SCM Inventory Part -II

Inventory Management

Part-II

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EOQ Problem 1:Let monthly demand at a retailer is 1000 units. Fixed ordering costs are Rs 4000 per order. Item cost is 500 per item. Inventory holding costs are 20%.

Determine: Nos. of units in each replenishment lot.Cycle inventoryNos. of orders per yearAnnual Inventory related costs (ordering and inventory holding costs)Average material flow time4-*Inventory Management

Annual demand, D = 1,000 x 12 = 12,000 unitsOrder cost per lot, Co = Rs 4,000Unit cost of item, C = Rs500Inventory holding cost per unit per year (as a fraction of unit cost) Cc = 0.2 x 500 = Rs 100

Qopt = 2 Co D / Cc = 2 x 4000 x 12000 / 100= 980 units

4-*Inventory Management

Cycle Inventory = Qopt / 2 = 980/2 = 490 Nos. of orders per year = D / Qopt = 12000 / 980 = 12.24Annual ordering and inventory holding costs

= (D / Qopt )x Co + (Qopt / 2 ) x Cc = 12.24 x 4000 + 490 x 100 = Rs 97960Average material flow time = Qopt / 2 D = 980 / 2 x 12000 = .041 year = .49 months = 14.96 days


Now if in the previous example, manager wants to reduce the lot size to 200, then what are the annual inventory related costs. With Q=200(D / Q )x Co + (Q / 2 ) x Cc = Rs 250,000. This lot size is undesirable as total costs have increased.What need to be done make the lot size reduction optimal ?Qopt = 200, D = 1000x12=12000, Cc = .2 x 500 = 100Qopt = 2 Co D / Cc can be written as :Co = Cc (Qopt)^2 / 2 x D = 166.7 Manager has to reduce the ordering cost from Rs 4000 to Rs 166.7 for the lot size of 200 to be optimal.


EOQ Problem 2:The epaint store stocks paint in its warehouse and sells it online on its internet website. The store stocks several brands of paint. However its biggest seller is Sharman-Wilson Ironcoat paint. The company wants to determine the optimal order size and total inventory cost for Ironcoat paint given an estimated annual demand of 10,000 gallons of paint, an annual carrying cost of $ 0.75 per gallon and an ordering cost of $150 per order. Also determine the nos. of orders per annum and time between orders (i.e. order cycle time) with 311 working days per year.


EOQ Problem 213-*

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Inventory ManagementReorder Point:Apart from the ordered quantity, decision maker also need to specify point of time when to place the order.This point of time is called Reorder Point. As the daily demand is d and supplier has a lead time of L days, the demand faced by retailer during lead time is L x d units.Therefore, retailer continuously monitors inventory and when inventory level reaches L x d (the Reorder point), retailer places a order of Qopt (i.e. EOQ). 4-*

Inventory ManagementInsights from cycle stock inventory modelLarger the cycle inventory, longer the material flow time which indicates longer time between production and sales. This in turn makes firm vulnerable to demand changes in market place.Also larger the cycle inventory, larger will be the firms working capital requirement.Also, larger inventory shall require larger space requirementsHence lower cycle inventory is always desirable.E.g. Toyota keeps cycle inventory of only few hours of production.

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Inventory ManagementInsights from cycle stock inventory modelLarger retailers (i.e. higher demand) shall have in general better inventory turn over ratio than smaller ones.

In case of stable demand, if retailer wants to improve inventory turnover ratio, ordering costs has to be decreased.

For high value items (in comparision to small value items), nos. of orders placed shall be more and lot sizes shall be small.4-*

Problem:Assume that epaint store has its own manufacturing facility in which it produces ironcoat paint. The ordering cost Co is the cost of setting up the production process. Co = $150. Cc= $0.75 per gallon and D=10,000 gallons per year. The manufacturing facility operates for 311 days in a year, same as store. Manufacturing facility produces 150 gallons per day. Determine the optimal order size, total inventory cost, length of time to receive an order, number of orders per year and maximum inventory level.

