(3) Inventory Management in SC0-1

8/10/2019 (3) Inventory Management in SC0-1

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Inventory Management and

Risk Pooling


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Forms of Inventory:

Raw material inventory

Work-in-process inventory

Finished product inventory

Suppliers Manufacturers Distribution

Centers

Warehouses Customers

Converts raw materials

Into finished products

Finished products

distributed to customers


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Reasons for keeping inventory

1.To protect firm from unexpected changes in

customer demand; uncertainty in customer

demand is due to:

Short life cycle of an increasing number of products Presence of many competing brands in the

marketplace; makes it difficult to predict demand for a

specific model

2. To protect against uncertainty in the quantityand quality of the supply, supplier costs and

delivery times.


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Single warehouse example

Factors affecting inventory policy include:

1. Customer demand

2. Replenishment lead time

3. Number of different products stored at the warehouse

4. Length of planning horizon

5. Costs:a. Order cost

i. Cost of product

ii. Transportation cost

b. Inventory holding costi. Taxes and insurance on inventories

ii. Maintenance costsiii. Obsolescence costs

iv. Opportunity costs

6. Service level requirement 100% is maximum level


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Economic Lot size model

Introduced in 1915

Model assumptions:

Single item

Demand is constant at a rate of D items per day

Order quantities are fixed at Q items per order; that is, each time the

warehouse places an order, it is for Q items A fixed setup cost K is incurred everytime the warehouse places an

order

An inventory carrying cost, h, also referred to as holding cost isaccrued for every unit held in inventory per day

Lead time is zero

Initial inventory is zero

Planning horizon is infinite


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-D

Gradient = demand

Inventori, I(t)

t0T

For every cycle

Q units are used up at rate D.

=> T=Q/D

Q

Cycle time


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Total inventory cost in a cycle of length T:

K +

Since fixed cost is charged per order, andholding cost is for every unit held ininventory per day ( altogether there are T Q inventories in one cycle)

Dividing by T and by using Q=TD

Total cost per unit time:

G(Q)=

2

hTQ

2

KD hQ

Q


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Can be shown that the optimal orderquantity that will minimize the cost function

is:

Q*=Popularly known as economic order quantity

or EOQ

2KD

h


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Sensitivity Analysis

How sensitive is the cost function to errors in

calculating Q (or if we deliberately order

something different that Q*)?

Let G* be the optimal cost:

G*= KD/Q* + hQ*/2

=

=

2

22 /

KD h KD

hKD h

2KDh


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Sensitivity Analysis

Can be shown that

G(Q)/G* = (KD/Q + hQ/2)

= [ Q*/Q + Q/Q*]

By substituting values, can be shown that G(Q) is

relatively insensitive to errors in Q.For instance, 100% error in Q results only 25%

error in G(Q) (Table 3.1)

2KDh


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Insights

Optimal policy balances between inventory

cost per unit time and setup cost per unit

time (Figure 3.2); if we equate hQ/2 and

KD/Q, we will get the EOQ formula.

Total inventory cost is insensitive to order

quantities


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Demand uncertainty

Case: Swimsuit example:

Illustrates:

Importance of incorporating demand

uncertainty and forecast demand

Importance of characterizing the impact of

demand uncertainty on the inventory policy


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Case example

Motivates a powerful inventory policy usedin practice to manage inventory:

Whenever the inventory is below a certain

value, say s, we order or produce to increase

the level to S.

Also known as the (s,S) policy or a min max

policy.

s is the reorder point and S is the order-up-tolevel

In the swimsuit example reorder point is 8500

units and the order-up to level is 12,000 units


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Multiple order

So far we only consider only a single

ordering decision for entire planning

horizon

For some products it might be true because of

short selling season and there is no

opportunity to reorder products

Usually a decision maker may orderproducts repeatedly during a planning

horizon


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Multiple order Consider a case where a distributor of TV sets

(pg 51). Here distributor faces random demand for the product

Manufacturer cannot instantly satisfy orders

There is a fixed lead time

Distributor has to keep inventory because: To satisfy demand that occurs during lead time

To protect against uncertainty in demand

To balance annual inventory holding costs and annual

fixed order costs More frequent orders lead to lower inventory levels and

hence lower holding costs but higher fixed costs

Distributor has to decide on an inventory policy

i.e when and how much to order


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No fixed order costs

Assumptions: Daily demand is random and follows a normal

distribution

No fixed order cost; every time the distributor orders,

it pays an amount proportional to the quantity ordered

Inventory holding cost is charged per item per unittime

If customer order arrives when there is no inventory

on hand, the order is lost Distributor specifies a required service level; the

probability of not stocking out


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Information needed:

AVG= average daily demand faced bydistributor

STD= standard deviation of daily demand facedby distributor

L = replenishment lead time from supplier todistributor in days

h = cost of holding one unit of inventory per dayat distributor

= service level


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Inventory position at any point in time is theactual inventory at the warehouse plus itemsordered by the distributor that has not yet arrived

Distributor can use (s,S) policy where s=S.

When distributor inventory drops below S it willorder a quantity that will bring the inventoryposition up to S.

