Question

Case Study: Managing Mollusks

Tando’s Restaurant of Virginia Beach offers one of the most varied and unusual menus in the resort city. The restaurant has acquired a fine reputation for exquisite and unique dishes and is best known for its entrees that are ethnic adaptations of sea scallops. Due to the unusual preparation of these dishes, this seafood has become the largest-selling menu item.

Tando’s does not purchase scallops locally, but receives shipments from a purveyor who serves its sister operation Tando’s of Branford Connecticut. This practice is followed for quality and price reasons. Tando’s management feels the transportation charges are minimal compared to the value derived from other factors. The New England purveyor has an established route to other local operations and is able to fill orders within three days.

Tom Gengler, one of the proprietors, has been ordering scallops by intuition. His results are dissatisfying: Tando’s experience spoilage and shortages too frequently. Tom is certain that now is a good time to reconsider his service policy and to test theoretical inventory methods as well.

Tom has spent the greater part of the week determining the cost data for the scallops and has itemized results as follows:

Annual demand= 2500 dozen

Ordering cost= $25 per order

Purchase cost= $7/dozen

Stockout cost= $3.50/dozen

Holding cost= 50% of value

Knowing the unpredictability of customers, Tom cringes at estimating daily demand. Even though scallops are a perennial favorite, demand can be erratic. Based on scanty documentation, he has constructed a table of daily demand for the scallops:

Demand (doz./day)	Frequency
6	35
7	35
8	15
9	10
10	5

Tom assumes his distribution does not differ significantly from the Poisson distribution. Considering the Poisson an adequate surrogate and stockouts as lost sales, he has found a reorder point of 16 dozen with an apparent safety stock of 3 dozen.

Questions:

1.  Assuming his inventory policy is consistent with his service policy, has Tom done a thorough and precise job?

Answer 1

Backorder cost for one dozen, Cb = 3.50
Carrying cost for one dozen, Ch = 50% of 7 = 3.5

So, the ideal in-stock probability should be Cb / (Ch+Cb) = 3.5/(3.5+3.5) = 0.50

Demand, d	Frequency	Probability, P(d)	d*P(d)
6	35	0.35	2.10
7	35	0.35	2.45
8	15	0.15	1.20
9	10	0.10	0.90
10	5	0.05	0.50
		Total	7.15

So, we can assume that the daily demand follows a Poisson distribution with mean (λ) = 7.15

So, the lead time demand (X) will follow a Poisson distribution with λ = 7.15 doz. per day x 3 days = 21.45 doz.

Generate a cumulative distribution table for X ~ Poisson (λ = 21.45) using Excel as follows:

X ~ Poisson(21.45)	F(X)	Formula
15	0.094	=POISSON.DIST(1,21.45,1)
16	0.141
17	0.199
18	0.269
19	0.348
20	0.432
21	0.519
22	0.603
23	0.681
24	0.751	=POISSON.DIST(10,21.45,1)

We realize that the in-stock probability of 0.50 is attained at X = 21

So, the appropriate reorder point should be 21 doz.

The safety stock = ROP - average lead time demand = 21 - 21.45 = -0.45 doz. So, there should be a planned shortage of 0.45 doz at every cycle.