# Question

Jed Walker is the manager of Have a Cow, a hamburger restaurant in the downtown area. Jed has been purchasing all the restaurant’s beef from Ground Chuck (a local supplier) but is considering switching to Chuck Wagon (a national warehouse) because its prices are lower.

Weekly demand for beef averages 500 pounds, with some variability from week to week. Jed estimates that the annual holding cost is 30 cents per pound of beef. When he runs out of beef, Jed is forced to buy from the grocery store next door. The high purchase cost and the hassle involved are estimated to cost him about $3 per pound of beef short. To help avoid shortages, Jed has decided to keep enough safety stock to prevent a shortage before the delivery arrives during 95 percent of the order cycles. Placing an order only requires sending a simple fax, so the administrative cost is negligible.

Have a Cow’s contract with Ground Chuck is as follows: The purchase price is $1.49 per pound. A fixed cost of $25 per order is added for shipping and handling. The shipment is guaranteed to arrive within 2 days. Jed estimates that the demand for beef during this lead time has a uniform distribution from 50 to 150 pounds.

The Chuck Wagon is proposing the following terms: The beef will be priced at $1.35 per pound. The Chuck Wagon ships via refrigerated truck, and so charges additional shipping costs of $200 per order plus $0.10 per pound. The shipment time will be roughly a week, but is guaranteed not to exceed 10 days. Jed estimates that the probability distribution of demand during this lead time will be a normal distribution with a mean of 500 pounds and a standard deviation of 200 pounds.

T (a) Use the stochastic continuous-review model presented in Sec. 18.6 to obtain an (R, Q) policy for Have a Cow for each of the two alternatives of which supplier to use.

(b) Show how the reorder point is calculated for each of these two policies.

(c) Determine and compare the amount of safety stock provided by the two policies obtained in part (a).

(d) Determine and compare the average annual holding cost under these two policies.

(e) Determine and compare the average annual acquisition cost (combining purchase price and shipping cost) under these two policies.

(f) Since shortages are very infrequent, the only important costs for comparing the two suppliers are those obtained in parts (d) and (e). Add these costs for each supplier. Which supplier should be selected?

(g) Jed likes to use the beef (which he keeps in a freezer) within a month of receiving it. How would this influence his choice of supplier?

Weekly demand for beef averages 500 pounds, with some variability from week to week. Jed estimates that the annual holding cost is 30 cents per pound of beef. When he runs out of beef, Jed is forced to buy from the grocery store next door. The high purchase cost and the hassle involved are estimated to cost him about $3 per pound of beef short. To help avoid shortages, Jed has decided to keep enough safety stock to prevent a shortage before the delivery arrives during 95 percent of the order cycles. Placing an order only requires sending a simple fax, so the administrative cost is negligible.

Have a Cow’s contract with Ground Chuck is as follows: The purchase price is $1.49 per pound. A fixed cost of $25 per order is added for shipping and handling. The shipment is guaranteed to arrive within 2 days. Jed estimates that the demand for beef during this lead time has a uniform distribution from 50 to 150 pounds.

The Chuck Wagon is proposing the following terms: The beef will be priced at $1.35 per pound. The Chuck Wagon ships via refrigerated truck, and so charges additional shipping costs of $200 per order plus $0.10 per pound. The shipment time will be roughly a week, but is guaranteed not to exceed 10 days. Jed estimates that the probability distribution of demand during this lead time will be a normal distribution with a mean of 500 pounds and a standard deviation of 200 pounds.

T (a) Use the stochastic continuous-review model presented in Sec. 18.6 to obtain an (R, Q) policy for Have a Cow for each of the two alternatives of which supplier to use.

(b) Show how the reorder point is calculated for each of these two policies.

(c) Determine and compare the amount of safety stock provided by the two policies obtained in part (a).

(d) Determine and compare the average annual holding cost under these two policies.

(e) Determine and compare the average annual acquisition cost (combining purchase price and shipping cost) under these two policies.

(f) Since shortages are very infrequent, the only important costs for comparing the two suppliers are those obtained in parts (d) and (e). Add these costs for each supplier. Which supplier should be selected?

(g) Jed likes to use the beef (which he keeps in a freezer) within a month of receiving it. How would this influence his choice of supplier?

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