Question

Westside Auto purchases a component used in the manufacture of automobile generators directly from the supplier. Westside’s generator production operation, which is operated at a constant rate, will require 8,000 components per month throughout the year.

Assume that the ordering costs are $80 per order, the unit cost is $3.00 per component, and annual holding costs are 20% of the value of the inventory. Westside has 300 working days per year and a lead time of 10 days.

Answer the following inventory policy questions:

1). Please identify the parameters (notations are following the slides)

D=

d=

C_h=

C_o=

m=

2) What is the optimal order quantity for Westside Auto? ----Formulas are required

3) How frequently (Every how many days) should Westside Auto order to replenish the component inventory?----Formulas are required

4) What is the reorder point? ----Formulas are required

5) How much is the total annual holding and ordering cost? ----Formulas are required. Are the two costs equal?

Answer 1

(a) Monthly demand (m) = 8000 components

Annual Demand (D) = 8000 × 12

Annual demand (D) = 96,000 components

Number of working days = 300

Daily demand (d) = Annual demand / Working Days

Daily demand (d) = 96000 / 300

Daily demand (d) = 320 components

Ordering cost per order (Co) = $80

Cost of each component = $3

Annual holding cost percent = 20%

Annual holding cost per unit (Ch) = Cost of each component × Annual holding cost percent

Annual holding cost per unit (Ch) = $3 × 20%

Annual holding cost per unit (Ch) = $0.6

(b) Economic order quantity (EOQ) =

EOQ =

EOQ = 5059.644 components

Therefore, optimal order quantity for Westside Auto = components is 5059.644 units

(c) Number of orders = D/EOQ

Number of orders = 96,000/5059.644

Number of orders = 18.97 orders

Time between orders = Working days / Number of orders

Time between orders = 300/18.97

Time between orders = 15.81 days

(d) Re-order point = Daily demand × Lead time

Given lead time = 10 days

Re-order point = 320 × 10

Re-order point = 3200

(e) Total annual holding cost = Ch × (Q/2)

Total annual holding cost = 0.6 × (5059.644/2)

Total annual Holding cost = $1517.893

Total Annual ordering cost = Co × (D/Q)

Total annual Ordering cost = 80 × (96000/5059.644)

Total annual Ordering cost = $1517.893

Therefore, we can conclude that at economic order quantity, Total Annual holding cost is equal to total Annual ordering cost.