Question

A company follows an EPQ model with production rate -180 units per month and a demand of 1,000 units per year the cost for production 35% of annual interest rate 4. 90. Starting the production line has a cost of $950 the holding cost is V hi a) b) Calculate optimal Q Draw the EPQ process and calculate total cycle time and production time use the diagram to get equations

Answer 1

4.

Demand =1000/12 = 83.3 per month

Production = 180 per month

d/p = 83.3/180 =0.462

Holding cost = h ( 1-d/p)

= 90x0.35 x( 1-0.462) =16.497

Production quantity = [ 2x1000x950 /16.497]^1/2 = 339.47 =340

In the diagram, AB represents the maximum inventory reached, which is equal to the difference in the items produced and items consumed

Items produced in a production time t = pt = p ( Q/p)

Itmes consumed during that time = t x daily consumption = dt = d xQ/p

Max items during time t = Items produced - Itmes consumed = t ( p-d)

= Q - d/pxQ

= Q ( 1-d/p)

= 340 x0.538 = 183

Time taken to produce 340 units = 340/180 = 1.88 months

These 183 items will be consumed at the rate of 83.3 per month

Consumption time t' = 183/83.3 = 2.19 months

Production run time t = 1.88 m

Cycle time = Production time + consumption time = t+t' = 1.88+2.19 =4.07 months

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