The Dine Corporation is both a producer and a user of brass couplings. The firm
ID: 325627 • Letter: T
Question
The Dine Corporation is both a producer and a user of brass couplings. The firm operates 220 days a year and uses the couplings at a steady rate of 4400 per year. Couplings can be produced at a rate of 370 per day. Annual storage cost is $3 per coupling, and machine setup cost is $79 per run.
What is the "daily" demand rate?
How many units the company should produce in each production run?
How many brass couplings are in the inventory when the firm stops the production in a given production run?
How many production runs per year will there be?
How often the firm starts the production? (in days)
How many days in a cycle the firm is producing the products?
How many days in a cycle the firm doe not produce any product?
How much is the total annual inventory related costs?
Explanation / Answer
Annual demand, D = 4400
Setup cost, S = $ 79
Holding/storage cost, H = $ 3
Daily Production rate, p = 370
1) Daily demand rate, d = 4400/220 = 20
2) Economic Production Quantity (EPQ) = SQRT(2DS/(H*(1-d/p)))
= SQRT(2*4400*79/(3*(1-20/370)))
= 495 sets
3) Number of production runs per year = D/Q = 4400/495 = 8.9
4) Production days = Q/p = 495/370 = 1.37 per production run
Total production days in a year = D/p = 4400/370 = 11.9 days
5) Number of days in a cycle, the firm is producing the products = 1.34 days
6) Cycle time = Q/d = 24.75 days
Number of days in a cycle, the firm is not producing the products = 24.75 - 1.34 = 23.41 days
7) Total annual inventory related costs = Setup cost + Storage cost = (D/Q)*S + (Q/2)*H*(1-d/p)
= (4400/495)*79 + (495/2)*3*(1-20/370)
= $ 1,405
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