Zhou Bicycle Case Study
Zhou Bicycle Case study
Annual demand = D = 439(441) (given in table)
Cost of Bicycle at whole sale (C) = 0.60*170 = $102
Carrying cost (h) = 12% of cost
Ordering cost (S) = $65 per order
Lead time = 4 weeks
Q.1 Use EOQ model for Inventory Management when we know demand day Q* = Sort [2*annual demand*ordering cost/holding cost] Q* = Sort [2*439*65/0.12*102] Q* = 68.28 or 69 units
Per order, no of bicycle are 69 units.
Average cycle inventory = Q*/2 = 69/2 = 34.5
Number of orders per year = D/Q* = 439/69 = 6.46
Annual material cost = CD = 102*439 = $44778
Annual order cost = (D/Q*)S = 6.46*65 = $422.3
Annual holding cost = (Q*/2)H = (Q*/2)hC = 34.5*0.12*102 = 422.3
Annual ordering and holding cost = $422.3 + $422.3 = $844.6
Total annual cost = TC = CD + (D/Q*)S + (Q*/2)hC = $44778 + $422.3 + $422.3 = $45622.6
Average flow time = (Q*/2D) = 69/(2*439) = 0.077 year = 28.10 days
Re order point = avg. demand of week * lead time = (439/52)*4 = 33.76 units
Q.2 when we have uncertainty when reorder point and total cost
Given Customer Service level = 9.5%
Mean demand per week = annual demand / no of week = 439/52 = 8.44 unit.
Mean monthly demand = 36.58 unit
Standard Deviation of demand = 25.67
Lead time = 4 weeks
Standard deviation of demand during lead time = mean demand per week * root of Lead time = 8.44*root of 4 = 16.88
Safety Stock = F-1 (CSL) * std. Dev. Of Demand during lead time
Safety stock (ss) = F-1(.095) * 16.88
Note- see value of F-1(.095) in normal distribution
Safety stock (ss) = 0.9139*16.88 = 15.42 unit
Re order point = demand during lead time + safety stock = (8.44*4) + 15.42 = 49.18 unit
Average Cycle inventory = (Q*/2) + safety stock = 69+49.18 = 118.18
Average holding cost = 118.18*0.12*102 = $1446.52
Annual order cost = (D/Q*)S = 6.46*65 = $422.3
Annual ordering and holding cost = $422.3 + $1446.52 = $1868.83
Total annual cost = TC = CD + (D/Q*)S + (Q*/2 + safety
Annual demand = D = 439(441) (given in table)
Cost of Bicycle at whole sale (C) = 0.60*170 = $102
Carrying cost (h) = 12% of cost
Ordering cost (S) = $65 per order
Lead time = 4 weeks
Q.1 Use EOQ model for Inventory Management when we know demand day Q* = Sort [2*annual demand*ordering cost/holding cost] Q* = Sort [2*439*65/0.12*102] Q* = 68.28 or 69 units
Per order, no of bicycle are 69 units.
Average cycle inventory = Q*/2 = 69/2 = 34.5
Number of orders per year = D/Q* = 439/69 = 6.46
Annual material cost = CD = 102*439 = $44778
Annual order cost = (D/Q*)S = 6.46*65 = $422.3
Annual holding cost = (Q*/2)H = (Q*/2)hC = 34.5*0.12*102 = 422.3
Annual ordering and holding cost = $422.3 + $422.3 = $844.6
Total annual cost = TC = CD + (D/Q*)S + (Q*/2)hC = $44778 + $422.3 + $422.3 = $45622.6
Average flow time = (Q*/2D) = 69/(2*439) = 0.077 year = 28.10 days
Re order point = avg. demand of week * lead time = (439/52)*4 = 33.76 units
Q.2 when we have uncertainty when reorder point and total cost
Given Customer Service level = 9.5%
Mean demand per week = annual demand / no of week = 439/52 = 8.44 unit.
Mean monthly demand = 36.58 unit
Standard Deviation of demand = 25.67
Lead time = 4 weeks
Standard deviation of demand during lead time = mean demand per week * root of Lead time = 8.44*root of 4 = 16.88
Safety Stock = F-1 (CSL) * std. Dev. Of Demand during lead time
Safety stock (ss) = F-1(.095) * 16.88
Note- see value of F-1(.095) in normal distribution
Safety stock (ss) = 0.9139*16.88 = 15.42 unit
Re order point = demand during lead time + safety stock = (8.44*4) + 15.42 = 49.18 unit
Average Cycle inventory = (Q*/2) + safety stock = 69+49.18 = 118.18
Average holding cost = 118.18*0.12*102 = $1446.52
Annual order cost = (D/Q*)S = 6.46*65 = $422.3
Annual ordering and holding cost = $422.3 + $1446.52 = $1868.83
Total annual cost = TC = CD + (D/Q*)S + (Q*/2 + safety