Data Research, Vol. 2, Issue 1, Feb  2018, Pages 33-42; DOI: 10.31058/ 10.31058/

A Mixed-Integer Lexicographic Goal Programming Model for Achieving Estimated Targets in Multi-Product Systems

Data Research, Vol. 2, Issue 1, Feb  2018, Pages 33-42.

DOI: 10.31058/

Iwuji, Anayo C 1 , Acha, Chigozie K 1*

1 Department of Statistics, Michael Okpara University of Agriculture, Umudike, Abia State, Nigeria

Received: 3 January 2018; Accepted: 20 January 2018; Published: 7 March 2018

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Multi-product systems, mostly business entities, are often faced with the challenge of achieving several target goals within a given period of time which are often conflicting and not measurable in same units. Even as it is most times impossible for such conflicting goals to be entirely optimally achieved, effort is made to minimize deviations from the estimated target of such goals. Priorities are sometimes also given to these goals such that the compromised solution obtained minimizes the deviation from these estimated targets according to a given prioritized order of importance. The Lexicographic Goal Programming technique is an appropriate method for solving such problems.  In this paper, we present a Mixed-Integer Lexicographic Goal Programming model for minimizing deviations from estimated target of goals set by multi-product systems. To demonstrate the model, we focused on a multi-product production company (Nigerian Breweries PLC) and developed a Mixed-integer lexicographic model based on the monthly targets established by one of the production factories of the company for the year 2016. The goals considered include the estimated monthly profit target, monthly production target of each of the drinks (Star, Gulder, Maltina, Goldsberg, 33 Export and Fayrouz), estimated machine production time and estimated target distribution cost. These goals were categorized into three priority levels with the second priority normalized. The LINGO Optimization software was used to obtain the satisfactory solution based on the collected data. The result obtained showed that all the target goals were met. This shows that the Mixed-integer Lexicographic goal programming model is an appropriate technique for solving multi-objective problems in multi-product systems.


Multi-Product, Programming, Mixed-Integer, Lexicographic Model, Minimization


© 2017 by the authors. Licensee International Technology and Science Press Limited. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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