A mass production product-to-plant allocation problem

Product-to-Plant allocations must respect the timing and forecast demand of the product introductions, limited tooling for each model, limited capacities of the plant and its subsystems, build out date of existing products and required changeover time, restrictions arising from limited changeover resources, as well as other special restrictions specific to particular plants and new products. Beyond satisfying these constraints, we would like to minimize the expected lost sales, balance the utilization among plants, and maximize the number of plants chained together by shared product. Since some productsʹ volumes require multiple lines, we also choose the volume assigned to each line supporting the same product. We enunciate this product-to-line allocation problem actually faced in the automotive industry, and provide an optimization based decision support approach.