1. The Supply Chain Customer Supplier Manufacturer Distributor
Inventory
Distributor
Manufacturer
Customer
Market research data
scheduling information
Engineering and design data
Order flow and cash flow
Ideas and design to satisfy end customer
Material flow
Credit flow
This slide might be used to make the point about the various “flows” - material, information, money.

2. Supply Chain Management
Facilities, functions, activities for producing & delivering product or service from supplier to customer
Production planning
Selecting suppliers
Purchasing materials
Identifying facility locations
Managing inventories
Distributing 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
Harbors (Sources)
Plants (Destinations)
$120
Amsterdam (500)
Leipzig (400)
$130
$62
$41
$61
Nancy(900)
$100
Antwerp (700)
$40
$110
Liege (200)
$90
$102.5
$122
Le Havre (800)
$42
Tilburg (500)

5. The Transportation TableauTo
Supply
From
Leipzig
Nancy
Liege
Tilburg
120
130 41 62
500
Amsterdam 61
100 40
110
700
Antwerp
102.5 90
122 42
800
Le Havre
Demand
400
900
200
500

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 <
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
Include an extra source into the model to supply the current shortage or
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 Problem1
$120 7
Amsterdam (-500)
Leipzig (400)
$62
$90
$61 6
Nancy(900) 2
Antwerp (-700)
$40
$55
$110 5
Liege (200)
$90
$122 3
$60
Le Havre (-800) 4
$42
Tilburg (500)

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: 62X X X X25
+61X X X X36
+ 60X X X67

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 = – } node 1
-X24 – X25 – X27 = } node 2
-X34 – X35 – X36 = } node 3
+ X14 + X24 + X34 – X45 = } node 4
+ X25 + X35 + X45 –X56 = } node 5
+ X36 + X56 – X67 = } node 6
+ X17 + X27 + X67 = } node 7
Nonnegativity conditions
Xij >= 0 for all ij

24. 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

25. Kpiller Transshipment Problem1
$120 7
Amsterdam (-500)
Leipzig (400)
$62
500
$90
400
$61 6
Nancy(900) 2
800
Antwerp (-700)
$40
100
$55
$110
300 5
Liege (200)
$90
$122 3
$60
Le Havre (-800) 4
$42
Tilburg (500)