You have signed a consignment contract to supply a chemical compound to a major customer. 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 2,000 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 $0.325/gallon/day short. Inventory carrying cost is 0.20 $/$/year.

a. Determine the optimal (s, Q) policy, assuming a stochastic lead time, L = 30 days, standard deviation of lead time = 6.

b. Your customer has realized that controlling the stockout charge is too burdensome. Two alternative charges have been proposed:

i. A flat charge of $1,000 per stockout occasion.

ii. A $65 charge per gallon short per cycle.

Under each alternative, what would your policy be? Are the proposed changes acceptable?