A discrete time optimal control model with uncertainty for dynamic machine allocation problem and its application to manufacturing and construction industries

This paper proposed a discrete time optimal control model in which machine failure time is modeled assuming a Weibull distribution and machine productivity is regarded as a fuzzy variable for dealing with a dynamic machine allocation problem (DMAP) in manufacturing and construction industries. The aim is to maximize total production or construction throughput when uncertainties such as machine breakdowns are taken into account. A failure probability-work time equation is presented to describe the relationship between machine failure probability and mean time to work. To transform the uncertain optimal control model into a deterministic one, the expected value model (EVM) was introduced for forming an equivalent crisp model. The fuzzy variables in the model are also defuzzified by using an expected value operator with an optimistic–pessimistic index. Then a number of lemmas and theorems are presented and proved to formulate the theoretical algorithm so that the crisp model of the DMAP can be solved. Three actual construction and production projects are used as practical application examples. The theoretical algorithm results for the three project examples are compared with a particle swarm optimization approach and a genetic algorithm method, which demonstrates the practicality and efficiency of our optimization method.