Effective Strategies for Improving

Supply Chain Operations

Inventory Management

Dr. David Ben-Arieh

• Static solutions verses dynamic• Deterministic approach verses Stochastic• Single level vs. multi level (multi echelon

inventory systems)• Single product or multiple products• …

Why is it so hard to “optimize”

A theory should be as simple possible, but no simpler.

Albert Einstein

Try to follow this “simple” example:

Demonstration: The Beer Game

Very Basic Inventory Management

Scenario:Minimize the cost of a single “node” in the chain.

Assume that you provide a product to a loyal customer. You know the demand for your product and you need to decide how to stock yourself to be able to provide the product at a minimum cost to you.

Very Basic Inventory Management

* No backorders * Real ordering costs* Real cost of carrying inventory (o.w. use JIT)* No limit on order size * Constant demand rate!* Fixed lead time! * Single item inventory

EOQ or POQ models:

Q/D 2Q/D 3Q/D 4Q/D

Q

Inve

ntor

y

Time

Q/2

Time

Inventory level

t1 t2

-dp-dImax

Very Basic Inventory Management

Static, deterministic, single level, single product.

0.00

2.00

4.00

6.00

8.00

10.00

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0 100 200 300 400 500

Order Quantity (Q)

Cost

($/un

it)hQ/2D

A/Qc

Y(Q)

Q*=169

* 2ADQh

=

Somewhat Basic Inventory Management

Scenario:

Now your customer sends you his list of orders

for the next few weeks in advance . Every week

you need to supply that demand. Due to your

cost structure you may want to order your

material using a different schedule.

Somewhat Basic Inventory Management

Static, deterministic, variable demand, single level, single product.Example:

Solution: Not hard – Dynamic Programming.How realistic is this optimal solution?

t 1 2 3 4 5 6 7 8 9 10Dt 20 50 10 50 50 10 20 40 20 30ct 10 10 10 10 10 10 10 10 10 10At 100 100 100 100 100 100 100 100 100 100ht 1 1 1 1 1 1 1 1 1 1

Somewhat Basic Inventory Management- Additional Issues

• Quantity discount• Variable (uncertain) lead time• Cost of lead-time commitment• Cost of contract flexibility (order quantities).• Many more…

Basic Stochastic Model – still StaticNewspaper Boy Model

Scenario:As a “node” in the supply chain you need to be able to provide an “uncertain” demand from your customer. The demand could come unexpectedly (but also could be scheduled in advance), and all you are trying to do is make sure that you can face the next order “effectively”.

Basic Stochastic Model – still StaticNewspaper Boy Model

Static, Single period but stochastic!(Newspaper boy model)

{ }so

s

ccc

QXPQG+

££= *)( *

z0

0.00

3.00

1 7 13 19 25 31 37 43 49 55 61 67 73 79 85 91 97 103 109 115 121 127 133 139 145 151 157

F(Z)

Less basic Stochastic Model – still StaticBase Stock Model

Scenario:You are a special node in the chain – possibly a retailer.You sell high cost items (refrigerators) and need to have certain number of items in your display room or inventory. Every time that you sell a refrigerator, you order a new one for your showroom. Now you need to decide how many refrigerators you keep in your inventory.

Main issue – you fight against the lead time.

Less basic Stochastic Model – still StaticBase Stock Model

Base Stock Model: No ordering costs• Multi period !• Order one item at a time. Prelude to a Kanban system.• Demand is approximated by a distribution

0

1

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7

0 5 10 15 20 25 30 35

Time

On Hand InventoryBackordersOrdersInventory Position

• Manageable but hard:• Concerns about cost

and Service Level!

Advanced Stochastic Model – still Static(Q,R) Model

Scenario:As a node in the supply chain you need to satisfy uncertain demand using a “continuous review” approach.You would like to protect yourself against “excessive” demand, but also control your inventory size.Again, you are trying to beat the “lead time” issue.

Advanced Stochastic Model – still Static(Q,R) Model

• Solvable but hard.• Produces a fixed strategy for many periods.

Q

Inve

ntor

y

rl

Advanced Stochastic Model – still Static(Q,R) Model

• Multi period• Service level or cost• Considers order quantity AND reorder point.• Generates “Safety Stock”

Advanced Stochastic Model – still Static(Q,R) Model

Dynamic Models –Multi Station Flow

Scenario:• You are responsible for several “nodes” in the supply

chain. • You would like to reach an overall good performance. • You know the rates of flow of your goods (i.e. demand

per time unit) and you have good control over each node.

• Now you have “many” parameters to control!

Dynamic Models –Multi Station Flow

• “horizontal” or one –way flow

• Based on rates of service • Consider Bottleneck Rate and “Raw

processing time”

Dynamic Models –Multi Station Flow

• Provide envelop of performance (one supplier “node” at a time)

Thro

ughp

ut(J

obs/

hr)

0 2 4 6 80

.2

.4

.3

.5

.1

WIP (Jobs)

Cyc

le ti

me

(Hou

rs)

0 2 4 6 80

8

16

12

20

4

WIP (Jobs)

Dynamic Models –Impeding FactorsIndividual Node

• But, things are never perfect - variability• Natural variability• Unexpected delays (issues of reliability/quality)• Planned delays (setups, batching etc. - management)

0

0.1

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0 1 2 3 4 5 6 7 8 9 10 11 12

WIP

TH

048121620242832

0 1 2 3 4 5 6 7 8 9 10 11 12

WIP

CT

Dynamic Models – Flow between Nodes

Flow Variability:• Arrivals variability• Departure variability• Utilization

22222 )1( aed cucuc -+=

cd2(i) = ca2(i+1)i i+1

ce2(i)ca2(i)

ra(i) re(i)rd(i) = ra(i+1)

ce2(i+1)

re(i+1)

Illustrating Flow Variability

t

Low variability arrivals

t

High variability arrivals

smooth!

bursty!

Putting it all together

• Considers individual variability of all types• Considers operational variability (Flow)• Combining each node to the next one• Allows quantitative modeling (no need for

simulation)

Putting it all together - Example