Exact algorithms for procurement problems under a total quantity discount structure

In this paper, we study the procurement problem faced by a buyer who needs to purchase a variety of goods from suppliers applying a so-called total quantity discount policy. This policy implies that every supplier announces a number of volume intervals and that the volume interval in which the total amount ordered lies determines the discount. Moreover, the discounted prices apply to all goods bought from the supplier, not only to those goods exceeding the volume threshold. We refer to this cost-minimization problem as the total quantity discount (TQD) problem. We give a mathematical formulation for this problem and argue that not only it is NP-hard, but also that there exists no polynomial-time approximation algorithm with a constant ratio (unless P = NP). Apart from the basic form of the TQD problem, we describe four variants. In a first variant, the market share that one or more suppliers can obtain is constrained. Another variant allows the buyer to procure more goods than strict...

• Type: Journal
• Year: 2007
• Where: EOR
• Authors: Dries R. Goossens, A. J. T. Maas, Frits C. R. Spieksma, Joris van de Klundert
• Keywords: EOR 2007, So-called Total Quantity, Total Quantity Discount, Volume Interval