Philip C. Jones

Prepositioning supplies in preparation for disasters

In this paper, we examine the decision of where to preposition supplies in preparation for a disaster, such as a hurricane or terrorist attack, and how much to preposition at a location. If supplies are located closer to the disaster, it can allow for faster delivery of supplies after the disaster. As a result of being closer, though, the supplies may be in a risky location if the disaster occurs. Considering these risks, we derive equations for determining the optimal stocking quantity and the total expected costs associated with delivering to a demand point from a supply point. We provide a sensitivity analysis to show how different parameters impact stocking levels and costs. We show how our cost model can be used to select the single best supply point location from a discrete set of choices and how it can be embedded within existing location algorithms to choose multiple supply points. Our computational experiments involve a variety of relationships between distance and risk and show how these can impact location decisions and stocking levels.

Parallel machine replacement

We consider the parallel replacement problem in which there are both fixed and variable costs associated with replacing machines. Increasing maintenance costs motivate replacements, and the fixed replacement cost provides incentive for replacing machines of different ages together in “clusters.” We prove two intuitive results for this problem. First, it is never optimal to split a cluster of like-aged machines, and second, it is never optimal to replace newer clusters before older clusters. By incorporating these two results into an algorithmic approach, we vastly reduce the amount of computation required to identify an optimal replacement policy.

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.

Coordinating the supply chain in the agricultural seed industry

This paper examines contract practices between suppliers and retailers in the agricultural seed industry. We construct and analyze single-retailer models of various contract types actually used in the industry, which include, for example, certain “bonus” and “penalty” features. With no assumption on the demand distribution, we establish sufficient conditions for contract parameters to guarantee supply chain coordination. Under the assumption of uniform demand, we fully characterize all coordinating contracts. In addition, we compare the models studied herein with other models in the literature and demonstrate that current behavior in the agricultural seed industry is substantively different than that captured by other models. Conversely, we argue why other existing models are not reasonable to implement in the agricultural seed industry.

Rationalizing Tool Selection in a Flexible Manufacturing System for Sheet-Metal Products

Substantial simplification of existing processes and designs may be required before the potential benefits of modern manufacturing technology can be realized. This paper analyzes implementation problems associated with a flexible system that produces flat sheet-metal parts with interior holes. The paper makes three main contributions. First, we formulate the problem of selecting tooling and design standards as an optimization model and demonstrate that the model yields insight by applying it to one manufacturers problem, thereby reducing substantially the required tooling. Second, we show that the model has a totally balanced constraint matrix, and hence, there are polynomial time algorithms for various versions of the problem. Third, we provide new algorithms with substantially improved performance bounds for two important versions of the problem.

Optimal inventory control in a production flow system with failures

We consider a continuous flow production process subject to failures with an intermediate buffer. Under the practical restriction to the class of (B, b) inventory control policies, we give a procedure for determining the optimal buffer size, B, and control parameter, b. We give conditions under which these parameters can be expressed in closed form and show that otherwise they can be computed as the solution of a two-dimensional nonlinear system.

Specially Structured Uncapacitated Facility Location Problems

This paper considers a specially structured uncapacitated facility location problem. We show that several problems, including certain tool selection problems, substitutable inventory problems, supplier sourcing problems, discrete lot sizing problems, and capacity expansion problems, can be formulated as instances of the problem. We also show that the problem with m facilities and n customers can be solved in O(mn), as a shortest path problem on a directed graph.

Matching problems in selective assembly operations

We consider several different matching problems that are motivated by applications to selective assembly operations. In the case of maximum cardinality problems, we provide linear time greedy algorithms which we prove optimal via a min-max theorem. We also consider a weighted version and provide a polynomial time algorithm to find the optimal solution.

An integer programming model for optimal pork marketing

Pork producers must determine when to sell pigs, which and how many pigs to sell, and to which packer(s) to sell them. We model the decision-making problem as a linear mixed-integer program that determines the marketing strategy that maximizes expected annual profit. By discretizing the barn population into appropriate weight and growth categories, we formulate an mixed-integer program that captures the effect of stocking space and shipping disruption on pig growth. We consider marketing to multiple packers via shipping policies reflecting operational sorting constraints. Utilizing data from Cargill Animal Nutrition, we implement the model to obtain solutions that characterize significant strategic departures from commonly-implemented industry rules-of-thumb and that possess the potential to increase profitability in an industry characterized by narrow profit margins.

Computing nonlinear network equilibria

This paper examines the problem of computing nonlinear network equilibria using a ‘Newton’ iteration. By exploiting the network structure, we are able to show that the iteration is globally convergent, monotonic, and (locally) quadratically convergent using only simple algebraic arguments.