Final Assignment Yann JACOBSEN Research Methods for Managers

Final Assignment Research Methods for Managers

Yann JACOBSEN International School of Management ISEG Group 1A

Agenda

1. During the seminar we worked with the following cases:

a. Color chips

b. Computers S and L

c. Make or buy

d. Bike-lib

e. Scheduling personnel

f. Assigning planes

g. A case of public health

Describe briefly the main lessons that you got from each one of these cases.

2. Explain with several practical examples why sensitivity analyses (objective function

coefficients and RHS constraints) are so important.

3.

Constraint A = 132.66

Constraint B = 79.02

Is it obvious that to increase to

increase

4. With this final assignment you will find in Connect the slides that we used during the

seminar Group 1A 2012 . Slides 14 to 16 were not used in

class. In slide 15 you will find a network composed of nodes (circles in different

colors) and arcs (links between nodes). White figures associated to each link represent

the capacity of this link and red figures represent the cost of this link. Develop a LP

model in order to answer the question at the bottom of the slide: which is the maximal

quantity of flow that can reach the destination nodes (7 and 8) from the source nodes

(1, 2 and 3)?

5. Slide 16 shows the same network in slide 15 but now the destination nodes have a

given demand associated to these nodes (77 for node 7 and 82 for node 8).

Considering that the capacity and unit cost of each link are the same indicated in slide

15, develop a LP model in order to answer the question at the bottom of the slide:

which is the optimal distribution of flow (from source nodes via transhipment nodes

to destination nodes) to satisfy demand in destination nodes (7 and 8) minimizing

transportation costs.

6. in order to know the minimal value

of the total fund in order to satisfy all proposed goals. Remember that several goals

should be expressed as percentages of the total fund you have to find. Explain very

clear your model and show the results you got.

All questions worth 10 points

Remember that this final assignment is strictly individual

1.

are

A: Color chips

In this case, chips we used permitted us to understand the way to maximize a production by

regarding resources. Furthermore, we discovered how to obtain the best profit according to

the way we use the resources.

On the other hand, the exercise permits us to discover that numerous possibilities exist in this

problem. Moreover, it has allowed us to understand that mathematical formulae make the

solution easier to find.

Accordingly, we noticed that there are many different numerous research methods which

permit to the manager to take the best decision.

B: Computers S and L

In this case, we had to find a way to organize the production of two different kinds of

computers with various components. It exists limitations we had to take in consideration,

which was the main difficulty.

So, this exercise showed us how we have to manage resources and also how we can manage

production which allows us to make the best choices in order to maximize the profit.

C: Make or buy

With this exercise, we had to discover if it was better to produce or to buy the product to

suppliers by taking in consideration the production costs of the product.

We had to decide how many sub-assemblies it should manufacture at home and also how

many it should buy abroad. The use of the solver permitted us to define the best profit for

each possibility.

D: Bike Lib

Here, the main idea is to arrive to minimize all the costs of bikes movement between a station

from another one. We had to develop an optimization tool in order to minimize reallocating

costs.

It allows us to understand how to optimize, in a company, the planning of tasks by a

diminution and minimizing the cost. We used to maximize the production to maximize the

profit.

E: Scheduling personnel

In this case, we were allowed to manage staff expenses. Moreover, we had to help the call

center proposing how many workers should participate in each schedule in order to minimize

the total costs.

So, we must minimize the cost of the payroll considering the timetable of the employees.

F: Assigning planes

Here, we had to propose an airplane assignment in order to minimize the number of

passengers that should change plane. So, we had to optimize a service which is offered by a

company. We must know how to spare time considering constraints.

G: A case of public health

Here, with our know-how in linear programming, we had to find an optimal allocation of

funds in order to meet the proposed goals.

considering limitations. We must maximize the distribution to reduce constraints as better we

can.

2.

The sensitivity analysis is a method which consists in modifying variables, a way to predict

used within specific boundaries. It consists to

analyze changes to anticipate consequences of diffe

important because in business, we can with this technique take the best decision we can in

order to maximize production and minimize costs.

