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INVENTORY MANAGEMENT PROF ASHIS CHATTERJEE
26

Inventory management

Nov 20, 2014

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Nilesh Ahuja

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Page 1: Inventory management

INVENTORY MANAGEMENT

PROF ASHIS CHATTERJEE

Page 2: Inventory management

MOTIVATION FOR STUDYING INVENTORY MANAGEMENT

• Economics involved in producing or purchasing in batches

• Uncertainty in both demand and supply

• Seasonality in demand pattern

• Availability of different Transportation and Distribution modes

Page 3: Inventory management

TYPES OF INVENTORY

• BATCH OR CYCLE STOCKManufacturing or purchasing an item at a rate higher than itsconsumption rate, to reduce set-up/ordering costs. Involvestrade-off between Inventory and set-up/ordering costs.

• BUFFER OR SAFETY STOCKMaintaining extra stock over the average requirement to guardagainst uncertainty. Involves trade-off between InventoryInvestment and Customer Service level.

Page 4: Inventory management

TYPES OF INVENTORY

• ANTICIPATION STOCK

Maintaining extra stock to meet peak season demand.

Involves trade-off between Inventory carrying costs and

costs related to changing production levels.

• TRANSPORTATION STOCK

Goods-in–transit arises because of the necessity of

moving material from one place to another. Movement rate

depends on Inventory carrying and Transportation costs.

Page 5: Inventory management

SELECTIVE CONTROL OF MATERIALS

ABC ANALYSIS

Classification of all consumption items, based on

the “Consumption Value”.

If Annual Demand = D units

Cost per unit =Rs.C

Then, Consumption value = Rs.(DxC). Based on

this, Inventory of a number of items can be

separated into A, B and C classes.

Page 6: Inventory management

ABC CLASSIFICATION

• 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.

• B items: say,25% of the items, accounting for 20% of the consumption value.

• C items: Bulk of the items, say,60%, that account for 10% of the consumption value.

Page 7: Inventory management

ABC CLASSIFICATION

EXAMPLE:

Annual Usage/ CV(Rs) Cum.Usage1. 39400 39400 (39.4%) A

2. 30500 69900 (69.9%) A

3. 10900 80800 (80.8%) B

4. 9800 90600 (90.6%) B

5. 3800 94400 (94.4%) B

6. 2000 96400 (96.4%) C

7. 1800 98200 (98.2%) C

8. 800 99000 (99.0%) C

9. 600 99600 (99.6%) C

10. 400 100000 (100%) C

Page 8: Inventory management

INVENTORY CONTROL MODELS

DEMAND

STATIC/ UNIFORM DYNAMIC/ VARIABLE

DETERMINISTIC

PROBLEM P1

PROBABILISTICPROBLEM P2

DETERMINISTIC

PROBLEM P3

PROBABILISTICPROBLEM P4

Page 9: Inventory management

PROBLEM P1: INVENTORY CONTROL FOR STATIC DETERMINISTIC DEMAND

• 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.

• Total annual cost = Annual ordering cost + Annual

inv. carrying costAnnual ordering cost = DA/QAnnual inv. carrying cost = ½ QIC

Page 10: Inventory management

PROBLEM P1: DETERMINING THE EOQ/ BATCH/CYCLE STOCK

Total annual cost = DA/Q + ½ QIC

On differentiating total cost with respect to Q, we

obtain the Economic Order Quantity (EOQ) as:

________

EOQ = √2DA / IC

D = Annual Demand (Units) = 12,000

A = Cost per Order = Rs. 120

I = Inv. carrying factor (Rs/Rs/ yr)= 0.2

C = Cost per unit = Rs 10

Thus, required Order Quantity = 1200 units

Page 11: Inventory management

PROBLEM P1: INVENTORY CONTROL FOR STATIC DETERMINISTIC DEMAND

• P1 allows us to determine the Batch/

Cycle stock.

• It brings out the economics that may exist in purchasing/producing items in batches.

• The typical tradeoff is between inventory carrying cost and ordering/setup cost.

• At optimum, the annual inventory carrying cost is equal to the annual ordering cost.

Page 12: Inventory management

PROBLEM P1: AN EXTENSION

• 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.

Page 13: Inventory management

PROBLEM P1: AN EXTENSION, EOQ WITH DISCOUNTS

Here, purchasing cost is also a relevant cost. Algorithm:Step 1: Determine EOQ using the lowest cost per unit(Rs.10). Check whether this EOQ is feasible i.e.whether it is above 1500. If feasible : Stop, optimal has beenfound. If not feasible go to next step.

Step 2: Calculate the total cost at the breakpoint, i.e., at 1500 units. For example, at Q= 1500 units, total cost = 12000 x 10 (purchase cost) + 8 x 120 (ordering cost) + ½ x 1500 x 0.2 x 10 (inventory carrying cost)

Page 14: Inventory management

PROBLEM P1: AN EXTENSION

Step 3: Determine EOQ using the next higher

cost/unit (Rs.12). Check whether this EOQ is

feasible i.e., whether it is between 800 and 1499. If

feasible, find the minimum of total cost at EOQ,

and total cost at Break Point i.e., TC(EOQ) and

TC(1500). Stop,Q corresponding to the min.cost is

optimal. If not feasible go to step 2. Continue till

end.

