1. Coffins ‘R Us

Coffins ‘R Us produces and sells pine and mahogany coffins to mortuaries. Demand is high and constant at 6,000 pine coffins and 12,000 mahogany coffins annually. An average coffin is comprised of 15 board feet of wood. Coffins ‘R Us buys both types of wood from a single supplier.

Igor, the head of purchasing, has heard that you are an expert at determining lowest cost inventory replenishment policies and has asked for your help. He estimates the ordering cost to be $42 and the inventory holding cost to be $2.00 per year per board foot of wood. (Note: these two cost figures apply to both products.)

(a) Compute the optimum order sizes for pine and mahogany wood, separately, in terms of board feet per order.

(b) Igor tells you that if he can combine orders for both types of wood into one weekly aggregate order (assume 50 weeks per year), it would still only cost $42 for each combined order. The variable per-board item cost will not change. If orders are placed weekly, then what is difference in the total annual procurement related cost between Igor's new policy and the policy calculated in (a)?

2.

Consider a retailer who sells UNC T-shirts. Their highest sales occur on the day of the first UNC-Duke basketball game in the Spring semester and they have special T-shirts made for that game with the date of the game printed on the T-shirts (March 5, 2016). Due to the long manufacturing and delivery lead times, the company must place orders for the T-shirts by mid-January. The company believes that the demand for UNC-logoed T-shirts will be normally distributed with mean 800 and standard deviation 300 and will fetch a price of $20. The retailer pays $7 per T-shirt to the T-shirt manufacturer and it costs $2 to get one T-shirt to the Chapel Hill store. The retailer sells any unsold T-shirts at a different, off Franklin Street store at a price of $6 and pays $1 per unsold T-shirt for the transfer between stores. How many T-shirts should the retailer order in mid-January (reordering is not possible)?

3. A tablet manufacturer is selling two popular models through two different retailers. Model 1 is exclusive to retailer A and model 2 is exclusive to retailer B. The manufacturer estimates that the annual demand for model 1 is normally distributed with mean 50,000 and standard deviation 10,000, whereas the annual demand for model 2 is normally distributed with mean 60,000 and standard deviation 12,000. It takes three days for the manufacturer to send a shipment of tablets to either retailer. The manufacturer is continuously monitoring inventory at both retailers and aims to achieve a cycle service level (probability of no stock-out) of 98% at both retailers. Assume that 1 year = 365 days and NORM.S.INV(0.98) = 2.054.

a. The tablet manufacturer currently carries separate pools of safety stock for models 1 and 2. Calculate the total number of tablets they should carry in safety stock under this policy.

b. One unit of model 1 costs $500 and one unit of model 2 costs $700. Compute the total annual cost of holding safety stock if the manufacturer carries separate pools of safety stock for models 1 and 2. The tablet manufacturer incurs an annual holding cost rate of 15%