4-*Production Quantity Model

Production Quantity Model Problem (related to Problem 2)13-*Cc = $0.75 per gallonCo = $150D = 10,000 gallonsd = 10,000/311 = 32.2 gallons per dayp = 150 gallons per day

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Production Quantity Model13-*

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Quantity discounts: Price per unit decreases as order quantity increasesIn basic EOQ model, purchase price was not considered as optimal order quantity / size remains same irrespective of the purchase price.However discount is associated with specific order size , different from optimal order size.Manager need to consider tradeoff between increased inventory related costs (specifically higher carrying costs) in case of discount (on account of bigger order size) versus total inventory costs with EOQ (i.e. with optimal order size).

4-*Quantity Discounts

Quantity Discounts13-*

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Quantity Discount Model13-*

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Problem:Avtek, a distributor of audio and video equipment, wants to reduce a large stock of televisions. It has offered a local chain of stores a quantity discount pricing schedule as follows:

The annual carrying cost for the stores for a TV is $190, ordering cost is $2500 and annual demand for this particular model TV is estimated at 200 units. The chain wants to determine if it should take advantage of this discount or order the basic EOQ order size.4-*Quantity Discount ModelQUANTITYPRICE

1 - 49$1,40050 - 891,10090+900

Quantity Discount13-*

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Inventory ManagementSafety Inventory :Cycle Safety Inventory model assumed that there is no uncertainty in demand and supply.

Actual Demand may differ from the forecasted demand for a given period due to demand fluctuations or forecast errors Demand Uncertainty

Also, supplier lead time may be uncertain Supply Uncertainty4-*

The uncertainty in demand or supply may lead to a stockout situation.

To take care of stockout situations, firms carry safety inventory


R= reorder pointSafety Inventory is the average inventory in hand when the replenishment lot arrives.

Inventory

TimeAverage Inventory Cycle Inventory Safety Inventory

Average inventory carried by the firm is the average cycle inventory plus safety inventory.

Tradeoff - Increases safety inventory improves product availability but it also increases inventory carrying costs of the firm.

In todays business environment, a firm faces:Increased product variety Pressure to improve product availability Shorter product life cyclea and b pushes a firm to increase safety inventory whereas c pushes it to decrease safety inventory.


Level of Safety inventory is decided by capturing :

1. Uncertainty in demand2. Uncertainty in supply

for a given Target service level4-*Inventory Management

Capturing Uncertainty:Uncertainty in demand is captured using demand distribution.

In real life situations, demand can be assumed to follow a normal distribution.

Uncertainty is measured using: Standard deviation , Coefficient of variation, Range.

Standard deviation is most widely used measure.


Coefficient of Variation = Standard deviation / Mean

Standard Deviation alone do not capture uncertainty

Slow moving items typically have higher uncertainty and higher CV while fast moving items have lower uncertainty and lower CV.

For a new item or new supplier where past data is not available, a subjective assessment of standard deviation can be made as :

Standard Deviation = Range (i.e optimistic estimate pessimistic estimate)/ 64-*Inventory Management

Demand distribution is characterized by mean demand and standard deviation of demand.Let d1, d2, d3, d4.. dn be the demand observed for n days.Mean or average demand = d=(d1 + d2+ d3+ d4 . dn )/ nStandard deviation of daily demand = d

= ((d1 - d)^2 + (d2 - d)^2 + .(dn - d)^2) / n

Similarly for supply uncertainty, mean lead time be L and standard deviation of lead time is L


Referring to the model, there is no possibility of stockout between the point the replenishment arrives and reorder point.Firm is exposed to stockout only after placement of order and arrival of replenishment i.e. during the lead time.

Let LTD denotes the mean value of the total lead time demand and Lead Time Demand is the standard deviation of lead time demand.

Uncertainty during the lead time is because of uncertainty in actual demand and/or uncertainty is supply.


Value of LTD and Lead Time Demand can be calculated from lead time demand distribution, if it is available from historical data.Or by using the formulas as:

(L= Average Lead time, d = Average Daily Demand)LTD = L x dLead Time Demand = L d2 + d2 L2 4-*Inventory Management

Safety Stock = K x Lead Time Demand

Here K is the Safety Factor= Nos. of standard deviation corresponding to service level probability.K indicates product availability.

