FINANCIAL MATHEMATICS AND BUSINESS STATISTICS

Financial Mathematics and Business Statistics

Financial Mathematics and Business Statistics

Answer 1

Dreamcatcher is negotiating in reducing the ordering costs with its main supplier from £280 to £190. Therefore, it is important for Dreamcatcher to analyze the market effectiveness of the ordering costs. In the given below, the table presents the demand and probability of the risks that are if the crisis continues, in the slow recovery, in the medium recovery and in the fast recovery.

Scenario

Crisis Continues

Slow Recovery

Medium Recovery

Fast Recovery

Probability

20 %

15 %

50 %

15 %

Demand

40000

65000

105000

250000

In the crisis scenario, from the given below table, it can be observed that demand is 40000 units, the order cost is £190 and Holding cost £1.45 then the company should order 12.35 per year in order to reach the optimal equilibrium point where the demand equal to the supply. This will save the extra cost of the company on holding the inventory; if they demand 40,000 units in the year their total cost will gather to £ 4694.68.

Parameter

Value

Parameter

Value

Demand rate(D)

40000

Optimal order quantity

3237.71

Setup/ Ordering cost

190

Maximum Inventory Level (Imax)

3237.71

Holding cost

1.45

Average inventory

1618.85

Unit cost

0

Orders per period(year)

12.35



Annual Setup cost

2347.34



Annual Holding cost

2347.34



Unit costs (PD)

0



Total Cost

4694.68

In the slow recovery scenario, from the given below table, it can be observed that the demand is 65,000 units, the order cost is £190 and Holding cost (H) £1.45 then the company should order 15.75per year in order to reach the optimal equilibrium point where the demand equal to supply. This will save the extra cost of the company on holding the inventory; if they demand 65,000 units in the year their total cost will accrue to £ 5984.56.

Parameter

Value

Parameter

Value

Demand rate (D)

65000

Optimal order quantity

4127.29

Setup/ Ordering cost (S)

190

Maximum Inventory Level (Imax)

4127.29

Holding cost (H)

1.45

Average inventory

2063.64

Unit cost

0

Orders per period(year)

15.75



Annual Setup cost

2992.28



Annual Holding cost

2992.28



Unit costs (PD)

0



Total Cost

5984.56

In the medium recovery scenario, from the given below table, it can be observed that if the demand is 105000 units, the order cost is £190 and Holding cost (H) £1.45 then the company should order 20.02per year in order to reach the optimal equilibrium point where the demand equal to the supply. This will save the extra cost of the company on holding the inventory; if they demand 105,000 units in the year their total cost will collect to £ 7606.25.

Parameter

Value

Parameter

Value

Demand rate (D)

105000

Optimal order quantity (Q*)

5245.69

Setup/ Ordering cost (S)

190

Maximum Inventory Level (Imax)

5245.69

Holding cost (H)

1.45

Average inventory

2622.84

Unit cost

0

Orders per period(year)

20.02



Annual Setup cost

3803.12



Annual Holding cost

3803.12



Unit costs (PD)

0



Total Cost

7606.25

In the fast recovery scenario, from the given below table, it can be observed that if the demand is 250000 units, the order cost is £190 and Holding cost (H) £1.45 then the company should order 30.89per year in order to reach the optimal equilibrium point where the demand equal to supply. This will save the extra cost of the company on holding the inventory; if they demand 250,000 units in the year the total cost will accrue to £ 11736.7.

Parameter

Value

Parameter

Value

Demand rate (D)

250000

Optimal order quantity (Q*)

8094.27

Setup/ Ordering cost (S)

190

Maximum Inventory Level ...