Allocation of Inspection Stations in a Multi-Product Serial Assembly Line With Delayed Inspection

In this study, we address an allocating inspection station problem with the inspection interval concept. That is, a number of inspection requests are released at assembly stations, so to guarantee a certain level of quality, we should cover these inspection requests as much as possible. However, based on the fact that production lines usually face capacity restrictions, we could have a possibility to postpone some portions of desired inspection requests to the later stages in an inspection interval starting at the release stage and ending at the due stage. In real case systems, however, we cannot be able to cover all inspection requests and consequently, these uninspected requests will reach customers with penalty costs. In this research, we consider this assumption to obtain a feasible solution. Thus, we can not only use the maximum capacity of the system but also define both optimal locations of inspection stations and the optimum number of performed inspection requests at each station. The main contributions of this study are threefold. First, we present an optimal inspection plan with a delayed inspection concept for a multi-product assembly line by which the manufacturer can balance inspection effort along an assembly line due to the limitation in the inspection capacity. Second, we provide mixed-integer programming for the problem with a multi-product setting in which capacity at each stage is considered. Third, a Lagrangian relaxation heuristic is developed to handle large-scale cases by providing a good lower bound.