Question

The A&M Hobby Shop carries a line of radio-controlled model racing cars. Demand for the cars is assumed to be constant at a rate of 40 cars per month. The cars cost $60 each, and ordering costs are approximately $15 per order, regardless of the order size. The annual holding cost rate is 20%.
(a) Determine the economic order quantity and total annual cost under the assumption that no backorders are permitted.
If required, round your answers to two decimal places.
Q* =
Total Cost = $
(b) Using a $45 per-unit per-year backorder cost, determine the minimum cost inventory policy and total annual cost for the model racing cars.
If required, round your answers to two decimal places.
S* =
Total Cost = $
(c) What is the maximum number of days a customer would have to wait for a backorder under the policy in part (b)? Assume that the Hobby Shop is open for business 300 days per year.
If required, round your answer to two decimal places.
Length of backorder period = days
(d) Would you recommend a no-backorder or a backorder inventory policy for this product? Explain.
If required, round your answers to two decimal places.
Recommendation would be - Select your answer -backorderno-backorderItem 6 inventory policy, since the maximum wait is only days and the cost savings is $ .
(e) If the lead time is six days, what is the reorder point for both the no-backorder and backorder inventory policies?
If required, round your answers to two decimal places.
Reorder point for no-backorder inventory policy is .
Reorder point for backorder inventory policy is .

Answer 1

Answer:

Task a:

Task a.1

EOQ = 34.64 orders

Task a.2

Total annual cost = $29,215.69

Task b:

Task b.1

Total Cost Minimum inventory policy=( bS2/ 2Qbo) + P (Qbo- S)2/2Qbo + K(D/Qbo)

Task b.2

Total annual cost = $207.91

Task c

The maximum number of days = 6.09 days

Task d

The saving in using backorder is $207.79

Task e

Task e.1:

Reorder point = 9.6

Task e.2:

Reorder point = 3.51

Explanation:

Demand per month= 40 cars

Annual Demand (D)= 12*40 = 480

Ordering cost per order (K)= $15

Holding Cost= 20% of cost= $60 *0.2 = 12

Task a

Determine the economic order quantity and total annual cost under the assumption that no backorders are permitted.

If required, round your answers to two decimal places.

Task a.1

Calculate EOQ

EOQ = $\sqrt\frac{2CoD}{Ch}$

EOQ = $\sqrt\frac{2*15*480}{12}$

EOQ = 34.64 orders

Task a.2

Total annual cost:

Total annual cost = P×D + Co × ($\frac{D}{EOQ}$)  + Ch × ($\frac{EOQ}{2}$)

Total annual cost = 60 × 480 + (15 × $\frac{480}{34.64}$) + (12 × $\frac{34.64}{2}$)

Total annual cost = $28,800 + $207.85 + $207.84

Total annual cost = $29,215.69

Task b:

Using a $45 per-unit per-year backorder cost, determine the minimum cost inventory policy and total annual cost for the model racing cars.

If required, round your answers to two decimal places.

S* =

Total Cost = $

Solution:

Task b.1

Minimum cost inventory policy:

Backorder Cost (b)= $45

Qbo= Q* × √( b+h/ h)

= 35*√(12+45/ 45)

= 35* 1.12

=39.28

Shortage (S)= Qbo * (K/K+b)

= 39* (15/15+45)

= 39* 0.25

= 9.75

Total Cost Minimum inventory policy=( bS2/ 2Qbo) + P (Qbo- S)2/2Qbo + K(D/Qbo)

Task b.2

Total annual cost = 45* 9.752 / 2* 392 + 60 (39-9.75)2/ 2* 392 + 15 ( 480/39)

= 1.40+ 21.9.+ 184.61

=$207.91

Task c:

What is the maximum number of days a customer would have to wait for a backorder under the policy in part (b)? Assume that the Hobby Shop is open for business 300 days per year.

If required, round your answer to two decimal places.

Solution:

Length of backorder days (d) = Demand ÷ amount of working days

d = 480 ÷ 300

d = 1.6

Calculate the backorders as the maximum number of backorders divided by the demand per day

s/d = 9.75/1.6 = 6.09 days (answer)

Task d

Would you recommend a no-backorder or a backorder inventory policy for this product? Explain. If required, round your answers to two decimal places.

Recommendation would be   inventory policy, since the maximum wait is only  days and the cost savings is $._____

Solution:

Calculate the difference in total between not using backorder:

$207.85 + $207.85 - 207.91 = $207.79

The saving in using backorder is $207.79.

Task e

If the lead time is six days, what is the reorder point for both the no-backorder and backorder inventory policies?  If required, round your answers to two decimal places.

Task e.1

Reorder point for no-backorder inventory policy is .

Task e.2

Reorder point for backorder inventory policy is .

Solution:

Task e.1

Reorder point for no-backorder inventory policy is .

Reorder point = d*lead time

Reorder point = 1.6*6

Reorder point = 9.6

Task e.2

Reorder point for backorder inventory policy is .

Reorder point = d*lead time - S

Reorder point = 1.6*6 - 6.09

Reorder point = 3.51