What is value of S?

It consists of 2 components:Average inventory during lead time; to make sure

there is enough inventory until next order arrives

Safety stock; inventory the distributor needs to keep

to safeguard against variations in demand


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S = (L AVG) + (z STD L)

Constant z is chosen from statistical tables, to

ensure that the probability of stockouts during

lead time is exactly 1- (table 3.2)

That the order-up-to level, S must satisfy,

P (demand during lead time S) = 1-

Read up on ex: 3.2.1


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Fixed order costs

Assume a fixed order cost of K for every item

order placed

In this case (s,S) inventory policy is used.

s = (L AVG) + (z STD L)

(the same as no fixed order cost)

S = max {Q, L AVG} + z STD LWhere Q =

From the economic lot size model

2K AVG

h


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ACME Problem

Current distribution system uses different

warehouses to serve separate markets

We have warehouses in Newton,

Massachusetts and Parasmus, New Jersey

The ACME example considers locating onlyone warehouse (somewhere between

Parasmus and Newton) to replace the existing

two, which is named central in the example

Conducts a detailed inventory analysis based on

two products and discover that a significant

reduction of average inventory can be achieved

for both products


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Risk pooling

Important concept in scm Replace existing warehouses with fewer strategically placed

ones

ACME example considers replacing two warehouses with one

Use the concept of coefficient of variation Coeff of var = std dev/ avg demand

Measures variability wrt average demand as opposed to standard deviationwhich measures absolute variabilty of customer demand

Suggests that demand variability is reduced if weaggregate demand across locations Because high demand from one customer will be offset by low

demand from another

Allows reduction in safety stock and therefore reduce inventory


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Risk PoolingEssentially it is a centralized distribution system

Critical points:1. Centralizing inventory reduces safety stock

and average inventory in the system.

---reallocation not possible in a decentralized

distribution system where different warehouses servedifferent markets

2. The higher the coefficient of variation, the greater thebenefit obtained from centralized systems

3. The benefits from risk pooling depend on the

behavior of demand from one market relative todemand from another.

Benefit decreases as correlation between demandfrom two markets become more positive


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Centralized vs decentralized

Safety stock Safety stock decreases for centralized

Service level Centralize is higher when both centralize and decentralize have same

safety stock

Overhead costs Costs are greater in a decentralized system because fewer economiesof scale

Customer lead time Decentralize is shorter

Transportation costs

If we increase number of warehouses, outbound transportation costsdecreases because warehouse are closer to markets

Inbound transportation cost increases

Net impact is not totally clear

Depends on situation


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Managing inventory in the supply

chain

Models described concerns a single facility

managing its inventory in order to minimize its

own cost as much as possible.

In a supply chain the objective is reducesystemwide cost

=> We have to consider the interaction of the

various facilities and the impact of this

interaction on the inventory policy employed by

each facility


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chain

Consider a retail distribution system with a

single warehouse serving a number of

retailers. Two assumptions:

Inventory decisions are made by a single

decision maker whose objective is to minimize

systemwide cost

Decision maker has access to inventoryinformation at each of retailers and at the

warehouse

M i i t i th l


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chainEchelon inventory concept

Echelon is defined as the stage or level in a supplychain.

Echelon inventory is defined as the on hand

inventory at any echelon plus all thedownstream inventory.

Eg: Echelon inventory at warehouse= inv atwarehouse + inv in transit to and in stock at

retailersEchelon inventory position at warehouse =

echelon inventory at warehouse + items orderedby warehouse that has not yet arrived


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chain=>the following effective approach in managing the single warehouse multi-

retailer system:

1. Individual retailers are managed as described before (see model (s,S)etc); i.e when inventory position at retailer falls below s, it will send anorder to warehouse to raise its inventory position to S.

2. Warehouse ordering decision is based echelon inventory position at

warehouse; also (s,S); this means that when echelon inventory positionfalls below s, it will order from its supplier so as to raise echelon inventoryposition to S.

s = (LeAVG) + (z STD Le)

Where Le= echelon lead time, defined as lead time between the retailers andthe warehouse plus leadtime between warehouse and its supplier

AVG= average demand across all retailers

STD= standard deviation of demand across all retailers

This technique can be extended to more complex supply chains


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Inventory reduction strategiesReferring to a survey in 1998; identified 5 top strategies

Periodic inventory review policy Inventory is reviewed at a fixed time interval and

every time it is reviewed, a decision is made on order

size

Possible to identify slow moving and obsoleteproducts and allows for reduction of inventory

Tight management of usage rates, lead times and safety

stock

Allows firm to make sure inventory is kept at theappropriate level

Can identify situations where usage rates decrease

for a few months which implies an increase in

inventory levels over the same period


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Inventory reduction strategies ABC approach

Here items are classified into 3 categories

Class A-all high value products, accounts for about

80% of annual sales

Class B- accounts for 15% of annual sales

Class C- low value items, no more than 5% of

sales

Reduce safety stock levels

Can be achieved by focusing on lead time reduction Quantitative approaches

Similar to the models described earlier

(3) Inventory Management in SC0-1

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