The DoorRed pharmacy has twenty-five retail outlets in the Chicago region. The current policy is to carry every drug in each retail outlet. DoorRed is investigating the possibility of centralizing some of the drugs in one location. Delivery charge would increase by $0.02 per unit if a drug were centralized. The increase in delivery charge comes from the additional cost of operating the shuttle from the central location to each of the other locations. At each retail outlet, DoorRed follows a periodic review policy with weekly replenishment (a replenishment order is placed once every seven days). The replenishment lead time is three days. DoorRed plans to stick to oncea- week ordering even if a drug is centralized. DoorRed incurs an annual inventory holding cost of 20 percent and aims for a cycle service level of 99 percent. Assume that demand across stores is independent.
a. Consider a drug with daily demand at each store that is normally distributed, with a mean of 300 and a standard deviation of 50. The drug costs $10 per unit. What is the annual holding cost of safety inventory across all retail stores? If the drug were centralized in one location, what would the annual cost of holding safety inventory at the central location be? What would the annual increase in delivery charge be? Do you recommend centralization?
b. Now consider a drug with daily demand at each store that is normally distributed, with a mean of 5 and a standard deviation of 4. The drug costs $10 per unit. What is the annual holding cost of safety inventory across all retail stores? If the drug were centralized in one location, what would the annual cost of holding safety inventory at the central location be? What would the annual increase in delivery charge be? Do you recommend centralization?
c. Do your answers to (a) and (b) change if the demand across stores has a correlation coefficient of 0.5?