Theoretically, any equipment replacement decision would be made based on thorough modeling equipment deterioration and projected remaining life. Practical approaches to equipment replacement decisions are mostly based on subjective appraisal. But it is generally accepted that tools for equipment replacement decision create important element of repair/replacement policy. Such a policy provides guidance to production and economic manager regarding when to replace existing equipment or its part; how to conduct the acquisition process; and what should be done with the equipment being replaced. Then, the main importance of developing of equipment replacement decision models in production planning consist in establishing rules for the replacement of old equipment or its part(s) by new. The main problem of establishing the rules is to find decision variables that minimize total incurred costs over a planning horizon (Dehayem Nodem et al 2009). Basically, the rules differ depending on what type of production type is used. For batch production organizations suitable criteria are built on the principle of economies of scale, where the large fixed costs of production are depreciation-intensive because of huge capital investments made in high-volume operations and are spread over large production batch sizes in an effort to minimize the total unit costs of owning and operating the manufacturing system (Sullivan, 2002). When solving equipment/parts replacement problem within a flexible manufacturing cell, it is necessary to consider the impacts of the replacement decisions on all of the components of the system. Therefore, possible equipment stoppages due to wrong decision results at least in diminishing capacity or stopping the operations in a manufacturing cell. Accordingly, proposed methods are dedicated for a multiple machine replacement problem that is also characterized as a flexible flow shop problem. A parallel flow shop production concept is consisting of a number of production lines. Jobs in such work shop may be composed of a series of works, each requiring several machines (Jianhua and Fujimoto, 2003).
Firstly we will model a simple case multiple machine replacement problem that is characterized for a parallel flexible flow shop environment, in which no technological improvement in equipment is in concern. Then we will consider the more complicated case where we also take account of technological improvement.