Selecting supply contracts is crucial for companies as major costs are involved in purchasing raw materials. For some companies up to 70% of the cost is from purchasing and therefore it is vital to the competitiveness of most companies to reduce the costs of such purchasing. For example, in refinery major cost is involved in purchasing crude. With the increase in global competition, companies are constantly pressurized to reduce costs and increase efficiency. As a consequence, selecting right contracts with right suppliers is very important. Contracts come in various shades of price, reliability, flexibility, durations, lead time, quality, discounts, terms and conditions, product bundling, etc hence selecting contracts is a nontrivial problem for many companies. Shah (2005) identifies negotiation of long term supply contracts as a common supply chain problem.

A contract is an agreement between a buyer (company) and a supplier for a fixed duration which comprises certain terms and conditions. The purpose of this commitment is to balance between flexibility for the buyer and reduction of the uncertainty for the supplier. Let's say that the company has a long term contract which is reliable but signed on a higher cost and the open market is offering a low price. On the other hand, there may be situations in which there is a long term contract on low cost but the open market price is high. Factors which complicate contract selection problem are the constraints of the contracts like contract length, minimum quantity commitment, price, quality, capacity, etc. There is a trade off among different criteria and hence selecting the right combination of these criteria is a challenging problem. Tsay et. al. (1999) reviewed supply chain contracts and classified the literature by contract clauses such as specification of decision rights, pricing, minimum purchase commitments, quantity flexibility, buyback or returns policies, allocation rules, lead time, and quality.

The objective of the current paper is to develop a model that provides company (buyer) with the ability to analyze different types of contracts and select multiple contracts in an integrated manner in order to make global decisions. Here we have considered optimal cost as the decision criterion. This approach is more meaningful when a relatively large number of suppliers are available, each offering a different type of contract and some suppliers act as open suppliers (spot market). In this case, the company may be interested in selecting one or multiple contracts depending upon the demand so as to reduce the overall cost. In this paper, we propose a model for selecting contracts considering different aspects such as contract length, price, discounts, transportation costs, product bundling, minimum quantity commitments, minimum dollar volume purchase commitments, etc. We have proposed a model in which different types of contracts can be analyzed and optimized. We focus on a multi-period environment with product bundling discount, tier pricing, spot market and inventory holding costs. We have modeled three types of contracts:

1) Total minimum quantity commitment with flexibility: Here, the commitment is on the quantity of purchases over the contract length. These contracts offer flexibility for the buyer. If the buyer decides to buy less than the committed amount, then they pay the normal price instead of the discounted price, and they may have to pay the penalty for not fulfilling the commitment.

2) Minimum quantity commitment at every time period: We have considered minimum quantity commitment contracts in every time period. The difference between total minimum quantity commitment with flexibility and minimum quantity commitment is that in the former the commitment is on the quantity for the entire contract length and company has the flexibility to buy less than the minimum quantity and pay the penalty for the remaining amount. Here, the commitment is on the minimum quantity in every time period and there is no flexibility for the company to buy less than the minimum amount.

3) Minimum dollar volume purchase commitment contracts. In this class of contracts, the buyer instead of making commitments on quantities of individual purchase items commits to a minimum dollar volume purchase for the planning horizon. The commitment is on dollars instead of quantities. Supplier offers discounts based on the dollar volume of commitment.

Even if the contracts are of the same class, they may have different features like different contract length, different normal and discounted price, different quantity commitment in case of minimum quantity commitment type contracts, different dollar commitment in case of minimum dollar volume purchase commitment type of contracts. Hence, analysis of contracts is very important for optimal cost before selecting any contracts. We have also considered spot market since this is also a source of supply. Some suppliers propose contract which have more than one material and hence offer product bundling discounts to persuade buyer to buy from them. Rosenthal et al. (1995) studied supplier selection problem and examined relationships among different bundling scenarios and found that the most general scenario is the one in which free items are given to the buyer when sufficient quantities are purchased. Giving free items as bundling discount is not practical in chemical market, so we have modeled product bundling discount as an additional discount instead of giving free items.

We have modeled using a mathematical programming approach and formulated the problem as multi-period mixed integer linear programming (MILP) based on uniform discrete time representation. We have solved problems in which there are 10 contracts of different class providing two materials for a company which has 3 plant sites. This small problem has 519 binary variables and 1651 continuous variables and shows 24.46% profit in selecting contracts instead of buying from the open market. We are also trying to solve some big problems with 30 contracts of different classes, 10 raw materials and company having more than 10 plant sites. In these cases, we have more than 10981 binary variables. We will report our experience with such large problems.

Key words: Supply Contracts; Procurement; Supply Chain Optimization

References: Rosenthal, E.C., Zydiak, J.L., Chaudhary, S.S., 1995. Vendor Selection with Bundling. Decision Sciences Volume 26 Number 1, 35-48.

Shah, N., 2005. Process industry supply chains: Advances and challenges. Computers and Chemical Engineering 29 (2005) 1225-1235.

Tsay, A.A., Nahmias, S., Agrawal, N., 1999. Modeling supply chain contracts: a review. In: Tayur, S., Ganeshan, R., Magazine, M. (Eds.), Quantitative Models for Supply Chain Management. Kluwer Academic Publishers, Dordrecht, pp 300-336.