Process flexibility and the chaining principle in lot sizing problems

We analyse the value of process flexibility in the context of a short-term deterministic lot sizing problem with backlogging, where several types of products can be made on several alternative resources. It may be very costly in practice to install resources that have complete flexibility. Therefore, it might be interesting to only implement a limited amount of flexibility so that each resource can produce only certain types of items. The flexibility decision is taken at the start of the horizon. In order to study the value of such process flexibility, we perform several analyses. First, for a standard formulation we analyse the benefits of a long chain configuration and compare this to several other configurations (such as the case with no flexibility, clustered flexibility and complete flexibility). To further analyse the benefits of the long chain, we propose a new model to determine the best long chain (given that many alternative long chain configurations exist with a different total cost). Second, we propose a new optimization model that considers the possibility of investing in flexibility and determines the best flexibility configuration for a given budget. Our computational results show that almost all benefits of process flexibility are found by adding a limited number of links, but not necessarily according to the chain principle. Further analyses also indicate that backlog cost heterogeneity, demand heterogeneity and the presence of setup times have a large impact on the value of flexibility.