Question

One large bakery still receives flour in 25-pound bags from their own company's warehouse. They use an average of 4300 bags a year. The production step that uses these bags use 45 bags per day while the usage is 23 bags per day. It costs $13.00 to configure the machines for each run. Annual carrying costs are $5.75 per bag. What will be their average number of bags on hand if they request the EPQ bags in each order? (Keep up to two decimal places in your answer)

Answer 1

Annual demand(D) = 4300 bags

Production rate(p) = 45 bags

Demand rate(d) = 23 bags

Setup cost(S) = $13

Carrying cost(H) = $5.75

Economic production quantity(Q) = √ {2DS / H [1-(d/p)]}

= √{(2x4300x13) /5.75[1-(23/45)]}

= √[111800/5.75(1-0.51) ]

= √ [111800/(5.75 x 0.49)]

= √(111800/2.8175)

= √39680.56787

= 199.20 bags

Maximum inventory (I-max) = (Q/p)(p-d)

= (199.20/45)(45-23)

= 4.43 × 22

= 97.46 bags

Average number of bags on hand = I-max/2 = 97.46/2 = 48.73 bags