Question

1. Richie is a bar owner and would like to determine an ordering policy for beers. He wants to use an (I, S) policy where he checks the inventory every week (I=1 week). According to the past data he collected, the following Table shows possible demand values for beer and the probability of observing this demand in one week.

   Demand	Probability
   100	0.04
   120	0.07
   140	0.08
   160	0.12
   180	0.16
   200	0.17
   220	0.13
   240	0.09
   260	0.07
   280	0.05
   300	0.02

The unit cost of beer is $2 per bottle, the price of beer is $4 per bottle and Richie pays $30 for collecting beers from the distributor every time he gives a new order. He estimates the holding cost as 20% per year.

a) Compute the service level and fill rate when Richie uses an inventory policy (I, S) where I=1 week and S = 220 bottles. Also compute the service level and fill rate when S = 260 bottles.

b) Compute the average size of an order in each case (i.e. when S=220 and when S= 260). In each case, how much inventory does Richie carry in each replenishment cycle on average? Compute the total cost of expected (inventory holding) + (stockout cost) in each case. Which of the two order-up-to levels, S=220 or S=260, makes more sense from a cost minimization perspective? (Hint: Stockout cost = Profit lost) What do you advise Richie to do?

Answer 1

First of all lets calculate the average demand based on the probabilities by multiplying probability with demand and totalling at the end

Demand	Probability
100	0.04	4
120	0.07	8.4
140	0.08	11.2
160	0.12	19.2
180	0.16	28.8
200	0.17	34
220	0.13	28.6
240	0.09	21.6
260	0.07	18.2
280	0.05	14
300	0.02	6
	1	194

So average expected demand is 194

Lets calculate service level at S=220

Service level =

194/220

88.18%

Lets calculate service level at S=260

Service level =

194/260

74.62%

As the average demand 194 is below the stocking levels of 220 and 260, Richie will rarely face stockout issues