Question

Assume an inventory control system for an independent demand item where the Lead-time is 4 days and the Review Period is 15 days. The expected demand for the end-item is 20,000 units per year.

Assume, further, that the manager wants to achieve a cycle service level of 95% in her Q system and she knows that the daily average demand is 10 units (demand is normally distributed). She has determined that her facility is open 250 days a year; her ordering cost is $50; and the holding cost is $4 per unit per year. She can assume that lead-time is 4 days; review period is 15 days; and standard deviation of daily demand is 2 units. [Round up all answers, if needed]

a) The EOQ can be calculated from the above given information.

b) The reorder point, R, cannot be calculated from the above given information.

c) The target level inventory, T, cannot be calculated from the above given information.

d) All of the above are false.

e) Only (a) and (c) are true.

Answer 1

Given Data:

Annual Demand, D = 20,000 units

Ordering Cost, S = $50

Holding Cost, H = $4 /unit/year

Average Daily Demand = 10 units

Standard deviation of Daily demand,$\sigma$ = 2 Units

Lead Time, LT = 4 Days

Review Period, RP = 15 Days

This represents the case of Periodic review system in which the inventory is brought back or replenished to the target inventory level, each time the new order is placed.

A) EOQ = $\sqrt{2DS/H}$

= $\sqrt{2*20000*50 / 4}$

= 707 Units

Thus, EOQ can be determined from the above statements. Option A is correct

B) ROP = Expected demand during lead Time + (Z*$\sigma$*$\sqrt{LT}$)

= Average daily demand * Lead Time + (Z*$\sigma$*$\sqrt{LT}$ )

= 10*19 + (1.65 * 2 * $\sqrt{4}$ )

= 197 Units   

ROP can be calculated; Option B is false.

C)

Z-Score at 95% Service Level = 1.65

Target Inventory level, T

= Expected Demand during (LT+RP) period + (Z-SCORE * $\sigma$ * $\sqrt{LT+ RP}$ )

= (Average Daily Demand)*(LT + RP) + (Z-SCORE * $\sigma$ * $\sqrt{LT+ RP}$ )

= 10* (4+15) + (1.65 * 2 * $\sqrt{4+15}$ )

= 204 Units

Thus, Target inventory level can be calculated; Option C is false.