Page 15: Inventory management

PROBLEM P2: INVENTORY CONTROL FOR STATIC PROBABILISTIC DEMAND

• Mean Rate of Demand not changing with respect to time.

• With uncertainty coming in, besides the ordering and inventory carrying costs, one more type of cost becomes relevant, i.e. the cost of shortage.

• Surrogate for the cost of shortage : service level (SL); 100% SL implies no stock out, 90% SL implies probability of stock out = 10%.

Page 16: Inventory management

PROBLEM P2: INVENTORY CONTROL FOR STATIC PROBABILISTIC DEMAND

For P2, Inventory Control implies answering the following questions:• How frequently to check the stock status.• How much to order • When to place an order.The policies for answering the first questioncan be broadly divided into two categories:• Continuous Review Policy, also known as

Transaction Reporting System, as the stock status needs to be checked only if a transaction occurs.

• Periodic Review Policy: checking the stock status every T period.

Page 17: Inventory management

PROBLEM P2: INVENTORY CONTROL FOR STATIC PROBABILISTIC DEMAND

• 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.

• 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.

Page 18: Inventory management

PROBLEM P2 : AN EXAMPLE

Say, the daily demand of an item is uncertain, and it can be 1,2 or 3 kg. with all the values beingequally probable. The average demand is notchanging with time. The lead time for procurementis 2 days. Assume, that (s,Q) policy is used forInventory Control, where Q has been found fromInventory holding and Ordering cost trade-off. TheManager is interested in finding, when to place theorder so that (a) there is no stock out, (b) ServiceLevel achieved is 80%.

Page 19: Inventory management

DETERMINING REORDER LEVEL (CONT.REVIEW POLICIES)

• Step 1 Find the Probability Distribution of Demand during the Lead time (L.T),

Demand during LT Prob. Cum.Prob.

2 1/9 1/9

3 2/9 3/9

4 3/9 6/9

5 2/9 8/9

6 1/9 9/9

Page 20: Inventory management

DETERMINING REORDER LEVEL (CONT.REVIEW POLICIES)

Interpretation of Cumulative probability : Say,

for demand of 4 during lead time, the cum.prob. is

6/9, i.e, 67%. It implies that during the lead time

there is 67% chance that demand will be ≤ 4 kg.

Thus, if an order is placed with 4Kg. in hand, the

demand will be satisfied for 67% of the time (SL).

Step 2 Find reorder level based on the desired SL.

Thus, 80% SL implies a Reorder Level of 5Kg.

Page 21: Inventory management

PROBLEM P2: INVENTORY CONTROL FOR STATIC PROBABALISTIC DEMAND

• P2 allows us to determine the Buffer/ Safety stock.

• It brings out the economics that may exist in not allowing shortages.

• The typical tradeoff is between inventory carrying cost and the shortage cost/ service level.

Page 22: Inventory management

PROBLEM P3: INVENTORY CONTROL FOR DYNAMIC DETERMINISTIC DEMAND

AN EXAMPLE: The forecasted monthly requirement

of a consumption item for the next one year is given below.

(Jan to Dec) 25, 55, 65, 85, 75, 63, 51, 57, 115, 87, 52, 91.

The cost per order is Rs.500 and the inventory carrying

cost calculated based on the quantity left at the end of

every month is given as Rs.10 per unit per month. The

manager has to decide how much to order, and when.

Page 23: Inventory management

PROBLEM P3: CONCEPT OF DOMINANT SEQUENCE

PROBLEM STATEMENT: the requirement of an item

in the upcoming two months are 100 and 50 units. The

problem is to find the minimum cost purchase plan. The

relevant costs are, ordering cost, and inventory carrying

cost (ICC). Cost per order is Rs. A and ICC is Rs. H per

unit per month levied on the end inventory.

ANALYSIS: As there is no shortage allowed, the

alternative purchase plans can be written as:

1. Procure 100 in first month and 50 in the second

2. Procure 101 in first month and 49 in the second

3. Procure 102 in first month and 48 in the second

n. Procure 150 in first month and 0 in the second

Page 24: Inventory management

PROBLEM P3: CONCEPT OF DOMINANT SEQUENCE cont.,

The costs of the alternative purchasing plans can be seen as 2A, 2A + H, 2A +2H……A + 50H. As His positive, it is sufficient to consider only the firstand the last alternative. Thus, if the requirement

for the two months are D1 and D2 respectively, it issufficient to consider the following two sequences/

plans for optimality: 1. D1 + D2 , 0

2. D1 , D2

These are called the dominant sequences.

Page 25: Inventory management

PROBLEM P3: CONCEPT OF DOMINANT SEQUENCE cont.,

The number of dominant sequences for a T period

problem = 2 T-1, thus for a 3 period problem with

requirements D1 ,D2 , D3 , The minimum cost plan

will be one among the following four plans:

1. D1 + D2 + D3 , 0,0

2. D1 + D2 , 0, D3

3. D1 , D2 + D3 , 0

4. D1 , D2 , D3

Page 26: Inventory management

CONCLUDING REMARKS

Approaches to Inventory Management

a) Decisions on Inventory taken without consideration of Production issues.

b) Simultaneous decisions on Inventory and Production

Approach (a) has been examined in this

session. Approach (b) will be taken up under

Operations Planning in the next session.