Production and Inventory Control for a Make-to-Stock/Calibrate-to-Order System with Dedicated and Shared Resources

Consider a firm that produces multiple products on dedicated production lines (stage 1), which are further customized/calibrated on a shared resource (stage 2), common to all products. The dedicated production lines and the shared resource for calibration face capacity uncertainties. The firm holds inventory of products that are not yet calibrated and carries out calibration when an order is received. We analyze a multiperiod inventory model for two products and derive the optimal production policy at stage 1 as well as the optimal allocation of the shared resource to demands at stage 2. For the shared resource, because of its capacity uncertainty, not only the total planned production quantities matter, but also the sequence in which the products are processed. We characterize the optimal allocation of the shared resource and show that the optimal policy keeps the ending inventories of products as close to a so-called “ target path ” as possible. For the dedicated production lines, because of their capacity uncertainty, the optimal production policy depends on the initial inventories. We identify and characterize the structural properties of the optimal production policy. Through a numerical study, we explore how the presence of finite shared capacity influences the inventory targets. We find that the behavior may be counterintuitive: when multiple products share a finite capacity in stage 2, the inventory target for the product having a larger dedicated production capacity or less capacity variability in stage 1 can be higher than the other product. We finally provide sensitivity analysis for the optimal policy and test the performance of simple heuristic policies.