Safety Stock = K d L if L is zero

Reorder Point (when to place the order)=

LTD + Safety Stock = LTD + K Lead Time Demand


Safety Stock Distribution of Demand During Lead TimeInventory ManagementLTD = d L Probability of Stockout

Reorder Point For a Service Level13-*Probability of meeting demand during lead time = service levelProbability of a stockoutRSafety stockdLDemandKd L

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Demand Data

d1

d2

d3

d4

d5

d6

d7

d 8

d 9

d10

Demand

115

95

150

125

28

90

93

115

93

96

Lead-time data

L1

L2

L3

L4

L5

L6

L7

L 8

L 9

L10

Lead-time

12

15

4

21

18

11

12

18

19

20

Daily Demand d, Mean d = 100 , d = 30Supplier Performance Mean lead time = L= 15 Days , L = 5LTD = 100 x 15=1500Lead Time Demand = 513

Now,Safety Stock = K x Lead Time Demand For a 95% service level, K = 1.65Safety Stock = 846Reorder Point = 1500 +846 = 2346


There exists a relationship between service level and K. Given the desired service level, value of K can be determined or vice versa( Using excel function :Service level = NORM.DIST(K,0,1,1) or K = NORM.INV (s/100, 0,1); or K = NORMSINV(s); Alternatively z table can be used.

In the present problem, if K=1 then Service Level = 84.1%, then Safety stock = 513 units.

It means with this safety stock chances of stockout in a replenishment cycle are 15.9 percent only (100-84.1).


Impact of Service Level On Safety Stock

Measuring Product AvailabilityCycle service level (CSL)Fraction of replenishment cycles that end with all customer demand being met.It is the probability of not having stockout in a replenishment cycleProduct fill rate (fr) : Fraction of product demand satisfied from product in inventory

Order fill rate: Fraction of orders filled from available inventory

Inventory Control Systems13-*Continuous system (fixed-order-quantity)Constant amount ordered when inventory declines to predetermined levelInventory is not tracked continuouslyTime between orders is not fixedOrder quantity is fixed

Periodic system (fixed-time-period)Order placed for variable amount after fixed passage of timeOrder is placed to raise the inventory to prespecified threshold.Inventory is not tracked continuouslyTime between orders is fixedOrder quantity is not fixed

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Impact of Supply Chain Redesign on Inventory: Impact of Aggregation : Centralisation vs Decentralisation

Any supply chain redesign has a significant impact on costs especially inventory and transportation costs.

With centralization, firm will be able to reduce inventory related costs but will increase its transportation cost to maintain same service level.

Supply chain managers need to justify the same with rigorous cost benefit analysis by taking into account inventory related costs and transportation costs.4-*Inventory Management

Impact of Aggregation on Safety InventoryAggregation and safety inventories in CentralisationDi:Mean weekly demand in region i, i = 1,, k si:Standard deviation of weekly demand in region i, i = 1,, k rij:Correlation of weekly demand for regions i, j, 1 i j k : Demand faced by Central location : Standard Deviation of weekly demand for central location

Centralization vs Decentralization

Illustration:Let us consider the case of a company that currently has 16 regional stock points/warehouses and serves its dealers from the closest stock point.

The supply chain manager is exploring the option of centralising its inventory.Let each region have similar demand distribution with mean daily demand=d= 100 and standard deviation = 30.Demand of different regions in independentEach stock point/ warehouse in both centralisation and decentralization gets served by plant with lead time of exactly 15 days.


Average transportation cost in decentralization case is Rs 1 / unit and in centralization case increases by 10% i.e. Rs 1.1 / unit.

