A Robust Joint Optimal Pricing and Lot-Sizing Model

The problem of jointly determining a robust optimal bundle of price and order quantity for a retailer in a single-retailer, single supplier, single-product supply chain is considered. Demand is modeled as a decreasing power function of product price, and unit purchasing cost is modeled as a decreasing power function of order quantity and demand. Parameters defining the two power functions are uncertain but their possible values are characterized by ellipsoids. We extend a previous study in two ways; the purchasing cost function is generalized to take into account the economies of scale realized by higher product demand in addition to larger order quantity, and an exact transformation into an equivalent convex optimization program is developed instead of a geometric programming approximation scheme proposed in the previous study.