$3)$ SELECTING THE BEST INVENTORY POLICY AND WORKABLE PLAN

a$)$ Should the station have safety stock as a measure of precaution? If so$,$ how much.

i$)$ Note: You can simplify this analysis using the estimate where safety stock $=$ z$*\backslash$sigma D$$ where L is the lead time and z is the standard normal distribution$$s value.

ii$)$ For your inventory analysis, use a probability factor of $99\%$ that current stock will not run out.

b$)$ What is an appropriate reorder point for the three products $$ the time or level of inventory to place an order in order to avoid stockout?

i$)$ Note: Reorder point can be estimated using $($average daily demand X lead time$)+$ safety stock.

c$)$ Summarize the costs related to inventory management.

i$)$ Ordering costs $$ The supplier bears most of these costs; however, the tanker truck is owned by the fuel station. Replenishing each fuel in the inventory takes about $10$ minutes. What are the costs incurred during this time due to lost sales for the three products?

$(1)$ What is an estimate of the order cost for each product and, then, what is the combined ordering cost for all the three fuel types?

ii$)$ What are the inventory carrying costs estimated as a percentage of product costs $(10\%)$

d$)$ Based on the economic order quantity $($EOQ$)$ approach, what is the optimal order quantity for each of the three products?

i$)$ Given that only five possible quantities can be ordered, how does this constraint impact the recommended order quantity $($based on the EOQ approach$)?$

ii$)$ What are the other constraints that impact the ability to order the $$optimal$$ quantity of the three fuels?

iii$)$ How would you adjust your recommendation to have a joint order policy for all three products that meet these requirements$/$constraints$?$ State concisely an $$economic order quantity$$ policy for Agarwal$$s fuel station.

e$)$ Apply a periodic review model based on the newsvendor approach.

i$)$ What would you provide as the overage cost for the three fuels?

ii$)$ What is your estimate for the cost per unit of unsatisfied demand $($i$.$e$.,$ lost sale$)?$

iii$)$ Based on your cost estimates, what are the critical ratio values or the probability that demand is satisfied for each product during L if Q$*$ are received at the beginning of each period?

iv$)$ What would you recommend as the periodic optimal order quantity $($Q$)$ for each product?

v$)$ How do the order constraints impact this policy?