1

The Supply Chain

Supplier

Supplier

Supplier

Inventory

Inventory

Distributor

Inventory Inventory

Manufacturer

Customer

Customer

Customer

Market research datascheduling information

Engineering and design dataOrder flow and cash flow

Ideas and design to satisfy end customer

Material flowCredit flow

2

Supply Chain Management

Facilities, functions, activities for producing & delivering product or service from supplier to customer

Production planningSelecting suppliersPurchasing materials Identifying facility locations Managing inventoriesDistributing product

3

Transportation Model

Given a set of facilities/locations, identify the shipping strategy that will minimize the total costs of distributing the product from the supply nodes to the demand nodes.

Supply nodes = sources where units are being sent from

Demand nodes = destinations where units are being received

4

Network Of Routes for KPiller

Le Havre (800)

Antwerp (700)

Amsterdam (500) Leipzig (400)

Tilburg (500)

Nancy(900)

$120

$61$100

$102.5

$42

$62

$110

$130

$90 Liege (200)

$41

$40

$122

Harbors (Sources)

Plants (Destinations)

5

The Transportation Tableau

To

From

Amsterdam

Antwerp

Le Havre

Demand

Leipzig Nancy Liege Tilburg

120

61

102.5

130

100

90

41

40

122

400 900 200 500

800

700

50062

110

Supply

42

6

Excel Model

Create a table for the unit shipping costs Create a table for the shipping quantity from

each source to each destination (sink) Calculate the total shipped from each source Calculate the total received at each destination Calculate the total shipping cost for a shipping

strategy Create the spreadsheet model for the problem

using the template outlined in TPmodels.xls

7

Solver Constraints for the TP Model

Total shipped from each source <= Supply

Total received at each destination = Demand

Amount shipped from each source to each destination >= 0

Note: if you are minimizing transportation costs and you do not require the model to satisfy demand, Solver will choose to not ship anything and incur a cost of $0.

8

Balanced Transportation Models

A transportation problem is balanced if

Total supply at all of the sources =Total demand at all of the destinations

The KPilller transportation problem is currently balanced with Total Supply = Total Demand = 2000 engines

In this case, all of the units are shipped from the sources (harbors) and all of the destinations (plants) receive their demand

9

Unbalanced Transportation Models

If Total supply at all of the sources >

Total demand at all of the destinations,

the problem is feasible. There will be unshipped units at some of the source locations though.

(Resolve model with Nancy’s plant demand set equal to 700 engines)

If Total supply at all of the sources <

Total demand at all of the destinations,

the problem will be infeasible. (Resolve model with Nancy’s plant demand set equal to

1000 engines)

10

Redefining an Infeasible Unbalanced Transportation Model

If the objective is changed to maximize profit or revenue, the problem can then be solved by changing the demand constraint:

Total received at each destination <= Demand

Note: with the new objective, Solver will choose to ship as much as possible. Not all demand will be satisfied even though the problem is now feasible. To ensure that all destinations receive a reasonable amount of product ,a minimum demand constraint can be added to the current demand constraint for each destination:

Total received at each destination >= Minimum Acceptable Demand

11

Solving an Infeasible Unbalanced Transportation Model

The model needs to be re-balanced in order to identify an optimal shipping strategy when minimizing costs remains the objective

1. Include an extra source into the model to supply the current shortage or

2. Set the minimal percent of demand at each destination that must be met to keep customer happy and yet does not result in an overall shortage (e.g. 95% of each plant’s demand) .

12

Balancing a Transportation Model By Adding a New Source

Include an Extra Source to Supply the Current Shortage

Extra capacity needed = Total demand at all destinations – Total supply at all current sources

To create this additional source of supply/capacity, either

Acquire a new facility/harbor and include it in the network design and spreadsheet model’s table structure or

add a Dummy source into the model’s table structure

13

Solving the KPiller Transportation Problem when Nancy wants 1000 engines

In this problem, the total demand exceeds the total supply by 2100 – 2000 = 100 engines

Insert a dummy harbor with a capacity of 100 engines and a unit shipping cost of $0 to each plant. Edit the spreadsheet model and Solver dialog box to include this new imaginary source.

