Transcript Value creating processes conceptual framework

Constraint
management
Constraint

Something that limits the performance of a
process or system in achieving its goals.
 Categories:


Market (demand side)
Resources (supply side)








Labour
Equipment
Space
Material and energy
Financial
Supplier
Competency and knowledge
Policy and legal environment
Steps of managing constraints
Identify (the most pressing ones)
 Maximizing the benefit, given the
constraints (programming)
 Analyzing the other portions of the
process (if they supportive or not)
 Explore and evaluate how to overcome
the constraints (long term, strategic
solution)
 Repeat the process

Linear programming
Linear programming…
…is a quantitative management tool to
obtain optimal solutions to problems that
involve restrictions and limitations (called
constrained optimization problems).
 …consists of a sequence of steps that
lead to an optimal solution to linearconstrained problems, if an optimum
exists.

Typical areas of problems
Determining optimal schedules
 Establishing locations
 Identifying optimal worker-job
assignments
 Determining optimal diet plans
 Identifying optimal mix of products in a
factory (!!!)
 etc.

Linear programming models
…are mathematical representations of
constrained optimization problems.
 BASIC CHARACTERISTICS:

Components
 Assumptions

Components of the structure of a
linear programming model

Objective function: a mathematical expression of the
goal



Decision variables: choices available in terms of
amounts (quantities)
Constraints: limitations restricting the available
alternatives; define the set of feasible combinations of
decision variables (feasible solutions space).




e. g. maximization of profits
Greater than or equal to
Less than or equal to
Equal to
Parameters. Fixed values in the model
Assumptions of the linear
programming model
Linearity: the impact of decision
variables is linear in constraints and the
objective functions
 Divisibility: noninteger values are
acceptable
 Certainty: values of parameters are
known and constant
 Nonnegativity: negative values of
decision variables are not accepted

Model formulation


1.
2.
3.
The procesess of assembling
information about a problem into a
model.
This way the problem became solved
mathematically.
Identifying decision variables (e.g.
quantity of a product)
Identifying constraints
Solve the problem.
2. Identify constraints

Suppose that we have
250 labor hours in a
week. Producing time of
different product is the
following: X1:2 hs,
X2:4hs, X3:8 hs
 The ratio of X1 must be
at least 3 to 2.
 X1 cannot be more than
20% of the mix.
Suppose that the mix
consist of a variables x1,
x2 and x3
2x 1  4x 2  8x 3  250
x1 3

x2 2
2x 1  3x 2  0
x1  0,2  (x1  x 2  x 3 )
0,8x1  0,2x 2  0,2x 3  0
Graphical linear programming
1.
2.
3.
4.
5.
Set up the objective function and the
constraints into mathematical format.
Plot the constraints.
Identify the feasible solution space.
Plot the objective function.
Determine the optimum solution.
1.
2.
Sliding the line of the objective function away
from the origin to the farthes/closest point of the
feasible solution space.
Enumeration approach.
Corporate system-matrix
1.) Resource-product matrix
Describes the connections between the
company’s resources and products as linear and
deterministic relations via coefficients of
resource utilization and resource capacities.
2.) Environmental matrix (or market-matrix):
Describes the minimum that we must, and
maximum that we can sell on the market from
each product. It also describes the conditions.
Contribution margin
Unit Price - Variable Costs Per Unit =
Contribution Margin Per Unit
 Contribution Margin Per Unit x Units
Sold = Product’s Contribution to Profit
 Contributions to Profit From All Products
– Firm’s Fixed Costs = Total Firm Profit

Resource-Product Relation types
P1
P6
P7
R5
a56
a57
R6
a66
a67
R1
P2
P3
P4
P5
a43
a44
a45
a11
R2
a22
R3
a32
R4
Non-convertible relations
Partially convertible relations
Product-mix in a pottery –
corporate system matrix
Jug
Plate
Capacity
Clay (kg/pcs)
1,0
0,5
50 kg/week
100 HUF/kg
Weel time
(hrs/pcs)
Paint (kg/pcs)
0,5
1,0
50 hrs/week
800 HUF/hr
0
0,1
10 kg/week
100 HUF/kg
Minimum (pcs/week)
10
10
Maximum
100
100
Price (HUF/pcs)
700
1060
Contribution
margin (HUF/pcs)
200
200
(pcs/week)
e1:
1*P1+0,5*P2 < 50
e2:
0,5*P1+1*P2 < 50
e3:
0,1*P2 < 10
m1, m2: 10 < P1 < 100
m3, m4: 10 < P2 < 100
ofCM:
200 P1+200P2=MAX
Objective function

refers to choosing the best element from
some set of available alternatives.
X*P1 + Y*P2 = max
weights
(depends on what we want to maximize:
price, contribution margin)
variables
(amount of produced goods)
Solution with linear programming
T1
33 jugs and 33 plaits a
per week
e1
100
ofF
e3
e1:
1*P1+0,5*P2 < 50
e2:
0,5*P1+1*P2 < 50
e3:
0,1*P2 < 10
m1,m2:
10 < P1 < 100
m3, m4: 10 < P2 < 100
ofCM:
200 P1+200P2=MAX
33,3
e2
100
33,3
Contribution margin: 13
200 HUF / week
T2
What is the product-mix, that maximizes the
revenues and the contribution to profit!
R1
R2
P1
P2
b (hrs/y)
2
2
3
2
6 000
5 000
MIN (pcs/y)
50
100
MAX (pcs/y)
1 500
2000
p (HUF/pcs)
50
150
f (HUF/pcs)
30
20

P1&P2: linear programming
r 1:
2*T5 + 3*T6 ≤ 6000
r 2:
2*T5 + 2*T6 ≤ 5000
m1, m2:
50 ≤ T5 ≤ 1500
p3, m4: 100 ≤ T6 ≤ 2000
ofTR: 50*T5 + 150*T6 = max
ofCM: 30*T5 + 20*T6 = max
T1
r1
3000
Contr. max: P5=1500, P6=1000
Rev. max: P5=50, P6=1966
r2
2500
ofCM
ofTR
2000
2500
T2
Thank you for your attention!