Procurement decisions over multiple periods under piecewise-linear shortage costs and fixed capacity commitments

Abstract We study optimal procurement in a case where the buyer must match supply against uncertain demand using combination of low-cost order-in-advance contracts and high-cost real-time balancing mechanism. The have two-level structure which commitment to procure fixed quantity for multiple periods has lower unit-price than period-specific commitments. Moreover, mechanism implies salvage value unused piecewise-linear shortage costs: small shortages (relative total procured) are balanced with unit cost larger shortages. Minimizing costs results stochastic non-linear multivariate optimization problem, can be interpreted as generalization classic newsvendor model. derive optimality conditions this problem show how they utilized obtain minimizing strategy by solving series single variable equations. model is then applied support decision making pulp & paper company that procures natural gas worth tens millions euros annually. This allows us highlight some key practical implications our work.