INVENTORY MANAGEMENT PROF ASHIS CHATTERJEE
MOTIVATION FOR STUDYING INVENTORY MANAGEMENT   <ul><li>Economics involved in producing or purchasing in batches  </li></ul...
TYPES OF INVENTORY <ul><li>BATCH OR CYCLE STOCK </li></ul><ul><li>Manufacturing or purchasing an item at a rate higher tha...
TYPES OF INVENTORY <ul><li>ANTICIPATION STOCK </li></ul><ul><li>Maintaining extra stock to meet peak season demand.  </li>...
SELECTIVE CONTROL OF MATERIALS <ul><li>ABC ANALYSIS </li></ul><ul><li>Classification of all consumption items, based on </...
ABC CLASSIFICATION <ul><li>A Items: Those relatively few items that account for high consumption value (CV), say,15% of th...
ABC CLASSIFICATION <ul><li>EXAMPLE: </li></ul><ul><li>Annual Usage/ CV(Rs) Cum.Usage </li></ul><ul><ul><ul><ul><ul><li>394...
INVENTORY CONTROL MODELS <ul><li>DEMAND </li></ul>STATIC/ UNIFORM DYNAMIC/ VARIABLE DETERMINISTIC PROBLEM P1 PROBABILISTIC...
PROBLEM P1: INVENTORY CONTROL FOR STATIC DETERMINISTIC DEMAND <ul><li>Consider the following problem: Demand for a particu...
PROBLEM P1: DETERMINING THE EOQ/ BATCH/CYCLE STOCK <ul><li>Total annual cost = DA/Q + ½ QIC  </li></ul><ul><li>On differen...
PROBLEM P1: INVENTORY CONTROL FOR STATIC DETERMINISTIC DEMAND <ul><li>P1 allows us to determine the Batch/  </li></ul><ul>...
PROBLEM P1: AN EXTENSION <ul><li>Consider the earlier problem with the only change that now, the supplier has offered a di...
PROBLEM P1: AN EXTENSION, EOQ WITH DISCOUNTS <ul><li>Here, purchasing cost is also a relevant cost.  </li></ul><ul><li>Alg...
PROBLEM P1: AN EXTENSION <ul><li>Step 3:  Determine EOQ using the next higher  </li></ul><ul><li>cost/unit (Rs.12). Check ...
PROBLEM P2: INVENTORY CONTROL FOR STATIC PROBABILISTIC DEMAND <ul><li>Mean Rate of Demand not changing with respect to tim...
PROBLEM P2: INVENTORY CONTROL FOR STATIC PROBABILISTIC DEMAND <ul><li>For P2, Inventory Control implies answering the  </l...
PROBLEM P2: INVENTORY CONTROL FOR STATIC PROBABILISTIC DEMAND <ul><li>A typical Continuous Review policy may read as follo...
PROBLEM P2 : AN EXAMPLE <ul><li>Say, the daily demand of an item is uncertain, and </li></ul><ul><li>it can be 1,2 or 3 kg...
DETERMINING REORDER LEVEL (CONT.REVIEW POLICIES) <ul><li>Step 1 Find the Probability Distribution of Demand during the Lea...
DETERMINING REORDER LEVEL (CONT.REVIEW POLICIES) <ul><li>Interpretation of Cumulative probability  : Say,  </li></ul><ul><...
PROBLEM P2: INVENTORY CONTROL FOR STATIC PROBABALISTIC DEMAND <ul><li>P2 allows us to determine the Buffer/ Safety stock. ...
PROBLEM P3: INVENTORY CONTROL FOR DYNAMIC DETERMINISTIC DEMAND <ul><li>AN EXAMPLE:  The forecasted monthly requirement  </...
PROBLEM P3: CONCEPT OF DOMINANT SEQUENCE <ul><li>PROBLEM STATEMENT:  the requirement of an item  </li></ul><ul><li>in the ...
