Decision Sciences Volume zyxwvutsrq 33 Number 3 Summer 2002 Prinied in the zyxwvutsr USA. The Production of Several Items in a Single Facility with Linearly Changing Demand Rates zyxw Bret J. Wagner Department of Management, Haworth College of Business, Western Michigan University, Kalamazoo, MI 49008, e-mail: bret.wagner@ wmich.edu Darwin J. Davis and Hemant V. Kher Department of Business Administration, College of Business and Economics, University of Delaware, Newark, L>E 19716-2710, e-mail: davisd@be.udel.edu, kher@udel.edu ABSTRACT In this paper we extend the ELSP model to allow for linearly changing demand rates over a fixed planning horizon. This extension of the ELSP research provides a model that can be used in coordinating the production and marketing planning activities in a firm. The model allows the user to evaluate the impact of changes in product demand on production costs and customer service. We solve the model using a standard nonlinear programming package (MINOS) and show through examples based on actual produc- tion data how the model can be used to support coordinated production and marketing planning. Subject Areas: Lot Sizing, Mathematical Programming Optimization, and Pro- duction Planning. INTRODUCTION Many industrial products are produced in a single facility, where the major sched- uling issue is how to allocate the capacity of the single facility to a set of products. This type of problem occurs frequently in the chemical industry, where an entire facility may be devoted to the production of a single product in a variety of grades. In addition, many manufacturing processes contain machines that produce multi- ple products. The problem of scheduling production on these machines is identical and, therefore, the single facility/machine problem is quite common. The research presented in this paper is motivated by a production-planning problem the authors have observed in chemical manufacturing plants. We describe the production set- ting observed in these companies, present a model to help managers develop pro- duction plans in coordination with marketing, and illustrate our model using data from a chemical manufacturer based in the Eastern United States. zyx 317