Question

Problem 13.4 The Sofaworld Company purchases upholstery material from Barrett Textiles. The company uses 47,000 yards of material per year to make sofas. The cost of ordering material from the textile company is $1,750 per order. It costs Sofaworld $0.70 annually to hold a yard of material in inventory. Determine the optimal number of yards of material Sofaworld should order, the minimum total inventory cost, the optimal number of orders per year, and the optimal time between orders. (Round all answers to 2 decimal places, e.g. 52.75. Use 365 days for calculation.)

Optimal number of yards to order ________ metres

Minimum total inventory cost ________ $

Optimal number of orders per year __________per year

Optimal time between orders ___________days

Answer 1

Solution:

(a) Optimal order quantity (Q):

Q = SQRT [(2 x D x Co) / H]

where,

D = Annual demand

Co = Cost of ordering

H = Holding cost

Putting the given values in the above formula,

Q = SQRT [(2 x 47,000 x $1,750) / $0.70]

Q = 15,329.71

Optimal number of yards to order = 15,329.71 metres

(b) Minimum total inventory cost:

Total annual inventory cost = Annual inventory holding cost + Annual ordering cost

Total annual inventory cost = [(Q / 2) x H] + [(D / Q) x Co]

Total annual inventory cost = [(15,329.71 / 2) x $0.70] + [(47,000 / 15,329.71) x $1,750]

Total annual inventory cost = $5,365.40 + $5,365.40

Total annual inventory cost = $10,730.80

(c) Optimal number of orders per year:

Number of orders = (Annual demand / Q)

Number of orders = (47,000 / 15,329.71)

Number of orders = 3.07 orders per year

(d) Optimal time between orders:

​​​​​​​Time between orders = (Q / Annual demand) x Number of days

Time between orders = (15,329.71 / 47,000) x 365

Time between orders = 119.05 days