Question

A manager of an inventory system has been asked to analyze the economics of a backorder policy for some products that can possibly be backordered. For a specific product with Demand of 3600 units per year, ordering costs equals $250, holding cost equals $3, and backorder costs equal $45.

Show your work calculating the following using the inventory backorder model:

1/Optimal Order

2/Planned Shortage

3/Total Cost

Answer 1

1.

EOQ with backorder
EOQ = Sqrt(((2*D*Co)/Ch)*(( Ch +Cb)/Cb)) where,
D = Annual demand = 3600
Co = ordering cost per order = $250
Ch = holding cost per unit per year = $3
Cb = backorder cost per unit = $45

EOQ = SQRT(((2*3600*250)/3)*((3+45)/45)) = 800

2.Planned shortage = EOQ calculated in shortage model*(Ch/(Ch+Cb)) = 800*(3/(3+45)) = 50 = B

3.Total cost = Annual carrying cost+Annual ordering cost+Annual backordering cost
Annual carrying cost = ((EOQ-B)^2/(2*EOQ))*Ch = ((800-50)^2/(2*800))*3 =1054.6875

Annual ordering cost = (D/EOQ)*Co = (3600/800)*250 = 1125

Annual backordering cost = (B^2/(2*EOQ))*Cb = (50^2/(2*800))*45 = 70.3125

Total cost = 1054.6875+1125+70.3125 = 2250