Inventory policy with uncertain demand and backorder:
1) A paint shop implements an inventory policy on its stock of white paint, which costs the store $6 per can. Monthly demand for cans of white paint is normal with mean 28 and standard deviation 8. The replenishment lead time is 14 weeks. Excess demand is back-ordered, but costs $10 per back ordered can in labor and loss of goodwill. There is a fixed cost of $15 per order, and the holding cost is based on 30% interest rate per annum. In your computations, assume 4 weeks per month.
Answer the following questions:
1.1) Write down the model name and parameters.
1.2) What are the optimal lot size and reorder points for white paint (include the formulas)?
1.3) What is the optimal safety stock (include the formula)?
2) Suppose the paint shop from the previous problem adopts a service level policy.
Answer the following questions:
2.1) What are the optimal lot size and reorder points for white paint, such that 90% of the cycles are filled without backordering (include all formulas)?
2.2) What is the fill rate corresponding to the reorder policy computed in the previous part (include all formulas)?
3) Suppose the paint shop from the previous problem adopts an (s,S) policy based on monthly reviews of its inventory instead of a continuous review. Orders are made at the beginning of each month and lead times are zero. The demand in the months January to June was 37, 33, 26, 31, 14, 40, respectively, and the starting inventory in January was 26 cans.
Answer the following questions:
3.1) Based on the (Q,R) solution you found in problem 2, what are the corresponding (s,S) values?
3.2) Under the (s,S) policy you found, what is the order size in each of the months (January to June)?