Decision Making in Supply Chains
Table of Contents
Decision Making in Supply Chains .....................................................................................1
Knowledge clip 1: Introduction to linear programming .............................................................. 2
Knowledge clip 2: Graphical solution of LPs with two variables .................................................. 3
Chapter 2 knowledge clip 1: Introduction to sensitivity analysis ................................................ 4
Chapter 2 knowledge clip 2: Variation of Right-Hand-Side value ................................................ 5
Chapter 2 knowledge clip 3: Variation of objection function coefficients .................................... 6
Lecture chapter 1 and 2 ............................................................................................................ 7
Chapter 3 knowledge clip 1: Blending problems ........................................................................ 8
Chapter 3 knowledge clip 4: Algebraic problems ....................................................................... 8
Chapter 3 knowledge clip 5: Linear programming in production management ............................ 9
Chapter 3 knowledge clip 6: Production scheduling ................................................................. 11
Chapter 3 knowledge clip 7: Workforce scheduling .................................................................. 12
Lecture Chapter 3 ................................................................................................................... 13
Chapter 4 knowledge clip 1: The transportation problem part 1............................................... 14
Chapter 4 knowledge clip 2: The transportation problem part 2............................................... 14
Chapter 4 knowledge clip 3: The assignment problem ............................................................. 16
Chapter 4 knowledge clip 4: The transshipment problem ........................................................ 17
Chapter 4 knowledge clip 5: Network flow problems ............................................................... 18
Lecture chapter 4 ................................................................................................................... 19
Chapter 5 knowledge clip 1, Facility location part 1 ................................................................. 21
Chapter 5 knowledge clip 3, Multi-period facility location 1 ..................................................... 21
Chapter 5 knowledge clip 5, Multi-echelon multi-commodity network design .......................... 22
Chapter 6, knowledge clip 1: simulation vs optimization.......................................................... 23
,Knowledge clip 1: Introduction to linear programming
Liner program: a mathematical model that optimizes a linear objective function over a set of
continuous decision variables subject to linear equality and inequality constraints
Example:
• A minimization problem can be converted to a
maximization problem (and vice versa) by
multiplying the objective function with -1
• Strict inequality is not allowed; should be ≥ or ≤
o At most (≤)
o At least (≥)
o Exactly (=)
Key assumptions of LPs:
1. Proportionality: the construction to the objective function and the amount of
resources used in each constraint are proportional to the value of each decision
variable
2. Additivity: the value of the objective function and the total resources used is the sum
of the objective function contribution and the resources used for alle decision
variables
3. Divisibility: the decision variables are continuous
4. Certainty: all parameters are known
How to derive LP formulations:
1. Understand the problem
2. Describe the objective in own words
3. Describe each constraints in own words
4. Define and describe the decision variables
5. Express the objective in terms of the decision variables
6. Express constraints in terms of the decision variables
, Knowledge clip 2: Graphical solution of LPs with two variables
Why use graphical representation → Useful insights into the structure and solution of LP
How to:
1. Identify the feasible region
a. Draw constraint boundary line for each constraint (from x1 ≤, to x1 = 6)
b. Determine which side of the line is permitted by the constraint
2. Draw the objective function line for some objective value and move it in direction of
improving objective value
3. Stop moving objective function line before leaving feasible region
4. Optimal solutions are all feasible points on objective function line
Table of Contents
Decision Making in Supply Chains .....................................................................................1
Knowledge clip 1: Introduction to linear programming .............................................................. 2
Knowledge clip 2: Graphical solution of LPs with two variables .................................................. 3
Chapter 2 knowledge clip 1: Introduction to sensitivity analysis ................................................ 4
Chapter 2 knowledge clip 2: Variation of Right-Hand-Side value ................................................ 5
Chapter 2 knowledge clip 3: Variation of objection function coefficients .................................... 6
Lecture chapter 1 and 2 ............................................................................................................ 7
Chapter 3 knowledge clip 1: Blending problems ........................................................................ 8
Chapter 3 knowledge clip 4: Algebraic problems ....................................................................... 8
Chapter 3 knowledge clip 5: Linear programming in production management ............................ 9
Chapter 3 knowledge clip 6: Production scheduling ................................................................. 11
Chapter 3 knowledge clip 7: Workforce scheduling .................................................................. 12
Lecture Chapter 3 ................................................................................................................... 13
Chapter 4 knowledge clip 1: The transportation problem part 1............................................... 14
Chapter 4 knowledge clip 2: The transportation problem part 2............................................... 14
Chapter 4 knowledge clip 3: The assignment problem ............................................................. 16
Chapter 4 knowledge clip 4: The transshipment problem ........................................................ 17
Chapter 4 knowledge clip 5: Network flow problems ............................................................... 18
Lecture chapter 4 ................................................................................................................... 19
Chapter 5 knowledge clip 1, Facility location part 1 ................................................................. 21
Chapter 5 knowledge clip 3, Multi-period facility location 1 ..................................................... 21
Chapter 5 knowledge clip 5, Multi-echelon multi-commodity network design .......................... 22
Chapter 6, knowledge clip 1: simulation vs optimization.......................................................... 23
,Knowledge clip 1: Introduction to linear programming
Liner program: a mathematical model that optimizes a linear objective function over a set of
continuous decision variables subject to linear equality and inequality constraints
Example:
• A minimization problem can be converted to a
maximization problem (and vice versa) by
multiplying the objective function with -1
• Strict inequality is not allowed; should be ≥ or ≤
o At most (≤)
o At least (≥)
o Exactly (=)
Key assumptions of LPs:
1. Proportionality: the construction to the objective function and the amount of
resources used in each constraint are proportional to the value of each decision
variable
2. Additivity: the value of the objective function and the total resources used is the sum
of the objective function contribution and the resources used for alle decision
variables
3. Divisibility: the decision variables are continuous
4. Certainty: all parameters are known
How to derive LP formulations:
1. Understand the problem
2. Describe the objective in own words
3. Describe each constraints in own words
4. Define and describe the decision variables
5. Express the objective in terms of the decision variables
6. Express constraints in terms of the decision variables
, Knowledge clip 2: Graphical solution of LPs with two variables
Why use graphical representation → Useful insights into the structure and solution of LP
How to:
1. Identify the feasible region
a. Draw constraint boundary line for each constraint (from x1 ≤, to x1 = 6)
b. Determine which side of the line is permitted by the constraint
2. Draw the objective function line for some objective value and move it in direction of
improving objective value
3. Stop moving objective function line before leaving feasible region
4. Optimal solutions are all feasible points on objective function line
