Modeling take-or-pay contract decisions

Long-term purchase contracts for natural resources, such as natural gas, often contain take-or-pay provisions that penalize the buyer for not purchasing (taking) a minimum quantity of output over some period of time. In some contracts for a limited time interval, known as the make-up period, the penalty payments can be credited against future ‘takes’ in excess of the take-or-pay level. Additionally, options to ‘buy down’ or ‘buy out’ existing contracts, or to initiate new contracts, may exist. The purchaser, faced with projected requirements over some planning horizon, must determine purchase levels from a selected set of take-or-pay contracts so as to minimize purchase, inventory holding, penalty costs, contract initiation, and buy-out or buy-down costs. This paper presents a mixed-integer programming model of take-or-pay decisions with and without make-up provisions.