Procurement portfolio planning for a newsvendor with supplier delivery uncertainty

We consider the problem of allocating procurement quantities for a required input to multiple suppliers in advance of a selling season with uncertain demand. Planning complexity is compounded by uncertainty in whether each supplier will deliver on time, in addition to the existence of an option for reserving capacity with a perfectly reliable supplier and the presence of a spot market for the input with an uncertain price. We apply analytical methods including two-stage stochastic programming with recourse, nonlinear optimization, and exact and efficient model-based heuristic solution methods. We show that for a selected supplier, the newsvendor's conditional service level, given that the supplier delivers on time, equals a critical ratio value determined by the supplier's cost and reliability parameters. Post-optimality analysis reveals interesting insights on the way reliability and cost parameters interact to determine whether a supplier receives a positive order allocation, as well as the impact of payment schemes on supplier selection decisions. The analysis clarifies an insightful relationship between the conditional service level and a critical ratio value for each selected supplier. The results also sharpen insights on the way relative supplier reliability and cost parameter values interact to determine an optimal supply portfolio. Furthermore, the ability to interpret a perfectly reliable supplier with a capacity reservation cost as an equivalent unreliable supplier reveals additional insights on the relative value of capacity reservation and facilitates direct comparison among seemingly disparate supply options.