# The corresponding period t is found from q d t the

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The corresponding period t* is found from * * Q D t = The optimum number of orders per year is determined from * * D Q N = where D is the demand per year.

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5 Example 1 : The demand rate for a particular item is 12 000 units/year. The ordering cost is Rs. 100 per order and the holding cost is Rs. 0.80 per item per month. If no shortages are allowed and the replacement is instantaneous, determine: (1) The economic order quantity. (2) The time between orders. (3) The number of orders per year. (4) The optimum annual cost if the cost of item is Rs. 2 per item. Solution: Note that the holding cost is given per month and convert the same into cost per year. C 1 = Rs. 2/item C 2 = Rs. 100/order C 3 = Rs. 0.80/item/month = Rs. 9.6/item/year D = 12000 items/year a) The economic order quantity 2 3 2 2 100 12000 9.6 * C D C Q × × = = 500 units = b) The time between orders * 500 /12000 . * Q D yr t = = 500 1000 month = 0.5 month = c) The number of orders/year * 12000 / 500 24 D Q N = = = d) The optimum annual cost (Number of orders) (Cost of one cycle) 24(500 2) 100 (500 / 2 0.5 0.80) . 28800 Rs = × = × + + × × =
6 References Kanti Swarup, P.K.Gupta, Man Mohan, Operation Research, Sultan Chand & Sons publisher, New Delhi. Ravindran, Phillips & Solberg, Operations research, John Wiley, Singapore, (2007). Richard Levin & David Rubin, Quantitative approach to Management, Mc GrawHill International, (1992). Pannerselvam, R. (2006) Operation Research, Prentice Hall of India Private Limited, New Delhi, Second Edition.
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