A multi-machine multi-product EPQ problem for an imperfect manufacturing system considering utilization and allocation decisions

This paper considers a multi-machine multi-product EPQ problem in an imperfect manufacturing system.The multi-machine multi-product EPQ problem is formulated as a mixed integer non-linear programming.A hybrid genetic algorithm (HGA) is proposed in order to solve the optimization problem.A numerical experimentation and a sensitivity analysis of the model are done. This paper considers a multi-product problem with non-identical machines. This manufacturing system consists of various machine types with different production capacities, production costs, setup times, production rates and failure rates. One of the major issues in the planning phase of a manufacturing system is to take the best decision about which machines must be utilized to manufacture which items. As a result, the decision makers face three critical questions: what machines must be purchased, which items should be allocated to each machine, and what is the optimal cycle length. These decisions must be made to minimize system costs including utilization, setup, production, holding and scrap costs. The multi-machine multi-product economic production quantity (EPQ) problem for an imperfect manufacturing system is formulated as a mixed integer non-linear programming (MINLP), where the convexity property of multi-product single machine EPQ model is used to convert the problem into a bi-level decision-making problem. In the first level, decisions about machine utilization and items allocation are made. After, in the second level the optimal cycle length for each machine is determined. To solve the problem at hand, a hybrid genetic algorithm (HGA) is proposed integrating genetic algorithm and derivatives method. In the proposed HGA, the solutions of the first level are obtained randomly and then, for the second level, the derivatives method is applied to obtain optimal cycle length based on solutions of the first level. Finally, the results of HGA method are compared to the results of general algebraic modeling system (GAMS) and it is found that HGA method has better and more efficient results. Also, a numerical experimentation and a sensitivity analysis of the model are done.

[1]  Earl E. Bomberger,et al.  A Dynamic Programming Approach to a Lot Size Scheduling Problem , 1966 .

[2]  S. Eilon.  Scheduling for batch production , 1957 .

[3]  R. W. Grubbström,et al.  A century of evolution from Harris׳s basic lot size model: Survey and research agenda , 2014 .

[4]  Amir Abbas Najafi,et al.  ECONOMIC PRODUCTION QUANTITY MODEL WITH SCRAPPED ITEMS AND LIMITED PRODUCTION CAPACITY , 2010 .

[5]  Ata Allah Taleizadeh,et al.  An imperfect multi-product production system with rework , 2013 .

[6]  Mohammad Saidi-Mehrabad,et al.  Multi-product unrelated parallel machines scheduling problem with rework processes , 2012 .

[7]  V. Sridharan,et al.  A hierarchical approach for capacity coordination in multiple products single-machine production systems with stationary stochastic demands , 1995 .

[8]  Leopoldo Eduardo Cárdenas-Barrón,et al.  Celebrating a century of the economic order quantity model in honor of Ford Whitman Harris , 2014 .

[9]  Ruhul A. Sarker,et al.  A genetic algorithm for solving economic lot size scheduling problem , 2002 .

[10]  Harvey M. Wagner,et al.  Dynamic Version of the Economic Lot Size Model , 2004, Manag. Sci..

[11]  Hui-Ming Wee,et al.  Economic production quantity model with repair failure and limited capacity , 2013 .

[12]  Ruhul A. Sarker,et al.  A disruption recovery model for a single stage production-inventory system , 2012, Eur. J. Oper. Res..

[13]  Christoph H. Glock,et al.  The Lot Sizing Problem: A Tertiary Study , 2014 .

[14]  Kenneth R. Baker.  Note---On Madigan's Approach to the Deterministic Multi-Product Production and Inventory Problem , 1970 .

[15]  Thom J. Hodgson,et al.  Addendum to Stankard and Gupta's Note on Lot Size Scheduling , 1970 .

[16]  L. Cárdenas-Barrón,et al.  Multi products single machine EPQ model with immediate rework process , 2012 .

[17]  Ata Allah Taleizadeh,et al.  Multiproduct single-machine production system with stochastic scrapped production rate, partial backordering and service level constraint , 2010, J. Comput. Appl. Math..

[18]  Edward A. Silver,et al.  Finding effective schedules for the economic lot scheduling problem: A simple mixed integer programming approach , 2004 .

[19]  Hui-Ming Wee,et al.  Multi-product production quantity model with repair failure and partial backordering , 2010, Comput. Ind. Eng..

[20]  Ford W. Harris,et al.  How Many Parts to Make at Once , 1990, Oper. Res..

[21]  Donald Erlenkotter,et al.  Ford Whitman Harris and the Economic Order Quantity Model , 1990, Oper. Res..

[22]  Yuan-Shyi Peter Chiu,et al.  A note on "Determining the optimal run time for EPQ model with scrap, rework, and stochastic breakdowns" , 2007, Eur. J. Oper. Res..

[23]  S. T. A. Niaki,et al.  A multiproduct single machine economic production quantity model for an imperfect production system under warehouse construction cost , 2015 .

[24]  Rasoul Haji,et al.  Constrained single period problem under demand uncertainty , 2011 .

[25]  David E. Goldberg,et al.  Genetic algorithms and Machine Learning , 1988, Machine Learning.

[26]  Singa Wang Chiu,et al.  Determining the optimal run time for EPQ model with scrap, rework, and stochastic breakdowns , 2007, Eur. J. Oper. Res..

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

[28]  Samuel G. Davis.  Scheduling Economic Lot Size Production Runs , 1990 .

[29]  S. T. A. Niaki,et al.  Multiproduct EPQ model with single machine, backordering and immediate rework process , 2011 .

[30]  Ata Allah Taleizadeh,et al.  A deterministic multi product single machine EPQ model with backordering, scraped products, rework and interruption in manufacturing process , 2014 .

[31]  Jack D. Rogers.  A Computational Approach to the Economic Lot Scheduling Problem , 1958 .