• You have signed a contract to supply a chemical compound to a company. This compound costs you $32.50/gallon and generates a contribution of $12.50/gallon. Delivery costs you $175 in shipping and handling. Demand for this year is estimated at 2000 gallons, standard deviation is 400 gallons. The contract says that the compound is inventoried at your client’s facility: he will draw the material from that stock as needed and pay you at such time. It also says that if the client finds that inventory empty when needed, you are subject to a fee of $1.325/gallon/day short. Inventory carrying cost is 0.2 $/$/yr. 

a. (10 points) Determine optimal (s,Q) policy, assuming a lead time, L=30 days. (Find the order quantity by EOQ, and then find the reorder point.) 

b. (10 points) Assume that the firm also wants to reach a probability of no stockout in a replenishment cycle of 90%. Is it possible with the above parameters? 

c. (10 points) Your customer has realized that controlling the stockout charge is too burdensome. Two alternative charges have been proposed: 

i. A flat charge of $1000 per stockout occasion. 

ii. A $65 charge per gallon short per cycle. Under each alternative, what would your policy be? 

d. (10 points) Which of the alternatives i and ii would you choose based on the expected cost?