on bottleneck product rate variation problem with batching

the product rate variation problem minimizes the variation in the rate at which different models of a common base product are produced on the assembly lines with the assumption of negligible switch-over cost and unit processing time for each copy of each model. the assumption of significant setup and arbitrary processing times forces the problem to be a two phase problem. the first phase determines the size and the number of batches and the second one sequences the batches of models. in this paper, the bottleneck case i.e. the min-max case of the problem with a generalized objective function is formulated. a pareto optimal solution is proposed and a relation between optimal sequences for the problem with different objective functions is investigated.