Optimal procurement strategies for contractual assembly systems with fluctuating procurement price

We consider a multi-component assembly system that produces a single end product in order to satisfy the one-time demand at a (known) future time with an exogenous selling price. Components can be outsourced from outside suppliers with positive leadtimes under either time-inflexible or time-flexible contracts. One of these components, say component 1, faces an uncertainty in its procurement price, depending on the spot market price that is governed by a geometric Brownian motion, while the prices of other components are constant. Given supply contracts, the assembler needs to determine the procurement strategy to maximize the total expected profit that equals the expected revenue minus procurement cost, holding cost, and tardiness penalty cost. Under time-inflexible contracts, the problem is static and a variant of the classic newsvendor problem. We show that leadtime uncertainty will cause the assembler to be more conservative in procurement quantity, but more aggressive in procurement timing than if the leadtime is deterministic. For time-flexible contracts, we show that under certain conditions, the original problem is equivalent to an optimal single stopping problem whose optimal strategies follow either upward or downward base-price procurement policies. Under the general condition, we propose an efficient Monte Carlo simulation method to calculate the optimal solutions. Numerical studies also provide several interesting insights: first, both procurement quantity and profit are non-monotone in the leadtime length; second, the value of time-flexible contracts compared to time-inflexible contracts is close to zero if the price of component 1 has a decreasing trend, but otherwise significant.