Optimizing loading policies at a bottleneck facility in an assembly line with random rejects

The work relates to an actual loading problem at a bottleneck facility in a large refrigerator manufacturing plant. Items are loaded in specific combinations called phases which then move along different flow lines encountering random rejections till assembly. To control shortages and inventory holdings, periodically, a heuristic convex program is formulated with two forms of loss function: (a) piecewise linear and (b) quadratic. For all problem versions, the items' buffer state space admitted partitioning into polyhedral regions, with a particular form of loading policy being optimal in each region. The shapes of these regions depend on the loss function, leading to certain constraints on the parameters in the loss function. In a related paper, numerous modifications to the policies derived here take into account the actual time-varying behaviour in several elements of the system.