IE 595 – OR/MS Applications in Healthcare Fall 2014 Homework 2

Please show all your work clearly and submit individually by 5 PM on December 29th , 2014.1. Blood Banking Supply Chain – Inventory Model: A Regional Blood Center (RBC)supplies blood to two hospitals, H1 and H2, in the region. Each year, the hospitals use anaverage of 600 liters and 450 liters of Type O blood, respectively. The cost of each order placedwith the RBC is $20 for both hospitals. The lead time for each order is one week for H1 andtwo weeks for H2. The cost of holding 1 liter of blood in inventory for a year is $25 for H1 and$30 for H2. The stockout cost per liter is estimated to be $60 for H1 and $65 for H2. Annualdemand for Type O blood is normally distributed, with standard deviation of 36.05 liters forH1 and 30.59 liters for H2. Assume that there are 52 weeks in a year and that all demand isbacklogged. Determine the following for each hospital: (a) optimal order quantity, (b) reorderpoint, (c) safety stock level.Recall that the economic order quantity is dened as EOQ = 2KE(D) , where K is the orderinghcost, D is the random variable for the annual demand, and h is the holding cost per unit per year.Recall also that the reorder point should meet the following condition: P (X r ) = h(EOQ) ,cB E(D)where X is the random variable for the demand during lead time and cB is the shortage costper unit. Since the annual demand is assumed to be normally distributed,P (X r ) = P (Z r E(X) ). Therefore, the normal distribution properties can be used toXnd the reorder point, such as by using the NORMINV() function of Excel.2. Blood Banking Supply Chain – Model Formulation: Consider a blood banking supplychain with two blood collection sites, one Regional Blood Center (RBC) where all collected bloodis gathered, two component labs where the collected blood is separated into components, onestorage facility, one distribution center, and two hospitals that are the demand points. Let Dibe the random variable for the amount of blood required by the demand points, i = 1, 2, andADi be the anticipated demand for the demand points. Let ca (fa ) be the cost of operation onlink a A where A is the set of links (or arcs) in the supply chain network and xa is the owon link a. Let ui be the unit shortage cost and oi be the unit outdating cost at demand point i.Assume that no blood is wasted on the paths from the origin nodes to the destination nodes inthis network. Formulate an optimization model for the described blood banking supply chainnetwork that minimizes the total cost of operating, shortage, and outdating according to theabove notation.3. Resource Allocation for Epidemic Control: Consider a compartmental epidemic modelwhere the population is divided into two groups: Susceptible and Infected. There are two possible interventions that can be invested in to control the epidemic: Vaccination and Treatment.The investment decisions are made at the beginning of each of the T time periods. Let pjtbe the proportion of available budget (Bt ) invested in intervention j at the beginning of timeperiod t. At any time period, at most 80% of the available budget can be invested in an intervention. The instantaneous benet of intervention j in period t is measured by vjt . Let xit (P )be the number of individuals in compartment i at time t given the investment proportion vectorP = (P1 , P2 , , PT ) where Pt = (p1t , p2t ). Assume that all initial values xi0 (0) are known.Let the quality adjustment for years lived in compartment i be Qi [0, 1] and r 0 be thediscount rate. Formulate the budget allocation model that maximizes the quality-adjusted lifeyears (QALYs) based on the description above.