Ordering Cost = Co (or S) = Rs 256 / order

Inventory holding cost per unit per year = Cc = Rs 6

Required service level = 97.7% (K=2)

Working days per year = 300


Cycle Inventory:

Centralized case

D = 16 x 100 x 300; Qopt = 6400, Hence Cycle Inventory = 6400/2 = 3200

Decentralized caseD for each Stock point in decentralized case = 100 x 300; Qopt = 1600, Hence Cycle Inventory = 1600/2 = 800


Safety Inventory:Demand faced by centralized stock point:

d = d1 +d2 + d3dnD = d12 + d22 + d32 . dn2 The phenomenon is called Risk Pooling which suggests that demand uncertainty is reduced when demand across demand locations is pooled.It happens because higher demand in one loaction offsets lower demand in another location.Lower demand uncertainty leads to lower safety stock in the centralized case.


Safety Stock:In case of centralisation

D = 302 x 16 = 120 Safety stock= K D L = 2 x 120 x 15 = 3600In case of Decentralisation

For each regional stock point,d= 30, K=2, Safety stock= K d L = 2 x 30 x 15 = 232For all 16 locations, Safety Inventory = 16 x 232


4-*Inventory ManagementOption of centralising the inventory should be chosen

Note:Safety stock decreases due to risk pooling and lower demand uncertainty faced by centralised location.

Cycle stock in centralized case reduces because of economies of scale.

If in this case, transportation costs say increases by say 25% , then centralisation will not be benificial


Impact of Aggregation on Safety InventoryThe Square-Root Law

Centralisation vs Decentralisation:

Higher the demand uncertainty of the product, higher will be the savings in safety stock when moving from decentralisation to centralisation.

For fast moving products like salt, wheat with low demand uncertainty and high transportation cost, centralisation is not beneficial.

For slow moving products with high demand uncertainty, it is better to centralise.

Higher the nos. regional stock points, higher will be the savings in cycle inventory in case of centralization because of economies of scale.4-*Inventory Management

Two possible disadvantages to aggregation

Increase in response time to customer orderIncrease in transportation cost to customerInventory Management

Managerial Levers to Reduce safety Stock:

Reduction in Demand Uncertainty: This can be achieved with better forecasting or entering into contracts with some customers with assured stable demand.

2. Reduction in Supplier Lead Time: This can be achieved by working with supplier and by using faster mode of transport.

3. Reduction in supply uncertainty: This can be achieved using more reliable modes of transport and working with supplier.4-*Inventory Management

Managing Seasonal Inventory:

A firm that faces seasonal variation in demand can follow either of the two basic approaches:Chase Option: Produce as per demand in each season and carry no seasonal inventory. During peak season demand can be met by either hiring more labour, running overtime, outsourcing etc.Level Option: Produce at the same level through out the year and build inventory during lean season and use this inventory to take care of excess demand during the peak season.


Illustration:A toy manufacturer faces demand for toys as given.Inventory carrying cost per unit per quarter is Rs3. Each worker can produce 500 units of toys per quarter.Each temporary worker hired during the peak demand quarter (Q4) will result in additional cost of Rs 6000.Manufacturer needs to decide whether to pursue chase or level option to meet demand.

Relevant costs to be considered are the incremental costs of hiring in chase option and inventory carrying costs in case of level option.


Illustration: Managing Seasonal StockCost: level option= 18,000 Chase option= 48000Inventory Management

Q1Q2Q3Q4Demand80008000800012000Level optionProduction9000900090009000Hiring Cost0000Inv. C. Cst3000600090000Chase optionProduction80008000800012000Hiring Cost00048000Inv. C. Cst0000

Short lifecycle products:

Selling season is small.Either physical deterioration (perishable goods) or perceived value (style goods) decreases after selling season.One does not have opportunity of replenishment during selling season.Sales should be anticipated before selling season and requisite stock carried.E.g. fashion products, bread, newspaper


Optimum Order size for short life cycle productsCu = Cost of understockingCo = Cost of OverstockingOptimal service level = (Cu x 100) / (Cu + Co)Optimal order size = Mean Demand + K x standard deviation of demandK = Service factorCost of understocking is an opportunity loss by the firm for each unit of lost sales.The cost of overstocking is the loss incurred by a firm for each unit at the end of the selling season.


