The Supply Chain
Market research data
scheduling information
Engineering and design data
Order flow and cash flow
Supplier
Inventory
Supplier
Customer
Ideas and design to
satisfy end customer
Material flow
Credit flow
Customer
Manufacturer
Inventory
Supplier
Inventory
Distributor
Customer
Inventory
1
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

2
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
3
Network Of Routes for KPiller
Harbors
(Sources)
Plants
(Destinations)
$120
Amsterdam (500)
$62
$61
Antwerp (700)
$130
$41
Leipzig (400)
Nancy(900)
$100
$40
$110
$102.5
$90
Liege (200)
$122
Le Havre (800)
$42
Tilburg (500)
4
The Transportation Tableau
To
From
Leipzig
Nancy
Liege
120
130
41
Tilburg
62
61
100
40
110
102.5
90
122
42
Amsterdam
Antwerp
Supply
500
700
800
Le Havre
Demand
400
900
200
500
5
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
6
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.
7
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
8
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)
9
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
10
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) .
11
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
12
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.
13
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
14
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?
15
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?
16
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.
17
Kpiller Transshipment Problem
Amsterdam (-500)
$120
1
7
Leipzig (400)
$62
$90
6
$61
Antwerp (-700)
2
$40
$55
$110
5
$90
Le Havre (-800)
3
Nancy(900)
Liege (200)
$122
4
$42
$60
Tilburg (500)
18
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!
19
Defining the Objective Function
Minimize total shipping costs.
MIN: 62X14 + 120X17 + 110X24 + 40X25
+61X27 + 42X34 + 122X35 + 90X36
+ 60X45 + 55X56 + 90X67
20
Constraints for Network Flow Problems:
The Balance-of-Flow Rules
For Minimum Cost Network
Flow Problems Where:
Apply This Balance-of-Flow
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
21
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
22
Defining the Constraints

Flow constraints
–X14 – X17 = –500
-X24 – X25 – X27 = -700
-X34 – X35 – X36 = -800
+ X14 + X24 + X34 – X45 = +500
+ X25 + X35 + X45 –X56 = +200
+ X36 + X56 – X67 = +900
+ X17 + X27 + X67 = +400

} node 1
} node 2
} node 3
} node 4
} node 5
} node 6
} node 7
Nonnegativity conditions
Xij >= 0 for all ij
23
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
Kpiller Transshipment Problem
Amsterdam (-500)
$120
1
7
Leipzig (400)
$62
500
$90
400
6
$61
Antwerp (-700)
2
3
100
5
300
$90
Le Havre (-800)
800
$40
$110
Nancy(900)
$55
Liege (200)
$122
4
$42
$60
Tilburg (500)
25