Homework 2 Solution of Question 3 (a)-Using the sea transportation: The standard deviation of demand:L=VLoD v36 x 4000=2400 The safety inventory,ss=Fs(0.99)oL=55832 The Re-order Point=DL+ss 5000 x 36+55832=235833 Using the air transportation: The standard deviation of demand:oL=VLop =v4x 4000=8000 The safety inventory,ss =F1(0.99)oL=18611 The Re-order Point=DL+ss=5000 x 4+18611 =38611 (b)Using the sea transportation: Days of safety inventory carried=ss/D =55832/5000 =11.2(day) Cycle inventory =100000/2 50000 Days of cycle inventory carried=cycle invenory/D=10(days) Using the air transportation: Days of safety inventory carried=ss/D 18611/5000 =3.72(day) Cycle inventory =5000/2 2500 Days of cycle inventory carried=cycle invenory/D=0.5(days) (c)Totol cost Holding cost+Transportation cost In-Transit Inventory cost Using the sea transportation: Inventory holding cost=(50000+55832)×100×0.2=2116640 Transportation cost for one year =5000 x 365 x 0.5 =912500 In-transit Inventory cost=D×L×l00×0.2=3600000 Total cost 6629140 Using the sea transportation: Inventory holding cost =(2500+18611)x 100 x 0.2 422220 Transportation cost for one year =5000 x 365 x 1.5 2737500Homework 2 Solution of Question 3 (a) – Using the sea transportation: The standard deviation of demand: σL = √ LσD = √ 36 × 4000 = 2400 The safety inventory, ss = F −1 s (0.99)σL = 55832 The Re-order Point=DL + ss = 5000 × 36 + 55832 = 235833 – Using the air transportation: The standard deviation of demand: σL = √ LσD = √ 4 × 4000 = 8000 The safety inventory, ss = F −1 s (0.99)σL = 18611 The Re-order Point=DL + ss = 5000 × 4 + 18611 = 38611 (b) Using the sea transportation: Days of safety inventory carried=ss/D = 55832/5000 = 11.2(day) Cycle inventory =100000/2 = 50000 Days of cycle inventory carried=cycle invenory/D = 10(days) Using the air transportation: Days of safety inventory carried=ss/D = 18611/5000 = 3.72(day) Cycle inventory =5000/2 = 2500 Days of cycle inventory carried=cycle invenory/D = 0.5(days) (c) Totol cost = Holding cost+ Transportation cost + In-Transit Inventory cost Using the sea transportation: Inventory holding cost =(50000 + 55832) × 100 × 0.2 = 2116640 Transportation cost for one year =5000 × 365 × 0.5 = 912500 In-transit Inventory cost = D × L × 100 × 0.2=3600000 Total cost = 6629140 Using the sea transportation: Inventory holding cost =(2500 + 18611) × 100 × 0.2 = 422220 Transportation cost for one year =5000 × 365 × 1.5 = 2737500 1