PROBLEM P3: CONCEPT OF DOMINANT SEQUENCE cont., <ul><li>The costs of the alternative purchasing plans can  </li></ul><ul><...
PROBLEM P3: CONCEPT OF DOMINANT SEQUENCE cont., <ul><li>The number of dominant sequences for a T period </li></ul><ul><li>...
CONCLUDING REMARKS <ul><li>Approaches to Inventory Management </li></ul><ul><li>Decisions on Inventory taken without consi...
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Inventory management

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Inventory management

  1. 1. INVENTORY MANAGEMENT PROF ASHIS CHATTERJEE
  2. 2. MOTIVATION FOR STUDYING INVENTORY MANAGEMENT <ul><li>Economics involved in producing or purchasing in batches </li></ul><ul><li>Uncertainty in both demand and supply </li></ul><ul><li>Seasonality in demand pattern </li></ul><ul><li>Availability of different Transportation and Distribution modes </li></ul>
  3. 3. TYPES OF INVENTORY <ul><li>BATCH OR CYCLE STOCK </li></ul><ul><li>Manufacturing or purchasing an item at a rate higher than its </li></ul><ul><li>consumption rate, to reduce set-up/ordering costs. Involves </li></ul><ul><li>trade-off between Inventory and set-up/ordering costs. </li></ul><ul><li>BUFFER OR SAFETY STOCK </li></ul><ul><li>Maintaining extra stock over the average requirement to guard </li></ul><ul><li>against uncertainty. Involves trade-off between Inventory </li></ul><ul><li>Investment and Customer Service level. </li></ul>
  4. 4. TYPES OF INVENTORY <ul><li>ANTICIPATION STOCK </li></ul><ul><li>Maintaining extra stock to meet peak season demand. </li></ul><ul><li>Involves trade-off between Inventory carrying costs and </li></ul><ul><li>costs related to changing production levels. </li></ul><ul><li>TRANSPORTATION STOCK </li></ul><ul><li>Goods-in–transit arises because of the necessity of </li></ul><ul><li>moving material from one place to another. Movement rate </li></ul><ul><li>depends on Inventory carrying and Transportation costs. </li></ul>
  5. 5. SELECTIVE CONTROL OF MATERIALS <ul><li>ABC ANALYSIS </li></ul><ul><li>Classification of all consumption items, based on </li></ul><ul><li>the “Consumption Value”. </li></ul><ul><li>If Annual Demand = D units </li></ul><ul><li>Cost per unit =Rs.C </li></ul><ul><li>Then, Consumption value = Rs.(DxC). Based on </li></ul><ul><li>this, Inventory of a number of items can be </li></ul><ul><li>separated into A, B and C classes. </li></ul>
  6. 6. ABC CLASSIFICATION <ul><li>A Items: Those relatively few items that account for high consumption value (CV), say,15% of the items accounting for 70% of the consumption value. </li></ul><ul><li>B items: say,25% of the items, accounting for 20% of the consumption value. </li></ul><ul><li>C items: Bulk of the items, say,60%, that account for 10% of the consumption value. </li></ul>
  7. 7. ABC CLASSIFICATION <ul><li>EXAMPLE: </li></ul><ul><li>Annual Usage/ CV(Rs) Cum.Usage </li></ul><ul><ul><ul><ul><ul><li>39400 39400 (39.4%) A </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>30500 69900 (69.9%) A </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>10900 80800 (80.8%) B </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>9800 90600 (90.6%) B </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>3800 94400 (94.4%) B </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>2000 96400 (96.4%) C </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>1800 98200 (98.2%) C </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>800 99000 (99.0%) C </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>600 99600 (99.6%) C </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>400 100000 (100%) C </li></ul></ul></ul></ul></ul>
