Answer to Question #293059 in Economics of Enterprise for george2000

Question

The store sells a special item whose daily demand can be described by the

following pdf:

Daily demand D 0 1 2 3

P(D) 0.15 0.3 0.45 0.1

The store is comparing two ordering policies: (1) Order up to 3 units every

3 days if the stock level is less than 2, else do not order. (2) Order 3 units if the

stock level is zero, else do not order. The fixed ordering cost per shipment is $200.

Immediate delivery is expected.

Which policy should the store adopt to minimize the total expected daily

cost of ordering?

Answer 1

Minimize Cost Policy

For the first policy, we have a chance of only ordering twice. the following illustrates the order probabilities given we have four likelihoods of demand. It is assumed that ordering is compulsory for Day 1. therefore multiplying the probability to order with ordering cost for possible ordering days we get;

$Day 1 = P(1\times200)=200$

$Day 2=Ordering\ not\ possible$

$Day 3=Ordering\ not\ possible$

$Day4 = (0.55\times 200)=110$

0.55 is achieved by adding $0.1+0.45$ the probabilities that the stock count will be below 2.

Total Ordering cost for the first policy is;

$200+110=310$

Evaluating the second policy, we realize the probability of ordering on a daily basis as shown below.

$Day 1=P(1\times 200)=200$

$Day 2=P(0.1\times 200)=20$

$Day3=P(0.1\times200)+$ $P(0.75\times 200)=170$

$Day4=P(0.1\times200)+$ $P(0.75\times 200)+$ $P(0.9\times 200)=350$

0.1 has been used to get the probability since we can only re-order if the stock is zero. the only way the stock will be zero, is if the previous demand was 3. For days 3 and 4, we have additional probabilities since for previous days probabilities of demand may vary to suit exhaustion of the stock by the third or fourth day.

Total cost likely to be incurred on embracing the second policy is;

$200+20+170+350=740$

It is therefore advisable to embrace the first policy in minimizing the total daily cost of ordering.