Inventory model (operation research)

Introduction to Inventory, Assumption of EOQ, Eg:- Parle Agro, Big Bazar.

1. A PROJECT REPORT ON “INVENTORY MODEL” SUBMITTED BY- Amrita Gharti . Madhavi Sharma. Nidhi Khetalpar . MMS( 2 nD Semester) Specialization: Finance 1

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3. 3 Introduction to inventory An inventory can be defined as a stock of goods which is held for the purpose of future production or sales. The stock of goods may be kept in the following forms : 1. Raw Material 2. Semi finished goods 3. Finished goods The objective of an inventory control is to minimize the total cost or to maximize profit.

4. Economic Order Quantity (EOQ) Costs = Too much + Too little = Holding + Ordering Inventory Time 4

5. Assumptions of EOQ : 1. Demand is uniform and known. 2. Delivery is perfectly reliable and instant. 3. Carrying Cost , Ordering Cost and unit price are constant. 5

6. Demand = 4000 units / year. Holding cost = 5 Rs/unit/yr. Ordering cost = 100 Rs/order. C1 C2 C3 C4 C5 C6 C7 Q 50 100 200 400 500 1000 2000 Average Inv 25 50 100 200 250 500 1000 Total holding 125 250 500 1000 1250 2500 5000 No. of order 80 40 20 10 8 4 2 Total order cost 8000 4000 2000 1000 800 400 200 Total cost 8125 4250 2500 2000 2050 2900 5200 6

7. Economic Order Quantity (EOQ) Formula: (EOQ) = √2DCo C h Where D = Yearly Demand Co= Ordering Cost Ch = Holding Cost 7

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9. ECONOMIC ORDER QUANTITY (EOQ) OF FROOTI: ECONOMIC ORDER QUANTITY OF FROOTI MANUFACTURED BY PADMESH BEVERAGES: FOR FROOTI ORDERING COST(PER CASE)   Quantity Amount (Rs ) 200ml 273 500ml 488 1200ml 528 1.5 litre 414 CARRYING COST= Rs 2/ case EOQ = 9 HERE , D   =   Demand for the year (1500000 ). β =   Cost to place a one order. α =   Cost to storing one unit of inventory for a year Q = Order Size.

10. 10 SOLUTION:-

11. EOQ FOR 200 ML: EOQ = √ (2 x 1500000 x 273) / 2 = 20236.10 cases EOQ FOR 500 ML: EOQ = √ (2 x 1500000 x 488) / 2 = 27055.49 cases EOQ FOR 1200 ML: EOQ = √ (2 x 1500000 x 528)/2 = 28142.49 cases 11 EOQ FOR 1.5 Litres: EOQ = √ (2 x 1500000 x 414)/ 2 = 24919.87 cases SOLUTION:-

12. RE-ORDER OF PADMESH BEVERAGES , A LICENSEE OF PARLE AGRO: CALCULATION: Re-order level maintained by Padmesh Beverages for the year 2011-2012. Re-order level= Average consumption x (lead time + safety stock) HERE, TOTAL CONSUMPTION = 15, 00,000 LEAD TIME= 15 days SAFETY STOCK= 7500 (6% of total consumption ). 12

13. 13 SOLUTION:-

14. 15,00,000 12 = = 1,25,000 units The re-order below is calculated on the basis of average consumption: Re-order level= average consumption x (lead time + safety stock) = (1,25,000 x 15) + 7500 = (18,75,000 + 7500) = 18,82,500 units 14 AVERAGE CONSUMPTION= Total consumption 12 SOLUTION:-

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16. Some important formulas to solve Q*(EOQ) =√2DCo/C h The optimal order cycle time, t * = Q*/D The minimum yearly variable inventory cost, TVC = √2DCoC h The minimum yearly total inventory cost, TC * = TVC * + DC

17. N otations Some general notations used in inventory models r- demand rate K- production rate C- Average total cost per unit time t- time interval between two consecutive replenishments of inventory z- order level or stock level use the following general notations in inventory models I- the cost of carrying one rupee in inventory for a unit time C₁- holding cost per unit time C₂- storage cost per unit time C₃-set up cost per production run q -lot size per production run L-lead time q *, t*,z*- optimal values of q,t,zrespectively for which the cost C is minimum

18. Some average results Q1) What is the store capacity of your warehouse? 45000 units Q2) What is the annual demand? 400000 units Q3) What is the average carrying cost to carry the inventory? 10% Q4) What is the setup cost of the inventory? Rs.4000 Q5) What is the average lead time? 3days Q6) What is the ordering cost to place an order of 1 unit Rs.4

19. 19 SOLUTION:-

20. SOLUTION :- The average price of commodity in Big Bazaar is Rs.200 (EOQ ) = √2DCo C h Where D = Yearly Demand Co= Ordering Cost Ch = Holding Cost = √ (2 x 400000 x 488) / 10% of 200 = √ (2 x 400000 x 488) / 20 = 400 unit/year. t* =Q*/D = 400/ 400000 = 0.001 Year.

21. 21 TVC =√2DC O C h = √ 2*400000*20 = Rs 4000/ year. TC* = TVC* + DC = 4000+ 400000 * 200 = Rs 8 cr 4 thousand / year.

22. T hank you! For Your Kind Attention 22

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