  8. 8. INVENTORY CONTROL MODELS <ul><li>DEMAND </li></ul>STATIC/ UNIFORM DYNAMIC/ VARIABLE DETERMINISTIC PROBLEM P1 PROBABILISTIC PROBLEM P2 DETERMINISTIC PROBLEM P3 PROBABILISTIC PROBLEM P4
  9. 9. PROBLEM P1: INVENTORY CONTROL FOR STATIC DETERMINISTIC DEMAND <ul><li>Consider the following problem: Demand for a particular item is uniform and 12,000 units per year. There is a fixed order placement and receiving cost of Rs. 120 each time an order is placed. Each item costs Rs. 10 and the retailer has a holding cost of 20%. Find the quantity that the store manager should order in each replenishment lot. </li></ul><ul><li>Total annual cost = Annual ordering cost + Annual inv. carrying cost </li></ul><ul><li>Annual ordering cost = DA/Q </li></ul><ul><li>Annual inv. carrying cost = ½ QIC </li></ul><ul><li> </li></ul>
  10. 10. PROBLEM P1: DETERMINING THE EOQ/ BATCH/CYCLE STOCK <ul><li>Total annual cost = DA/Q + ½ QIC </li></ul><ul><li>On differentiating total cost with respect to Q, we </li></ul><ul><li>obtain the Economic Order Quantity (EOQ) as: </li></ul><ul><li> ________ </li></ul><ul><li>EOQ = √2DA / IC </li></ul><ul><li>D = Annual Demand (Units) = 12,000 </li></ul><ul><li>A = Cost per Order = Rs. 120 </li></ul><ul><li>I = Inv. carrying factor (Rs/Rs/ yr)= 0.2 </li></ul><ul><li>C = Cost per unit = Rs 10 </li></ul><ul><li>Thus, required Order Quantity = 1200 units </li></ul>
  11. 11. PROBLEM P1: INVENTORY CONTROL FOR STATIC DETERMINISTIC DEMAND <ul><li>P1 allows us to determine the Batch/ </li></ul><ul><li>Cycle stock. </li></ul><ul><li>It brings out the economics that may exist in purchasing/producing items in batches. </li></ul><ul><li>The typical tradeoff is between inventory carrying cost and ordering/setup cost. </li></ul><ul><li>At optimum, the annual inventory carrying cost is equal to the annual ordering cost. </li></ul>
  12. 12. PROBLEM P1: AN EXTENSION <ul><li>Consider the earlier problem with the only change that now, the supplier has offered a discount based on the batch size that is ordered, say if the order size is between 0 and 799 units, the cost per unit will be Rs.13 for all units, if the size is between 800 to 1499 units the cost will be Rs.12 and finally cost per unit will be Rs.10 if the order size is ≥ 1500 units. </li></ul>
  13. 13. PROBLEM P1: AN EXTENSION, EOQ WITH DISCOUNTS <ul><li>Here, purchasing cost is also a relevant cost. </li></ul><ul><li>Algorithm: </li></ul><ul><li>Step 1: Determine EOQ using the lowest cost per unit </li></ul><ul><li>(Rs.10). Check whether this EOQ is feasible i.e.whether </li></ul><ul><li>it is above 1500. If feasible : Stop, optimal has been </li></ul><ul><li>found. If not feasible go to next step. </li></ul><ul><li>Step 2: Calculate the total cost at the breakpoint, i.e., at </li></ul><ul><li>1500 units. For example, at Q= 1500 units, total cost = </li></ul><ul><li>12000 x 10 (purchase cost) + 8 x 120 (ordering cost) + </li></ul><ul><li>½ x 1500 x 0.2 x 10 (inventory carrying cost) </li></ul>
  14. 14. PROBLEM P1: AN EXTENSION <ul><li>Step 3: Determine EOQ using the next higher </li></ul><ul><li>cost/unit (Rs.12). Check whether this EOQ is </li></ul><ul><li>feasible i.e., whether it is between 800 and 1499. If </li></ul><ul><li>feasible, find the minimum of total cost at EOQ, </li></ul><ul><li>and total cost at Break Point i.e., TC(EOQ) and </li></ul><ul><li>TC(1500). Stop,Q corresponding to the min.cost is </li></ul><ul><li>optimal. If not feasible go to step 2. Continue till </li></ul><ul><li>end. </li></ul>
