Question

Sweet Endings 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.

1. Assuming ROP is used, calculate the level at which Sweet Endings should reorder. What is the best estimate for days of supply are on-hand at this point?   
2. 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 Sweet Endings runs out before this order is received?
3. 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%