Illustration: Optimum Order for a New Music CDCD purchase price = Rs. 200CD sales price = Rs. 300CD sales price after first weeks = Rs. 62.Demand: Average 100 and Standard Deviation 30

Find optimum order quantity.If manufacturer offers buyback scheme with cost of administering return- Rs. 53, what would be the decision?


With Cu = 100, Co = 138Optimum service level = .42 = 42 %Corresponding K = -0.2Optimum order size = 100 0.2 x 30 = 94In case of buyback:Cu = 100, Co = 53

Optimum service level = .655 = 65.5 %Corresponding K = 0.4Optimum order size = 100 + 0.4 x 30 = 1124-*Inventory Management

Multiple item, Multiple location Inventory Management:

Managing inventory in actual supply chain involves dealing a large number of items often stocked at multiple stock points at various stages in the supply chain.

Inventory management need to be carried out at each of these stock points and integrated with the rest of the supply chain.Inventory Management

Inventory ManagementFor multiple items, theoretically inventory management and supply chain analysis is to be carried out for each and every items.

Since nos. of items are in general large and have varying importance, managers divide items into multiple categories and handle different categories in different ways.

There are several classification schemes for categorizing items or SKU

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Inventory Management1. ABC Classification:Items are classified on the basis of sales on value terms. A = very ImportantB = Moderate ImportantC = Little Important

ABC analysis is used for a) allocation of management time b) Improvement Efforts c) Setting up service levels d) Stocking decisions e.g. A category items at regional distribution points, C category items at central warehouse, B category at few regional locations4-*

ABC ClassificationClass A5 15 % of units70 80 % of value Class B30 % of units15 % of valueClass C50 60 % of units 5 10 % of value

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Illustration:The maintenance department for a small manufacturing firm has responsibility for maintaining an inventory of spare parts for the machinery it services. The parts inventory, unit cost, annual usage are given in following table.The department manager wants to classify the inventory parts according to the ABC system to determine which stocks of parts should be closely monitored.4-*ABC Classification

ABC Classification- Illustration13-*

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ABC Classification13-*

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ABC Classification13-*Example 10.1

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2. FSN classificationItems are classified as Fast moving , slow moving and non-moving.Slow moving items are stored centrally and fast moving items are stocked de-centrally.Non-moving items are candidates for disposal.This type of classification is popular in retail industry.


3. VED Classification:Items are classified on criticality:Vital = V, Essential = E , Desirable = DThis type of classification is popular in maintenance management.One can fix different service levels for different items.


Two Forms of Demand13-*DependentDemand for items used to produce final products Tires for autos are a dependent demand itemIndependentDemand for items used by external customersCars, appliances, computers, and houses are examples of independent demand inventory

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Inventory ManagementDecoupling Inventory:Entire supply chain is usually divided into multiple stages with multiple decision makers.Decision making units can be both at both organisational and departmental level.At organisational and departmental boundaries large inventories can be held.The decoupling inventory provides the flexibility needed by each decision making unit to manage its operations independently and to optimise its performance.Improved coordination among stages can reduce decoupling inventory significantly.4-*

Inventory ManagementPipeline Inventory:Also called in-transit inventory.It consists of materials actually being worked on (work-in-process inventory) or being moved from one location to another in the chain (on transit inventory).Pipeline inventory of an item between two adjacent locations is the product of the process time or transport time and usage rate of an item Pipeline inventory may be reduced by using faster rater of transporting or by reducing manufacturing lead time. 4-*

Illustration :

LT -Shipment by air = 7 daysLT- Shipment by sea = 45 daysAverage demand = 100/dayPipeline Inventory ( Shipment by air) = 700 unitsPipeline Inventory ( Shipment by Sea = 4500 unitsInventory Management

Inventory ManagementDead Inventory or Stock:Dead Stock refers to that part of non-moving inventory that is unlikely to be of any further use in supply chain operations or markets.Dead Stock, essentially includes items that have become obsolete because of changes in customer preferences, design, production processes.Unfortunately, in many firms dead stock is allowed to accumulate as disposal of dead stock show up in balance sheets as financial loss. Rather it is wrongly shown as assets.Firms should carefully monitor dead stock and find means to reduce it.

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SCM Inventory Part -II