Analysis of supply contracts with total minimum commitment

Abstract

In this paper we analyze a supply contract for a single product that specifies that the cumulative orders -placed by a buyer, over a finite horizon, be at least as large as a (contracted upon) given quantity. We assume that the demand for the product is uncertain, and the buyer places orders periodically. We derive the optimal purchase policy for the buyer for a given total minimum quantity commitment and a discounted price. We show that the policy is characterized by the order-up-to levels of the corresponding finite horizon and a single-period standard newsboy problem with no commitment but with discounted price. We show that this policy can be computed easily. We can use this to evaluate any discount schedule characterized by a set of (price discount, minimum commitment) pairs.

Retailer-Supplier Flexible Commitments Contracts: A Robust Optimization Approach

“…In Bassok and Anupindi (1997), the authors specify a model in which the buyer commits to purchasing at least a given total quantity of a single product over a finite time horizon. The model specifies an additional volume that is also available at the same price and a higher price is charged for any quantity larger than that volume.…”

“…The upper bound is generated by maximizing the probability of being able to raise the inventory in each period to the base stock level (as obtained by the newsvendor solution). For the T -period RSFC problem with minimum total commitments, Bassok and Anupindi (1997) showed that the optimal policy is given by T critical numbers, consisting of T order-up-to levels S 1 S 2 S T and an additional order-up-to level S M that corresponds to a single-period newsvendor problem with zero purchase costs. Until the minimum commitment is met (say, at period t), the retailer orders according to S M , and from that period onward he orders according to S t−1 S 1 .…”

Capacity Planning in the Semiconductor Industry: Dual-Mode Procurement with Options

“…Also see Wu et al (2005) for a review of the literature on capacity planning in the high-tech industry. DMEP is also closely related to the literature on procurement and option contracts (e.g., Bassok andAnupindi 1997, Vaidyanathan et al 2005). In particular, the reservation stage of DMEP builds on the paper by Vaidyanathan et al (2005), which focuses on capacity contracts at Intel and discusses capacity options to better enable factory ramps.…”

Multi-period supplier selection under price uncertainty

“…When the demand is stochastic, existence of a contract with volume discounts entangles the inventory decisions of a buyer. For example, see Bassok and Anupindi (1997) who analyse a supply contract of a single product in which the cumulative orders over multiple periods should be larger than a prespecified quantity in order to qualify for a discount. The authors extend their work (Anupindi and Bassok, 1998) to the case of multiple products with business volume discounts.…”