The deterministic multi-item dynamic lot size problem with joint business volume discount

This paper considers the multi-item dynamic lot size model where joint busi ness volume discount is applied for all items purchased whenever the total dollar value of an order reaches a certain level. Multi-item discounts are prevalent in practical applications, yet the literature has only considered limited instances of single-item models. We establish the mathematical for mulation and design an effective dynamic programming based heuristic. Compu tational results disclose our approach obtains high quality solutions that dominate the best known heuristic for the simplified one-item case, and tha t proves vastly superior to the state-of-the-art CPLEX MIP code for the mul ti-item case (for which no alternative heuristics have been devised). We ob tained significantly better solutions than CPLEX for the more complex probl ems, while running from 4800 to over 100,000 times faster. Enhanced variant s of our method improve these outcomes further.