  15. 15. PROBLEM P2: INVENTORY CONTROL FOR STATIC PROBABILISTIC DEMAND <ul><li>Mean Rate of Demand not changing with respect to time. </li></ul><ul><li>With uncertainty coming in, besides the ordering and inventory carrying costs, one more type of cost becomes relevant, i.e. the cost of shortage. </li></ul><ul><li>Surrogate for the cost of shortage : service level (SL); 100% SL implies no stock out, 90% SL implies probability of stock out = 10%. </li></ul>
  16. 16. PROBLEM P2: INVENTORY CONTROL FOR STATIC PROBABILISTIC DEMAND <ul><li>For P2, Inventory Control implies answering the </li></ul><ul><li>following questions: </li></ul><ul><li>How frequently to check the stock status. </li></ul><ul><li>How much to order </li></ul><ul><li>When to place an order. </li></ul><ul><li>The policies for answering the first question </li></ul><ul><li>can be broadly divided into two categories: </li></ul><ul><li>Continuous Review Policy, also known as Transaction Reporting System, as the stock status needs to be checked only if a transaction occurs. </li></ul><ul><li>Periodic Review Policy: checking the stock status every T period. </li></ul>
  17. 17. PROBLEM P2: INVENTORY CONTROL FOR STATIC PROBABILISTIC DEMAND <ul><li>A typical Continuous Review policy may read as follows: “Go on checking the stock status continuously, order Q units when the inventory position drops down to s or below.” Q and s are respectively the order qty and the reorder level, the answers to the two major decision variables. </li></ul><ul><li>A typical Periodic Review Policy on the other hand may read as “ check the stock status every T months and order so as to bring the inventory position to S units.” The decision variables in this case are the review period T and the order up-to level S . </li></ul>
  18. 18. PROBLEM P2 : AN EXAMPLE <ul><li>Say, the daily demand of an item is uncertain, and </li></ul><ul><li>it can be 1,2 or 3 kg. with all the values being </li></ul><ul><li>equally probable. The average demand is not </li></ul><ul><li>changing with time. The lead time for procurement </li></ul><ul><li>is 2 days. Assume, that (s,Q) policy is used for </li></ul><ul><li>Inventory Control, where Q has been found from </li></ul><ul><li>Inventory holding and Ordering cost trade-off. The </li></ul><ul><li>Manager is interested in finding, when to place the </li></ul><ul><li>order so that (a) there is no stock out, (b) Service </li></ul><ul><li>Level achieved is 80%. </li></ul>
  19. 19. DETERMINING REORDER LEVEL (CONT.REVIEW POLICIES) <ul><li>Step 1 Find the Probability Distribution of Demand during the Lead time (L.T), </li></ul><ul><li>Demand during LT Prob. Cum.Prob. </li></ul><ul><li>2 1/9 1/9 </li></ul><ul><li>3 2/9 3/9 </li></ul><ul><li>4 3/9 6/9 </li></ul><ul><li>5 2/9 8/9 </li></ul><ul><li>6 1/9 9/9 </li></ul>
  20. 20. DETERMINING REORDER LEVEL (CONT.REVIEW POLICIES) <ul><li>Interpretation of Cumulative probability : Say, </li></ul><ul><li>for demand of 4 during lead time, the cum.prob. is </li></ul><ul><li>6/9, i.e, 67%. It implies that during the lead time </li></ul><ul><li>there is 67% chance that demand will be ≤ 4 kg. </li></ul><ul><li>Thus, if an order is placed with 4Kg. in hand, the </li></ul><ul><li>demand will be satisfied for 67% of the time (SL). </li></ul><ul><li>Step 2 Find reorder level based on the desired SL. </li></ul><ul><li>Thus, 80% SL implies a Reorder Level of 5Kg. </li></ul>
