Note---An Early Classic Misplaced: Ford W. Harris's Economic Order Quantity Model of 1915

The familiar square-root formula for the optimal economic order quantity was derived originally by Harris in 1915 (Harris, F. W. 1915. What quantity to make at once. The Library of Factory Management, Vol. V. Operation and Costs. A. W. Shaw Company, Chicago, 47--52.). Since all citations found to Harris's paper over the past 35 years are incorrect, it seems that no one has been able to locate the paper during this period. The paper's apparent misplacement probably stems from an inaccurate citation given by Raymond in 1931 (Raymond, F. E. 1931. Quantity and Economy in Manufacture. McGraw-Hill, New York.). Harris's paper exemplifies skillful presentation of the concepts of management science, and still merits reading. Today's researcher can learn much from Harris's modeling approach, and would do well to emulate his expositional clarity and motivational effectiveness.inventory/production: economic order quantity, lot sizing, sensitivity analysis, philosophy of modeling

On the Management Science Ten Page Constraint

In December 1971, a ten page constraint was instituted for most papers published in Management Science. The implications of this page constraint policy are examined, and a modified policy is proposed which retains all of the advantages of the current policy while eliminating some of its disadvantages.

Note--A Dynamic Programming Approach to Capacity Expansion with Specialization

The capacity expansion problem with specialization involves two classes of growing demand and two types of capacity. One type of capacity can supply both demands, while the second can supply only one. The specialization problem is an extreme case of the multilocation capacity expansion problem, and dynamic programming approaches for the multilocation problem can be adapted to solve the specialization problem.

Note--Dynamic Facility Location and Simple Network Models

Wesolowsky [Wesolowsky, G. O. 1973. Dynamic facility location. Management Sci. 19 (11, July) 1241-1248.] has examined a dynamic version of the location problem for a single facility, obtained by allowing relocation of the facility over time to optimize a cost or benefit expression. This problem is essentially one of facility replacement, and may be expressed and solved through a simple network model as in deterministic equipment replacement situations ([Veinott, A. F., Jr., H. M. Wagner. 1962. Optimal capacity and scheduling--I. Oper. Res. 10 (4, July-August) 518-532 and Wagner, H. M. 1969. Principles of Operations Research. Prentice-Hall, Englewood Cliffs, New Jersey, pp. 180-181 and pp. 340-342.]).

Capacity Expansion for India's Nitrogenous Fertilizer Industry

A massive investment program is under way to meet the increased demand for chemical fertilizers in India. This paper reports on a preinvestment survey of that program. Such a survey cannot be viewed as a master plan for the development of the entire chemical fertilizers industry. Rather, it is intended to provide a rough framework within which to draw up a detailed proposal on the next few units to be built. The conculsions are intended to serve as the initial premises for a specific project: when, where, and how large a plant to construct. Necessarily, a preinvestment survey will contain fewer engineering details and will be less realistic than a report on a specific unit.

Optimal Investment Scheduling with Price-Sensitive Dynamic Demand

A model is developed that integrates capital investment decisions with output and pricing decisions for a situation of growing demand. Conditions are derived for the model that permit application of a general approach for determining the optimal sequence and timing of investments in a continuous-time framework. The behavior of optimal pricing and output decisions is characterized analytically. Specific results are given for a quadratic cost and revenue case, and an example illustrates the form of a solution. Possible extensions of the model are also discussed.

A Dual-Based Procedure for Dynamic Facility Location

In dynamic facility location problems, one desires to select the time-staged establishment of facilities at different locations so as to minimize the total discounted costs for meeting demands specified over time at various customer locations. We formulate a particular dynamic facility location problem as a combinatorial optimization problem. The formulation permits both the opening of new facilities and the closing of existing ones. A branch-and-bound procedure incorporating a dual ascent method is presented and shown, in computational tests, to be superior to previously developed methods. The procedure is comparable to the most efficient methods for solving static (single-period) location problems. Problems with 25 potential facility locations, 50 customer locations, and 10 time periods have been solved within one second of CPU time on an IBM 3033 computer. Extensions of the dynamic facility location problem that allow price-sensitive demands, linearized concave costs, interdependent projects, multiple stages, and multiple commodities also can be solved by the dual ascent method. The method can serve as a component of a solution process for capacitated dynamic location problems.facilities/equipment planning: location, programming: integer algorithms, branch and bound, programming: integer algorithms, test

Planning for Surprise: Water Resources Development Under Demand and Supply Uncertainty I. The General Model

A study of water resources development in South Sweden revealed that water consumption unexpectedly stopped growing after construction had begun on a large project to expand water supplies. The project had a long lead time for completion, and planning had been based on traditional deterministic forecasts of future water use. To explore the implications of such an uncertain structural shift in future consumption patterns, we develop a model for determining the timing for initiating such a project. In this model, the original consumption forecast may be disrupted at some random future time by an event called a "surprise." As in the Swedish situation, we have modeled the surprise as an unexpected stagnation in future demand growth and benefit levels. We show that this form of uncertainty makes desirable delaying the initiation of the project beyond the time optimal under the original forecast. We then extend the model to include the lead time for the project as a variable, and demonstrate that the lead time should be reduced from that optimal under a deterministic future. Finally, we incorporate the option of abandoning the project when the surprise occurs, and show that higher salvage values for the project lead to earlier optimal commitment times.facilities/equipment planning: capacity expansion, probability: stochastic model applications, natural resources: water resources