Stockpiling and resource allocation for influenza preparedness and manufacturing assembly

Stockpiling resources is a pervasive way to handle demand uncertainty and future demand surges. However, stockpiling is subject to costs, including warehousing costs, inventory holding costs, and wastage of expired resources. Hence, how to stockpile in an economically efficient manner is an important topic to study. Furthermore, if the inventoried supply is insufficient for a surge in demand, how to best allocate available resources becomes a natural question to ask. In this dissertation, we consider three applications of stockpiling and resource allocation: (i) we stockpile ventilators both centrally and regionally for an influenza pandemic; (ii) we allocate limited vaccine doses of various types to target populations for an influenza pandemic; and, (iii) we investigate inventory needs for low cost, high usage (class C) parts in an engine assembly plant. First, we describe and analyze a model for estimating the number of ventilators that the Texas Department of State Health Services (DSHS), and eight health service regions in Texas, should stockpile for an influenza pandemic. Using a probability distribution governing peak-week demand for ventilators across the eight health service regions, an optimization model allows investigation of the tradeoff between the cost of the total stockpile and the expected shortfall of ventilators under mild, moderate, and severe pandemic scenarios. Our analysis yields the surprising result that there is little benefit to DSHS holding a significant stockpile, even when those centrally held ventilators can be dispatched to regions after observing the peak-week demand realization. Three factors contribute to this result: positively correlated regional demands, a relatively low coefficient of variation, and wastage of the central stockpile once it is dispatched to the regions. Second, we formulate an optimization model for allocating various types of vaccines to multiple priority groups in 254 counties in the state of Texas that DSHS can use to distribute its vaccines for an influenza pandemic. For reaching the public, vaccines are allocated to the state’s Registered Providers (RPs), Local Health Departments (LHDs), and Health Service Regions (HSRs). The first two allocations are driven by requests from RPs and LHDs while HSR allocation is at DSHS’s discretion. The optimization model aims to achieve proportionally fair coverage of priority groups across the 254 counties, as informed by user-specified weights on those priority groups, using the HSR doses. With proportional fairness as our primary goal, the optimal allocation also counts policy simplicity and regional equity. Sensitivity analysis on the portion of the state’s vaccines reserved for HSRs shows that a small portion can effectively shrink the gap of vaccination coverage between urban and rural counties. Finally, we derive short-cut formulae for estimating the extra inventory needed for managing class C parts in units of bins that an engine assembly plant can use to achieve a desired fill rate at workstations. The plant orders a class C part from its supplier based on the part’s aggregated next-day demand across all workstations. After receiving the part, the plant first stores the supply in the warehouse and delivers the part to workstations in bins whenever the line-side inventory at a workstation is empty. We study four cases of various information availability in the order quantity calculation and derive associated formulae for estimating the extra inventory needed due to demand aggregation and bin delivery. We demonstrate the performance of our short-cut formulae, showing the tradeoff between extra inventory needed and the associated risk of not satisfying all workstation requests. Our sensitivity analysis shows that workstation demand variation and bin size have little or no influence on the performance of our short-cut formulae.