Problem 13.4 The Sofaworld Company purchases upholstery material from Barrett Te
ID: 425750 • Letter: P
Question
Problem 13.4 The Sofaworld Company purchases upholstery material from Barrett Textiles. The company uses 41,000 yards of material per year to make sofas. The cost of ordering material from the textile company is $1,250 per order. It costs Sofaworld $1.30 annually to hold a yard of material in inventory dy 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 7Ue 36s day all answers to 2 decimal places, e.g. 52.75. Use 365 days for calculation.) Optimal number of yards to order Minimum total inventory cost Optimal number of orders per year Optimal time between orders metres per ear daysExplanation / Answer
Given values:
Annual demand, D = 41,000 yards
Cost of ordering, Co = $1,250 per order
Holding cost, H = $1.30 per year
Number of working days = 365
Solution:
(a) Optimal order quantity (Q*) is calculated as;
Q* = SQRT [(2 x D x Co)/H]
where,
D = Annual demand
Co = Ordering cost
H = Annual holding cost
Putting the given values in the above formula, we get;
Q* = SQRT [(2 x 41000 x 1250)/1.30]
Q* = 8879.54
Optimal number of yards to order = 8879.54 metres
(b) Minimum total inventory cost is calculated as;
Inventory cost = (Q*/2) x H
Inventory cost = (8879.54/2) x $1.30
Inventory cost = $5,771.70
Minimum total inventory cost = $5,771.70
(c) Optimal number of orders per year is calculated as;
Number of orders = Annual demand / Optimal order quantity
Number of orders = 41,000 / 8879.54
Optimal number of orders per year = 4.62 per year
(d) Optimal time between orders is calculated as;
Optimal time between orders = Working days per year / Number of orders
Optimal time between orders = 365 / 4.62
Optimal time between orders = 79 days