Optimal fuzzy scheduling and sequencing of multi-phase sample tests at third-party laboratories

This research proposed optimization models for fuzzy scheduling and sequencing multi-phase sample tests over multiple periods for preparation and testing stages in testing in third-party laboratories. In the preparation phase, sample tests were assigned to multi-skilled technicians at workshops. In the three-stage testing phase, tests were assigned to multi-skilled inspectors at laboratories. The scheduling model aimed at minimizing the total delay time, idle time, and overtime in all workshops and laboratories, maximizing the number of scheduled tests. Moreover, the model aims to maximize both the satisfaction on the sample completion dates, which were expressed by a fuzzy membership function, and maximizing the partial completion of samples. The sequencing model aimed to minimize the total overtime in workshops and laboratories and minimize the sum of test finish times. A real firm that offers testing services in four laboratories and three workshops was provided to illustrate the developed models. Fifty distinct samples of 10 distinct types with a total of 125 tests were considered. Results revealed that the optimal schedule and sequence of sample tests efficiently maximized the number of scheduled tests at minimal total costs. Further, a comparison between the optimal results from the multi-objective model with those from a single objective model that only minimized the total costs was conducted. Results showed that the maximization of satisfaction on samples and partial completion of samples resulted in larger costs than that with a single objective model. Despite that, meeting customer satisfaction enables testing laboratories gain a competitive advantage. In conclusion, the proposed models provide great assistance in developing an optimal plan for testing activities to save costly testing resources and maximize satisfaction on sample deliveries.