Question

1. Safeway supermarkets sells, among thousands of other items, delicious scrumptious bananas.  They’re fantastic, but spoil easily, so they can’t keep too many in inventory at a time.   Their temperture-controlled storage unit can hold 600 bunches of bananas, which is how much they order at a time.  Annual banana demand is 12,000 bunches.  The annual holding cost rate is $1.5 per banana bunch, and each order costs him $50 to place each order. Assuming a uniform rate of consumption:    

a)  How much does Safeway spend on total inventory with their current ordering policy?

b)  How much would Safeway save in inventory costs if they used an economic order quantity (EOQ) model for order quantities?

Answer 1

Answer)

Given that,

D = Annual quantity demanded = 12000

H = Holding cost = 1.5

S = Ordering cost = 50

Q = 600

a)

Total inventory cost = Annual Ordering Cost + Annual Holding Cost = ((D x S) / Q) + ((Q x H) / 2)

=> Total inventory cost = ((12000 x 50) / 600) + ((600 x 1.5) / 2) = 1000 + 450 = 1450

Total inventory cost = 1450

Therefore, total inventory with their current ordering policy that Safeway will spend = 1450

b)

EOQ = √ ((2 x D x S) / H) = √ ((2 x 12000 x 50 )/ 1.5) = √ 8,00,000 = 894.42

EOQ = 894.42

Using EOQ = Q = 894.42 in Total inventory cost formula,

Total inventory cost = Annual Ordering Cost + Annual Holding Cost = ((D x S) / Q) + ((Q x H) / 2)

= ((12000 x 50) / 894.42) + ((894.42 x 1.5) / 2) = 670.825 + 670.815 = 1341.64

Total inventory cost = 1341.64

Therefore, save in inventory costs = Total inventory cost (Q = 600) + Total inventory cost (Q = 894.42)...........(values of Q as calculated above with EOQ formula)

= 1450 - 1341.64

= 108.36

Therefore, save in inventory costs is 108.36

Therefore, save in inventory costs if Safeway used an economic order quantity (EOQ) model for order quantities = 108.36