Question

In: Operations Management

A discount appliance store sells iPhones. The store purchases iPhones at a price of $95 per...

A discount appliance store sells iPhones. The store purchases iPhones at a price of $95 per unit. The following information applies to this product.

  • Demand = 20 units/day
  • Order cost = $56/order
  • Annual holding cost = 25% of purchase price
  • Desired cycle-service level = 90%
  • Lead time = 10 days
  • Standard deviation of daily demand = 4 units
  • Current on-hand inventory 220 units, with no open orders or back orders

The store operates 52 weeks per year, 6 days per week. It has a continuous inventory review system.

  1. What is the annual cost saved by shifting from the 500-unit lot size to the EOQ?

Suppose that the discount appliance store uses a P system instead of a Q system. They order inventory every 12 days.

  1. What should T be?
  2. How much more safety stock (than with a Q system) is needed?
  3. It is time for the periodic review. How much should be ordered?

Solutions

Expert Solution

a.

Unit Cost P = 95

Daily Demand d = 20 units

Annual Demand D = 20*52*6 = 6240

Ordering cost S = 56

Holding cost H = 25%*95 = 23.75

SD of daily demand = 4 units

Service Level = 90%

Z = 1.28

Lead Time L = 10 days

On hand Inventroy = 220 units

EOQ = (2DS/H)^(1/2)

EOQ = (2*6240*56/23.75)^(1/2)

EOQ = 171.54

EOQ = 172 units

Total Cost at Q = (D/Q)*S + (Q/2)*H + P*D

Total Cost (Q=172) = (6240/172)*56 + (172/2)*23.75 + 6240*95 = 596874.13

Total Cost (Q=500) = (6240/500)*56 + (500/2)*23.75 + 6240*95 = 599436.38

Saving in Cost = 599436.38 - 596874.13 = 2562.25

_____________________________________________________________________________

Review Period = 12 days

T = d*(L + Review Period) + Z*SD of daily demand*(L+Review Period)^(1/2)

T = 20* (10+12) + 1.28*4*(10+12)^(1/2)

T = 464.01 units

T = 464 units

b.

Safety Stock with Q System = Z*SD of daily demand*(L+Review Period)^(1/2)

SSq = 1.28*4*10^(1/2)

SSq = 16.19 = 16 units

Safety Stock with P System = Z*SD of daily demand*(L+Review Period)^(1/2)

SSp = 1.28*4*(10+12)^(1/2)

SSp = 24.01

SSp = 24 units

Increase in Safety Stock = 24 - 16 = 8 units

c.

Order Quantity Q = T - On Hand Inventory

Q = 464 - 220

Q = 244 units

keosha answered 3 months ago
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