Lead time and quantity decision in assembly system with spot market

A two-stage assembly system is considered. An assembler procures associated component parts and assembles final products to fulfill a random quantity of demand. The final product must be delivered in a certain time; otherwise a delay cost is incurred. Lead times of the components are independent stochastic variables. And, in our model except regular channels from which the components is procured before the demand reason, components spot markets exist for the need when ordered quantity is not enough. That is, we consider random demand quantity and random operation times at the same time in an assembly system with components spot market. The objective is to minimize the total expected cost. We investigate the structure of optimal operation time plan and quantity decision. The analytical and heuristics numerical result manifest some management insights of the system.