Question

Modified from textbook: SweetEndings is a shop open 7 days a week. Demand for Chocolate Frozen Yogurt* can be approximated by a normal distribution with a mean of 21 gallons/wk and a standard deviation of 3.5 gallons/wk. The manager wants a 90% service level, and lead time is 2 days.

a) Assuming ROP is used, calculate the level at which SweetEndings should reorder. What is the best estimate for days of supply are onhand at this point?

b) If FOI is used instead with a 10-day order interval, • how much should be reordered if there is 8 gallons on-hand, assuming we must order in 1 gallon increments? • What is the chance SweetEndings runs out before this order is received?

c) If ROP is used and if the manager gets a call from the Yogurt supplier a day after placing the order (and after 2 more gallons have been sold) that the order will be late. • What is the chance she runs out if the order is 1 day later than planned? • What the order arrives 2 days later than planned?

Answer 1

Reorder point = demand during lead time + Safety stock

= 2/7 x21 + z xSD x( LT)^0.5

= 6+ 1.28x3.5 x(2/7)^0.5 = 8.39

If ROP of 8 is used, the days of supply = 8/consumption per day = 8/3 =2.66 days

If actual point 8.39 gallons is used, the days of supply will be 8.39/3 =2.8 days

b. For fixed order interval, the order up to level is

demand during ( lead time + review time) + zxSD x ( LT+RT)1/2

= 21 x( 12/7) + 1.28x3.5x ( 12/7)^0.5

Order up tol level = 36+5.86 = 41.86 gallons

Since 8 gallons are already on hand, the order size = 42-8 =34 gallons.

c. Since the safety stock will be depleted by 2 gallons ( when the order comes one day late),

safety stock = 2.39-2 = 0.39

z x3.5x( 2/7)^0.5 = 0.39

which gives z = 0.2084

which gives a service level of 0.583

Hence the chances of stockout in this option will be 0.417 or 41.7%

If the order arrives 2 days later than planned, and assuming that on next day 3 gallons ( as per average ) are sold, the safety stock is now 2.39-(2+3) = -2.61

Now z = -1.395

which gives a service level of 0.081

chances of stockout is now 1-0.081 =0.919 = 91.9%.

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