We can now illustrate this method with a concrete example. A car company wants to

schedule a negotiation. In this way, the want to buy to the suppliers all resources needed to

manufacture cars that they want to sell in the market. They have to know the number of units

they want to produce with all the different elements of the car. This car company resolved

this problem knowing variables like quantities and also the all constraints which correspond

to the price or the discounts. Moreover, the company imagines a negotiation in order to

minimize costs and also to maximize quantity. The aim is to manufacture as much units they

can starting from their resources they negotiated forward.

3.

Shadow price is an opportunity cost of an activity to a society and also the value of a profit

which corresponds to the number of resources.

In this case, we have two constraints corresponding to A (132,66) and B (79,02). If the

shadow price of A is 132,66, that means that when we have an additional resource A, we are

hat when we have

an additional resource B of 79,02, we are going to obtain a better profit than 79,02.

arrive to a better profit. Moreover,

the solver and also the sensitivity are very important. We must on the one hand look the final

result but also to see how we can diversify this result taking into consideration the constraints

and variables affected.

4.

We have to develop a Linear Program in order to answer this question: which is the maximal

quantity of flow that can reach the destination nodes from the source nodes?

First of all, we must define a model with these decision variables:

- X1= the quantity of products that can travel from node 1 to node 4

















In consequence, we can define the objective function which is:

Max (X1+X2+X3+X4+X5+X6+X7+X8+X9+X10+X11+X12+X13+X14+X15+X16+X17)

Now, I can define the constraints:

- Total quantity of products total capacities of flows (that can reach the

destination nodes)

-

- Consider all products that can reach the transhipments nodes

- The last one have to be redistributed to reach the destination nodes

Now this is the Excel document:

Here we have two boards. The first one corresponds to the translation of the PowerPoint

slides. The second one corresponds to the translation of the equation solver. So we can now

solve the objective function which determines the maximal quantity of products that can

reach the destination nodes.

Furthermore, there are different colours in the boxes. The yellow ones represent the variables

cells we have to need to find out.

The blue ones are here to represent the maximal quantity that can reach the transhipments

nodes.

The salmon ones define the total quantity that can reach the destination nodes according to

the blue boxes.

Different formulas were used like:

- J12 = SOMME(B12:I12)

- E18 = SOMME(E12:E17)

- H18 = SOMME(H12:H17)

- J22 = the result we are trying to find out

- L22 = SOMMEPROD(B2:I7;B12:I17)

After the use of the solver, we can say that the maximal quantity of flow that can reach the

destination nodes from the source nodes is 182.

5.

The decision variables are the same as the fourth question:


















The objective function is this one:

Min (X1*its cost+X2*its cost+X3*its cost+X4*its cost+X5*its cost+X6*its cost+X7*its

cost+X8*its cost+X9*its cost+X10*its cost+X11*its cost+X12*its cost+X13*its cost

+X14*its cost+X15*its cost+X16*its cost+X17*its cost)

Moreover, constraints are the same as the fourth question but there are two more. That means

the six constraints are:

-

destination nodes)

-

- Consider all products that can reach the transhipments nodes

- The last one have to be redistributed to reach the destination nodes

- Maximal cost we can have to the destination 7 is 77

- Maximal cost we can have to the destination 8 is 82

In Excel, there are the costs (board which translates the constraints representing by costs

associated to each flow), the capacity (boards which translates the decision variables) and a

third board which translates the equation solver in order to solve the objective function.

The different formulas are:

- K13 =SOMME(C13:J13) lines (K14

=SOMME(C14;J

- F19 =SOMME(F13:F18) formula for the others columns (F20

- K19 =SOMME(K13:K18)

- K26 =SOMMEPROD(C3:J8;C13:J18)

These next pictures correspond to the solver I made:

This is why I can say that the optimal flow

distribution to satisfy the demand

minimizing costs is 1434 .

6.

Now we are going to modify the A problem. We have to find the minimal value of the total

fund in order to satisfy all proposed goals.

If we compare to the exercise from the public health, we can try to take into consideration the

money constraints and we can also try to minimize then objective function.

If we put it on Excel, we can say that the answer on the Excel document is:

These are the formulas:

- A17 =SOMMEPROD(A6:E6;$A$5:$E$5)






- E16 =SOMME(A20:A22)

Final Assignment Yann JACOBSEN Research Methods for Managers

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