An Application of Goal Geometric Programming to Equipment Replacement Under Fuzziness

Abstract

This paper presents an investigation of equipment replacement policy problem using an approach which solve geometric programming problems with fuzzy parameters and fuzzy goals. Almost all types of equipment are subject to deterioration over time through age and usage and therefore decisions regarding the need for replacement and cost reduction are required. Such an analysis is based on existing functional relationships between costs (overhaul, replacement, and operating costs) and predictor variables (replacement, overhaul, and inspection intervals). Replacement strategies are directly connected with deterioration and its permanent dynamic changes. Deterioration is continuously subjected to influence of many factors that cannot always be predicted by company engineers and experts. As a result the optimisation model is based on uncertain of data as well as target values and model parameter values are usually specified by experts, which implies for subjectivity. The approach adopted here solves a series of multiobjective linear programming problems in order to build fuzzy regression models to represent such responses. The obtained geometric programming problem with fuzzy parameters is completed with fuzzy target values of the cost objective function. Deterministic transformation of the model as well as its computational treatment are considered.