The identified optimal solution will identify how many engines to ship from each harbor to each of the plants. The engines shipped from the dummy harbor are units that will not actually be distributed; these are the amounts that the receiving plants will be short in the eventual distribution.

14

Contracting a new harbor deal when Nancy’s demand is 1000 engines

In this problem, the total demand still exceeds the total supply by 2100 – 2000 = 100 engines

Insert a possible location for a harbor with a capacity of at least 100 engines along with the identified unit shipping costs from this location to each plant. Edit the spreadsheet model and Solver dialog box to include the new harbor warehouse at this location.

The identified optimal solution will identify how many engines to ship from each harbor, including the additional harbor at the new location, to each of the plants so as to minimize total costs

15

Questions to Reflect on….

How would you use the transportation model to identify whether Hamburg or Gdansk might be a better location for an additional harbor?

What happens when you do not add a new “real location” to the network but use a dummy source which ends up shipping primarily to one destination? What can you do to resolve this problem?

16

Ragsdale Case 3.1

“Putting the Link in the Supply Chain”

What type of models have we studied in this class to help you analyze this case? Sketch out the layout of the different models that you would need to integrate on a piece of paper.

How would you link the models together?

17

Network Flow Problem Characteristics

There are three types of nodes in network flow models: Supply Demand Transshipment

Transshipment nodes can both send to and receive from other nodes in the network

In transshipment models, negative numbers represent supplies at a node and positive numbers represent demand.

18

Kpiller Transshipment Problem

Le Havre (-800)

Antwerp (-700)

Amsterdam (-500) Leipzig (400)

Tilburg (500)

Nancy(900)

$120

$61

$42

$62

$110

$90 Liege (200)

$40

$122$60

$55

$90

1

2

34

5

6

7

19

Defining the Decision Variables

For each arc in a network flow model we define a decision variable as:

Xij = the amount being shipped (or flowing) from node i to node j

For example…X14 = the # of engines shipped from node 1 (Amsterdam) to node 4 (Tilburg)

X56 = the # of engines shipped from node 5 (Liege) to node 6 (Nancy)

Note: The number of arcs determines the number of

variables!

20

Defining the Objective Function

Minimize total shipping costs.

MIN: 62X14 + 120X17 + 110X24 + 40X25

+61X27 + 42X34 + 122X35 + 90X36

+ 60X45 + 55X56 + 90X67

21

Constraints for Network Flow Problems:The Balance-of-Flow Rules

For Minimum Cost Network Apply This Balance-of-Flow

Flow Problems Where: Rule At Each Node:

Total Supply > Total Demand Inflow-Outflow >= Supply or Demand

Total Supply < Total Demand Inflow-Outflow <=Supply or Demand

Total Supply = Total Demand Inflow-Outflow = Supply or Demand

22

Defining the Constraints

In this illustration: Total Supply = 2000

Total Demand = 2000

For each node we need a constraint:Inflow - Outflow = Supply or Demand

Constraint for node 1: –X14 – X17 = – 500

This is equivalent to: +X14 + X17 = 500

23

Defining the Constraints

Flow constraints–X14 – X17 = –500 } node 1

-X24 – X25 – X27 = -700 } node 2

-X34 – X35 – X36 = -800 } node 3

+ X14 + X24 + X34 – X45 = +500 } node 4

+ X25 + X35 + X45 –X56 = +200 } node 5

+ X36 + X56 – X67 = +900 } node 6

+ X17 + X27 + X67 = +400 } node 7

Nonnegativity conditions

Xij >= 0 for all ij

Excel’s Sumif Function

The sumif function adds the cells specified by a given condition or criteria

=sumif(range, criteria, sum range) range are the cells which will be looked at to see if they

meet a specified criteria Criteria specifies the conditions that will allow a row or

column to be included in a sum calculation (i.e. = # or label, >0)

Sum range are the cells that are to summed assuming the row or column meets the criteria

Use cautiously as is not always linear

24

25

Kpiller Transshipment Problem

Le Havre (-800)

Antwerp (-700)

Amsterdam (-500) Leipzig (400)

Tilburg (500)

Nancy(900)

$120

$61

$42

$62

$110

$90 Liege (200)

$40

$122$60

$55

$90

1

2

34

5

6

7

500400

300

800100