  21. 21. PROBLEM P2: INVENTORY CONTROL FOR STATIC PROBABALISTIC DEMAND <ul><li>P2 allows us to determine the Buffer/ Safety stock. </li></ul><ul><li>It brings out the economics that may exist in not allowing shortages. </li></ul><ul><li>The typical tradeoff is between inventory carrying cost and the shortage cost/ service level. </li></ul>
  22. 22. PROBLEM P3: INVENTORY CONTROL FOR DYNAMIC DETERMINISTIC DEMAND <ul><li>AN EXAMPLE: The forecasted monthly requirement </li></ul><ul><li>of a consumption item for the next one year is given below. </li></ul><ul><li>(Jan to Dec) 25, 55, 65, 85, 75, 63, 51, 57, 115, 87, 52, 91. </li></ul><ul><li>The cost per order is Rs.500 and the inventory carrying </li></ul><ul><li>cost calculated based on the quantity left at the end of </li></ul><ul><li>every month is given as Rs.10 per unit per month. The </li></ul><ul><li>manager has to decide how much to order, and when. </li></ul>
  23. 23. PROBLEM P3: CONCEPT OF DOMINANT SEQUENCE <ul><li>PROBLEM STATEMENT: the requirement of an item </li></ul><ul><li>in the upcoming two months are 100 and 50 units. The </li></ul><ul><li>problem is to find the minimum cost purchase plan. The </li></ul><ul><li>relevant costs are, ordering cost, and inventory carrying </li></ul><ul><li>cost (ICC). Cost per order is Rs. A and ICC is Rs. H per </li></ul><ul><li>unit per month levied on the end inventory . </li></ul><ul><li>ANALYSIS: As there is no shortage allowed, the </li></ul><ul><li>alternative purchase plans can be written as: </li></ul><ul><li>Procure 100 in first month and 50 in the second </li></ul><ul><li>Procure 101 in first month and 49 in the second </li></ul><ul><li>Procure 102 in first month and 48 in the second </li></ul><ul><li>n. Procure 150 in first month and 0 in the second </li></ul>
  24. 24. PROBLEM P3: CONCEPT OF DOMINANT SEQUENCE cont., <ul><li>The costs of the alternative purchasing plans can </li></ul><ul><li>be seen as 2A, 2A + H, 2A +2H……A + 50H. As H </li></ul><ul><li>is positive, it is sufficient to consider only the first </li></ul><ul><li>and the last alternative. Thus, if the requirement </li></ul><ul><li>for the two months are D 1 and D 2 respectively, it is </li></ul><ul><li>sufficient to consider the following two sequences/ </li></ul><ul><li>plans for optimality: 1. D 1 + D 2 , 0 </li></ul><ul><li> 2. D 1 , D 2 </li></ul><ul><li>These are called the dominant sequences. </li></ul>
  25. 25. PROBLEM P3: CONCEPT OF DOMINANT SEQUENCE cont., <ul><li>The number of dominant sequences for a T period </li></ul><ul><li>problem = 2 T-1 , thus for a 3 period problem with </li></ul><ul><li>requirements D 1 ,D 2 , D 3 , The minimum cost plan </li></ul><ul><li>will be one among the following four plans: </li></ul><ul><li>D 1 + D 2 + D 3 , 0,0 </li></ul><ul><li>D 1 + D 2 , 0, D 3 </li></ul><ul><li>D 1 , D 2 + D 3 , 0 </li></ul><ul><li>D 1 , D 2 , D 3 </li></ul>
  26. 26. CONCLUDING REMARKS <ul><li>Approaches to Inventory Management </li></ul><ul><li>Decisions on Inventory taken without consideration of Production issues. </li></ul><ul><li>Simultaneous decisions on Inventory and Production </li></ul><ul><li>Approach (a) has been examined in this </li></ul><ul><li>session. Approach (b) will be taken up under </li></ul><ul><li>Operations Planning in the next session. </li></ul>

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