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OPTIMAL CONTROL, LINEAR PROGRAMMING, AND GOAL PROGRAMMING TECHNIQUES IN AN INTEGRATED PRODUCTION PLANNING

IP.com Disclosure Number: IPCOM000128150D
Original Publication Date: 1978-Dec-31
Included in the Prior Art Database: 2005-Sep-15
Document File: 7 page(s) / 27K

Publishing Venue

Software Patent Institute

Related People

S. L. Narasimhan: AUTHOR [+4]

Abstract

This paper descr ibes a comparison of optimal control, linear programming, and goal programming techniques for an Integrated R&D production, and inven-tory planning situation. The objective is the minimization of the total cost of the factors of production - R&D, labor, and capital - subject to dynamic constraints based on a Leontlef type Input-output model. Representative numerical results using each technique are presented.

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THIS DOCUMENT IS AN APPROXIMATE REPRESENTATION OF THE ORIGINAL.

OPTIMAL CONTROL, LINEAR PROGRAMMING, AND GOAL PROGRAMMING TECHNIQUES IN AN INTEGRATED PRODUCTION PLANNING

S. L. Narasimhan* W. A. Gruver

TR 78-07

* School of Business, North.Carolina Central University, Durliam, N.C.

ABSTRACT

This paper descr ibes a comparison of optimal control, linear programming, and goal programming techniques for an Integrated R&D production, and inven-tory planning situation. The objective is the minimization of the total cost of the factors of production - R&D, labor, and capital - subject to dynamic constraints based on a Leontlef type Input-output model. Representative numerical results using each technique are presented.

INTRODUCTION

Whereas the R&D literature has concentrated on planning and control of research and development activities I work In production planning often deals with strategies for determining production rate and workforce level for a given demand. A familiar example of this latter type of problem has been considered by Holt, Mod1gliani, Muth and Simon (WiS) 2. The IR114S model determines Lite production rate and the workforce level for a given demand while minimizing an objective based on the factors of production and inventory. However, HMS and other related models do not Include the possi- bility of increasing the production rate by applied R&D engineering activities of the firm during the planning period. Typically engineering includes re- search in product and process engineering, industrial engineering, equipment, and other labor training activities. Neither the R&D nor production planning 3 literature addresses the Integrated approach This research addresses the formulation and solution of integrated R&D, production, and inventory planning models using optimization techniques, based on optimal control, linear programming and goal programming models. The Inputloutput relationship Is represented by a Leontief type production function which serves as an inven- tory constraint of the system.

PRODUCTION FUNCTIONS

A production function Is a relationship between the production and the factors of production. Production functions have been extensively used by economists in the theory of firms. Leantlef has utilized production func- tions in economic planning and forecasting 4. Solow in growth theory Smith in production planning 6, and Arrow in investment and return appli- cations7. One of the most thorough studies involving research and devel- opment is due to Mansfield 8.

Most empirical studies made In Lite area of production functions can be classified according to the following two types: a linear Leontief type input-output function,

North Carolina State University Page 1 Dec 31, 1978

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OPTIMAL CONTROL, LINEAR PROGRAMMING, AND GOAL PROGRAMMING TECHNIQUES IN AN INTEGRATED

PRODUCTION PLANNING

(Equation Omitted)

and a nonlinear Cobb Douglas type futictiou,

(Equation Omitted)

where L and K are inputs of labor and cap...