An operation manager of a chemical manufacturing plant must determine the lot si

Question

An operation manager of a chemical manufacturing plant must determine the lot size for a chemical that has a steady demand of 1,450 litres per day. The production rate is 6,850 litres per day, setup cost is $200, annual holding cost is $0.21 per litre, and the plant operates 350 days per year.

Determine the production order quantity (POQ), the number of orders and the time between orders. What is the total annual setup cost? What is the total holding cost per year? Using an appropriately labelled diagram, graph setup cost, holding cost, and total inventory cost, and show the optimal production order quantity and the minimum total inventory cost. What is the setup time in hours, based on a $25 per hour setup labour cost?

Explanation / Answer

POQ = sqrt (2*1450*350*200/(0.21*(1-1450/6850)))

= sqrt (203000000/0.165) = 35075.67 = 35076

No. of orders = (1450*350)/35076 = 14.46 = 15

Time between orders = 350/15 = 23.3 days

Annual Setup Cost = (1450*350/35076) * 200 = $ 2893.71

total holding cost per year = 0.5*0.21*35076*(1-1450/6850) = $2903.37

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