actual costs, prices, and yields encountered in the seed corn industry, we gain some insight into the value that the second production period provides. Third, for a representative sample of hybrids from a major seed corn producer, we show that margins could be enhanced considerably by using the model. The results of this paper will assist seed corn producers in making production-scheduling decisions.

Flow network design for manufacturing systems layout

Abstract One way to solve a facilities layout planning problem is to use a component approach; the components being a) block design, b) input/output station location, c) material flow network design, and d) aisle netting out (accounting for aisle space). Material flow network design is an important component of this approach. In this paper a shortest rectilinear flow network problem is defined and formulated as an optimization problem. A Lagrangean relaxation of the problem gives separable, linear-time solvable, shortest-path problems. A heuristic, with ties to this formulation, is presented. An expression for the gap between the heuristically derived solution and the optimal solution is given. Some computational experiments using the heuristic are reported.

On the location of a tree-shaped facility

This paper considers the problem of locating a central facility on a tree network. The central facility takes the form of a subtree of the network, and provides service to several demand points located at nodes of the network. Two types of costs are involved in evaluating a given facility. The setup cost represents the cost of establishing the facility and is taken to be directly proportional to the total length of the facility. The transportation cost is the cost associated with the travel of customers to the facility. The objective function is to select a tree-shaped facility that will minimize the sum of the setup cost and the total transportation cost. We introduce a general model and a simple {open_quotes}bottom-up{close_quotes} dynamic programming algorithm for its solution. We then focus on the important class of covering problems, where the transportation cost of a customer to the serving facility is zero if the distance between the two is below a certain threshhold, and is equal to some penalty term otherwise. We improve upon the performance of existing methods, and present algorithms with subquadratic complexity.