FINANCIAL MATHEMATICS AND BUSINESS STATISTICS

Financial Mathematics and Business Statistics

Financial Mathematics and Business Statistics

Answer 1

It is found that the company named Dreamcatcher is in the process of bargain to reduce its ordering costs with its major supplier from £ 280 to £ 190. For that reason, it is imperative and essential for Dreamcatcher that the effectiveness of market should be analyzed for the ordering costs. The following table shows the probability and demand of the risks that are associated in the case if the crisis persists in the fast recovery, in the medium recovery and in the slow recovery.

Scenario

Probability

Demand

Crisis Continues

20%

40000

Slow Recovery

15%

65000

Medium Recovery

50%

105000

Fast Recovery

15%

250000

Parameter

Value

Parameter

Value

Demand rate(D)

40000

Optimal order quantity

3238

Setup/ Ordering cost

190

Maximum Inventory Level (Imax)

3238

Holding cost

1.45

Average inventory

1619

Unit cost

0

Orders per period(year)

12



 

Annual Setup cost

2347



 

Annual Holding cost

2347



 

Unit costs (PD)

0



 

Total Cost

4695

It is found from the above table that when the demand is 40000 units, the order cost is £ 190 and Holding cost £ 1.45 then the Dreamcatcher should order 12.35 per year in order to reach the equilibrium level of output where the demand becomes equivalent to the supply, will save the extra cost of the Dreamcatcher on holding the inventory; if they demand 40000 units in the year, the total cost will be £ 4694.68.

Parameter

Value

Parameter

Value

Demand rate (D)

65000

Optimal order quantity

4127

Setup/ Ordering cost (S)

190

Maximum Inventory Level (Imax)

4127

Holding cost (H)

1.45

Average inventory

2064

Unit cost

0

Orders per period(year)

16



 

Annual Setup cost

2992



 

Annual Holding cost

2992



 

Unit costs (PD)

0



 

Total Cost

5985

From the above table which is based on the slow recovery scenario, it is found that the order cost is £190 and Holding cost (H) £1.45 when the demand is 65000 units, therefore, the company should order 15.75 each year to attain the equilibrium level of output where the demand becomes equivalent to the supply, which will help Dreamcatcher in saving the extra cost to firm for keeping the inventory. In addition to this, if their demand is 65,000 units in the year then the total cost will be to £ 5985.

Parameter

Value

Parameter

Value

Demand rate (D)

105000

Optimal order quantity (Q*)

5246

Setup/ Ordering cost (S)

190

Maximum Inventory Level (Imax)

5246

Holding cost (H)

1.45

Average inventory

2623

Unit cost

0

Orders per period(year)

20



 

Annual Setup cost

3803



 

Annual Holding cost

3803



 

Unit costs (PD)

0



 

Total Cost

7606

From the above table which is based on the medium recovery scenario, it is found that the order cost is £190 and Holding cost (H) £1.45 when the demand is of Dreamcatcher is 105000 units, thus, the Dreamcatcher should order 20.02 each year to attain the equilibrium level of output where the demand becomes equivalent to the supply, which will help Dreamcatcher in saving the extra cost to firm for keeping the inventory, if the demand of company is 105,000 unit in the year then the total cost will be £ 7606.

Parameter

Value

Parameter

Value

Demand rate (D)

250000

Optimal order quantity (Q*)

8094

Setup/ Ordering cost (S)

190

Maximum Inventory Level (Imax)

8094

Holding cost (H)

1.45

Average inventory

4047

Unit cost

0

Orders per period(year)

31



 

Annual Setup cost

5868



 

Annual Holding cost

5868



 

Unit costs (PD)

0



 

Total Cost

11737

From the above table which is based on the fast recovery scenario, it is found that the order cost is £190 and Holding cost (H) £1.45 when the demand is of Dreamcatcher is 250000 units, ...