Water Wheelies manufactures high-pressure sprinkler heads. These are produced pe
ID: 351281 • Letter: W
Question
Water Wheelies manufactures high-pressure sprinkler heads. These are produced periodically at a rate of 960 per day. Demand is steady at 720 per day. Assume 250 days per year. Each production run has a set-up cost of $120. Water Wheelies uses an annual inventory holding cost of $2.4 for carrying one unit for one year. a. (1 point) Determine the optimal production quantity during each production run. b. (2 points) Determine the annual holding cost, set-up cost and total cost. c. (1 point) Determine the maximum inventory. d. (3 points) Determine the cycle time between two production runs in days. In each cycle compute the number of days the production facility is busy (uptime) and the number of days the production facility is idle (downtime). e. (3 points) Water Wheelies can double its production rate by using a new technology, but the setup cost per production run will also double. Determine the economic production quantity and the annual holding and set-up costs.
Please Answer Part E
Explanation / Answer
To be calculated:
Economic production quantity (EPQ)
Annual holding costs
Annual set-up costs
Given values:
Production rate, p = 960 per day
Demand rate, d = 720 per day
Number of days in a year = 250 days
Annual demand, D = 720 x 250 = 180,000
Set-up costs, S = $120
Annual inventory holding costs = $2.4 per unit per year
(E) As per the values given in Part (E) of the question, the daily production rate and the setup cost per production run has been doubled with the introduction of the new technology. Therefore, new values are:
Production rate, p = 960 x 2 = 1,920 per day
Set-up costs, S = $120 x 2 = $240
The Economic production quantity (EPQ) can be calculated as;
EPQ = 2DS / H (1 - d/p)
EPQ = (2 x 180000 x 240) / 2.4 x (1 - 720/1920)
EPQ = 86400000 / 1.5
EPQ = 7589 units
Annual holding cost is calculated as;
Please Note: While calculating the Annual holding cost for Economic production quantity, the daily demand (d) and daily production (p) are also considered. Therefore the formula of Annual holding cost is given as;
Annual holding cost = (EOQ / 2) x H x (1 - d/p)
Annual holding cost = (7589 / 2) x 2.4 x (1 - 720/1920)
Annual holding cost = (7589 / 2) x 2.4 x 0.625
Annual holding cost = $5,691.75
Annual set-up cost is calculated as;
Annual set-up cost = (D / EOQ) x S
Annual set-up cost = (180000 / 7589) x 240
Annual set-up cost = $5,692.45
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