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.

Q#1. Assume that the system is perpetual inventory system. Then,

a) The expected demand during lead-time is simply the sum of daily average demand for each of 19 days constituting the lead-time.

b) We do not have sufficient information here because we do not know whether the environment is deterministic or probabilistic.

c) We can tell from the statement in (a) that the demand is deterministic.

d) We can tell from the statement in (a) that the demand is probabilistic.

e) None of the above is true.

Q#2. Assume that the system is periodic review system. Then,

a) The expected demand during the protection period is simply the sum of daily average demand for each of four days constituting the protection period.

b) We do not have sufficient information here because we do not know whether the environment is deterministic or probabilistic.

c) We can tell from the statement in (a) that the demand is deterministic.

d) We can tell from the statement in (a) that the demand is probabilistic.

e) None of the above is true.

Q#3. Assume that the system is perpetual inventory system. The lead-time remains four days, but we now also know that the standard deviation of the daily demand is 2. Which of the following is true?

a) The standard deviation of the demand during lead-time is simply the sum of the standard deviation of the demand for each day during lead-time.

b) The standard deviation of demand during lead-time is 4 days.

c) The standard deviation of demand during lead-time cannot be determined in this case because sufficient information is not available.

d) We cannot say whether the system is probabilistic or deterministic.

e) None of the above is true.

Q#4. 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. Henc

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.

Q#5. Now assume that the manager wants to achieve a cycle service level of 95% in her P system and she knows that the demand during the protection period is normally distributed. She can also assume the following: average daily demand is 10 units; ordering cost is $50.00; holding cost is $4 per unit per year; lead-time is 4 days and the review period is 15 days. Assume 250 days in a year.

a) It is possible to calculate the value of an optimal review period based on the economics of EOQ. In this case, the optimal review period turns out to be 15 days.

b) The reorder point, R, cannot be calculated from the above given information because we do not know the nature of the distribution of demand during the protection period.

c) Assuming that the distribution of demand during the protection period is normally distributed, we can calculate both the EOQ and the Target level, T, by using the P value of 15 days. But it will not yield the optimal value of T.

d) All of the above are false.

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

Answer 1

Q#1. b

Statement a is wrong, because it says lead time of 19 days, whereas lead time is 4 days only.

Statement b is right, because we do not know whether the demand is deterministic or probabilistic

Because statement b is correct, therefore, statements c,d, and e are incorrect

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Q#2. b

Protection period is sum of lead time and review period = 4+15 = 19 days. statement (a) says protection period of four says, which is incorrect. so statement (a) is incorrect.

Statement b is right, because we do not know whether the demand is deterministic or probabilistic

Because statement b is correct, therefore, statements c,d, and e are incorrect

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Q#3. b

Standard deviation of demand during lead time = square root of sum of squares of standard deviation of daily demand for each day during lead time. therefore, statement (a) is incorrect.

Standard deviation of demand during lead time = sqrt(4*2^2) = 4 units. Therefore, statement b is correct

Because statement b is correct, therefore, statements c,d, and e are incorrect

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Q#4. a

EOQ can be calculated from the given information

EOQ = sqrt(2DS/H), where D is annual demand, S is ordering cost per order and H is holding cost per unit

Annual demand, D = daily demand * working days per year = 10 units * 250 days per year = 2500 units per year

EOQ = sqrt(2*2500*50/4)

= 250 units

Therefore, Statement a is correct.

Using EOQ, review period, P = EOQ/d = 250/10 = 25 days

Reorder point and Target inventory level both can be calculated from the above information

R = d*L+z*s*sqrt(L), where s is standard deviation of daily demand, and L is the lead time in days. z =NORMSINV(csl) = NORMSINV(0.95) = 1.645

R = 10*4+1.645*2*sqrt(4) = 47 units

T = d*(L+P)+z*s*sqrt(L+P)

= 10*(4+25)+1.645*2*sqrt(4+25)

= 308 units

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