| 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 strategies including how much to purchase and when to purchase each component.The objective is to maximize the total expected profit that equals the expected revenue minus the procurement costs,the costs of holding components prior to their assembly and penalties for tardiness posterior to the due date.Under time-inflexible contracts,we provide the optimal solutions under both certain and uncertain lead-time and further show that leadtime uncertainty will causes the assembler to be more conservative in procurement quantity,but more aggressive in procurement timing than if the leadtime is deterministic.Under time-flexible contracts,we show that the original problem is equivalent to an optimal single stopping problem when ??0 0 or ?<0 and ?L is empty,whose optimal strategies follow upward and downward base-price procurement policies,respectively,where ? is the Brownian motion drift and ?L is a set of components whose leadtime is strictly longer than that of component 1.For the setting with ?<0 and non-empty ?L,we propose an efficient Monte Carlo simulation method to calculate the optimal solutions.Numerical studies also reveal several interesting insights:First,both the procurement quantity and profit are non-monotone in the leadtime length,depending on the sign of ?.Second,the value of time-flexible contracts compared to time-inflexible contracts is close to zero when ??0,but significant when?>0. |
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