COURSE : INDUSTRIAL ENGINEERING LESSON: PROBABILISTIC MODEL

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PROBABILISTIC MODEL In reality the idle situation that the demand rate, production rate and lead time are constant and known with certainity rarely occurs. Thus there is a need to provide for safety or buffer stock in order to meet adverse situations like demand rate during lead time in excess of what was expected or delivery of goods is delayed Avesage ve dl Inu Level da 2-1 Safels Stocle Time daKd - ouseo

FACTORS AFFECTING HIGHER SAFETY STOCK I. 2. 3. 4. 5. When stock out cost or loss due to stock out are very high. Safety stock carrying cost is very low and is not of much concern. Uncertainity of demand rate and lead time is more and variable. No. of orders in a year are more To provide better service level to customers. S. To provide beter service levelto customers Ro Safey SHock + Avenge De a dlug leest iue Avesage-Inventory level . SS t Eoa 2 eve - maval Cost of mataini

STATIC INVENTORY OR DEMAND PROFIT In this model decision making is based on single cycle only. Demand is uncertain and re-ordering is not allowed. It is also called a newspaper boy problem These are normally applied for perishable goods like vegetables, fruits, flowers,etc or seasonable items or perishable goods In these models replacement orders are either not Possible or became abnormally expensive. lf D is demand and 'Sis supply 'P is profit or gain for each unit sold and'L' is loss for each unit not used or wasted D>S Its is basically under supplying. Demand is more but supply is limited means you can make more profit but can't Profit(D-S Loss Then choose the order quantity such that S>D Loss (S-D) Where Prob (S-I is cumulative demand probability of cumulative demand probability S units units and Prob(S)

QUESTION A shop keeper wishes to optimize the no. of perishable items. He needs to stock in any in his store. The demand distribution for the item is given below The shop keeper pays Rs 70/- for each item and sell it at Rs 90/-. If the stock is left unsold in any month he can sell the item at Rs 50/- To maximize the expected profit. Find the expected stock level? Demand 4 Probability 0.35 0.35 20

SOLUTION Demand Probability Cumulative Probability 0. 0.45 08 I 2 3 0.1 0.35 0.35 20 Profit 20 0.5 Profit +Loss 20 20 Prob (S-1)< 0.5 Prob (S) Answer 4 If Probability is 0.45, then answer is 3 If it is 0.8, Answer is 4

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Harshit Aggarwal

Cleared UPSC ESE twice with Rank 63 and 90 in mechanical engg. Got 99 percentile in GATE. Cracked ONGC, BHEL,ISRO, SAIL, GAIL successfully

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Ziaul haque

2 years ago

Good work sir

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