Multi-product production planning: A goal programming approach

Abstract Cost minimization multi-product production problems with static production resource usage and internal product flow requirements have been solved by linear programming (LP) with input/output analysis. If the problem is complicated by interval resource estimates, interval linear programming (ILP) can be used. The solution of realistic problems by the above method is cumbersome. This paper suggests that linear goal programming (LGP) can be used to model a multi-product production system. LGP's unique modeling capabilities are used to solve a production planning problem with variable resource parameters. Input/output analysis is used to determine the technological coefficients for the goal constraints and is also used to derive an information sub-model that is used to reduce the number of variable resource goal constraints. Preliminary findings suggest that the LGP approach is more cost-efficient (in terms of CPU time) and in addition provides valuable information for aggregate planning.

[1]  R. S. Stainton Production Scheduling with Multiple Criteria Objectives , 1977 .

[2]  Edward R. Clayton,et al.  A goal programming approach to multi-period production line scheduling , 1978, Comput. Oper. Res..

[3]  David A. Goodman,et al.  A Goal Programming Approach to Aggregate Planning of Production and Work Force , 1974 .

[4]  Arthur J. Keown,et al.  A Chance-Constrained Integer Goal Programming Model for Capital Budgeting in the Production Area , 1980 .

[5]  K. Lawrence,et al.  A multiple goal linear programming model for coordinated production and logistics planning , 1976 .

[6]  E. Newson Multi-Item Lot Size Scheduling by Heuristic Part I: With Fixed Resources , 1975 .

[7]  A. G. Lockett,et al.  A problem of aggregate scheduling An application of goal programming , 1978 .

[8]  J. G. Church Sure Staf: A Computerized Staff Scheduling System for Telephone Business Offices , 1973 .

[9]  E. Hannan Using Duality Theory for Identification of Primal Efficient Points and for Sensitivity Analysis in Multiple Objective Linear Programming , 1978 .

[10]  R. Fetter A Linear Programming Model for Long Range Capacity Planning , 1961 .

[11]  H. M. Wagner,et al.  Optimal Multi-Product Production Scheduling and Employment Smoothing with Deterministic Demands , 1975 .

[12]  J. S. H. Kornbluth,et al.  Duality, Indifference and Sensitivity Analysis inr Multiple Objective Linear Programming , 1974 .

[13]  Ulf Peter Welam Note---Comments on Goal Programming for Aggregate Planning , 1976 .

[14]  Bernard W. Taylor,et al.  Goal programming approach to marketing/ production planning , 1979 .

[15]  John C. Fisk,et al.  Production Scheduling for High-Volume Assemblies -- A Case Study , 1980 .

[16]  Allen L. Soyster,et al.  Technical Note - Convex Programming with Set-Inclusive Constraints and Applications to Inexact Linear Programming , 1973, Oper. Res..

[17]  David J. Thuente Technical Note - Duality Theory for Generalized Linear Programs with Computational Methods , 1980, Oper. Res..

[18]  J. G. Madigan,et al.  Scheduling a Multi-Product Single Machine System for an Infinite Planning Period , 1968 .

[19]  T. R. White,et al.  Practical Applications of Linear Programming to Shell's Distribution Problems , 1976 .

[20]  Abraham Charnes,et al.  An Algorithm for Solving Interval Linear Programming Problems , 1977, Oper. Res..

[21]  V. Chandru,et al.  Inverse Optimization: An Application to the Capacitated Plant Location Problem , 1981 .