An outsourcing-scheduling problem in a two-stage supply chain via improved immunoglobulin-based artificial immune system

The proposed problem is inspired by final testing houses in semiconductor manufacturing. Due to outsourcing policies, several final testing houses located in different areas are selected by a customer to test their jobs. After final testing, vehicles belonging to this customer are arranged to pick up the jobs from those final testing houses. The problem can be described as a two-stage supply chain problem where the first stage is to produce jobs by several suppliers and the second stage is to transport those jobs by a number of vehicles. The objective function is to minimize makespan. A mathematical model is established to describe and define the proposed problem. A heuristic algorithm named Processing-time Supplier-speed and Transportation-time (PST) is proposed. The basic idea of PST is to arrange jobs to suppliers by an expected working loading value and then adjust the arranged jobs before transporting to decrease the idle time of vehicles. A metaheuristic algorithm, named memory B cells Immunoglobulin-based Artificial Immune System (B-IAIS) algorithm, is proposed by extending an immune system algorithm. In B-IAIS, secondary immune response is considered and the function of secondary immune response is to increase the convergence speed. To evaluate PST and B-IAIS algorithms, relative percentage deviation, percentage deviation and hypothesis test are considered in the experiments. Computational results show that B-IAIS algorithm performs better than other algorithms for solving the proposed problem.