Assignment PMOR

8/2/2019 Assignment PMOR

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University of Wales

Coursework Assignment Feedback Form

B.Sc. (Hons) in Management with Accounting

B.Sc. (Hons) in Entrepreneurship & ManagementB.Sc. (Hons) in Business & Marketing

Master of Business Administration

Master of Science in Management with specialization in

Banking & Finance X

Marketing

Management

Student Name : Shoikromov Sh. M1100067 Class : ______________

Module Title : __PMOR________________ Lecturer : Siew Ngung Chia

Criteria A B C D FBackground Theory

Methodology explanation

Limitation of LP

Analysis of case

Range of Optimality

Range of Feasibility

Reduced Cost

Shadow Price

Solutions of case

Modeling / QSB printout

Discussion of 3 Options

Recommendations

Conclusions

Organisation of report

Layout and flow

Overall presentation, references and layout.

*Grade:

1. This form should accompany all pieces of assessed coursework.

2. Please note that only *LETTER GRADES are permitted.a. 70-100 A

b. 60-69 B

c. 50-59 C

d. 40-49 De. 0-39 F


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Contents

Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Analysis of the case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

WinQSB solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Analyzing the alternatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Choosing the best alternative . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Recommendations and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

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Background

Bay City Movers is a company, which earns money from cargo between cities. According

to its business plan, companys trucking capacity is at least 36 tons. Company decided to purchase

only two types of truck for further work existence. One of them are Pick up trucks with 1 ton

capacity and second ones are moving Vans with capacity of 2.5 tons. Only one worker is needed

for one Pick up and moving Vans need 4 employees because of the larger moves. Furthermore,

costs of the trucks are also different, 24000 USD is cost of one Pick up and one moving Van will

cost the company 60000 USD. Company already has 48 employees and facility for 40 trucks.

Objectives of the company are finding the optimal solution for further existence without

making any changes in number of staff or facility and with the smallest investment which is

possible.

Above problem will be solved with Linear Programming and the optimal solution will be

find, if it exists.

There are also three alternatives, which also will be examined during the paper writing.

They are:

Choosing only one type of truck (Pick ups or moving Vans)

Choosing the equal number of both trucks

Purchasing the minimum total number of the trucks

Methodology

Linear programming is a mathematical systematic procedure which is used in computer

modeling to find the optimal solution of problems, which are faced by the managers of the

companies. Mostly, these problems are about allocating scarce resources (labour, investments,

facility and so forth). In case of Bay City movers problem, linear programming will be used t find

out the optimal number of employees, trucks, capacity and facility (Lawrence, J. and Pasternack,

B, 2002).

Before linear programming solves the problem, some steps must be done beforehand. They

are shown in the figure below:

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Limitations of linear programming

Linear programming is getting widespread nowadays and helping to solve vast number of

problems. However, it still has own disadvantages. In the world of economics and programming

they are termed as Limitations of Linear programming (Anderson, D., and Kipp, M, 2008). List of

them is given below:

Linear programming can be used if the restrictions and objectives of the problem have

linear nature. This makes it impossible to be used in real life business situation.

Write the constraints as a system of inequalities

Find the set of feasible solutions that graphicallyrepresents the constraints

Calculate the value of the objective function at each of thevertices to determine which of them has the maximum or

minimum values. It must be taken into account the possible non-

existence of a solution if the compound is not bounded.

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Analyze the problem and find all unknowns.Designate all of them with X and Y

Write the objective function

Calculate the coordinates of the vertices from thecompound of feasible solutions


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Program doesnt take on discount such factors as uncertainty or weather conditions.

Numbers of the optimal solution may be continuous (non - integer). For instance, number

of trucks which is needed for Bay City may be continuous and the closest integer may not

be the optimal solution.

Program solves only one objective, but in real life situation, problem never comes alone.

Parameters are assumed to be constant, but in real business they may not remain constant.

2.1 Setting up the mathematical model for Bay City Movers.

There are two variables:

Let X1be Pick up trucks with 1 ton capacity

X2 be Van trucks with 2.5 ton capacity

Also, there are three constraints in the case, namely:

Let C1 carrying capacity f the trucks

C2 number of workers, which is needed for each type of trucks

C3 trucks facilities

The objective function of this case is:

Min 24000X1+60000X2

Subject to:

X1+2.5X2>=36 (Capacity)

X1+4X2


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WinQSB:

Below information was entered to the program:

And the optimal solution was provided:

Range of optimality

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The 100% rule states that simultaneous changes in right-hand sides will not change the

dual prices as long as the sum of the percentages of the changes divided by the corresponding

maximum allowable change in the range of feasibility for each right-hand side does not exceed

100% (D. Taylor and M. Pacelli, 2010).

Range of optimality is analyzed according to prices of Pick ups and Vans.

For pick ups:

One Pick up costs the company 24000, which is the minimum for range of optimality. The

maximum limit doesnt exist. It is M (infinity). So, costs of one Pick up can be increased without

any limits, but costs cannot be lower than 24000.

For Vans:

One Vans cost is 60000. In comparison with Pick ups, Vans cost is the maximum limit,range of optimality is between M (infinity) and 60000. Company may decrease prices on Vans if

there is any point of doing so. However, Bay City cant increase prices even if they want. Because,

maximum limit and cost of one Van are equal.

Range of feasibility

Range of feasibility illustrates the range within which the optimal solution for the company

can be achieved without making any changes in number of constraints.

Range of feasibility for Bay City movers will be analyzed according to all three constraints.

According to capacity:

As it can be seen, the range of feasibility for Bay City is between 30 and 44. But, in our

case, capacity must be at least 36. So, minimum capacity is 36 and maximum is 44. As the results

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show, company can allow itself increasing the capacity maximum for 8 units. But before enlarging,

company should analyze, will this changes increase output or not.

According to the number of employees:

Optimal number of staff is from 36 to 57.6 workers. 48 workers are already employed by

the company, so company can employ another 9 or 10 employees.

According to facility:

Minimum number of facility is 24. Everything is clear with this number, but there is no

maximum limit for the company (M infinity). This is somehow might be good for the company,

because it can increase its facility without any bands. On the other side of the coin, this may have a

negative effect on the company. Cause of this is that company doesnt have exact number when to

stop increasing.

Shadow price

Shadow price associates changes in contribution margin or prices according to the type of

problem and constraints. Shadow price is the maximum cost that company should pay for each

extra unit of the resource.

Shadow price of Capacity:

As it was expressed above, company can increase capacity for 8 units and every increased

units cost will be 24000.

Shadow price of Workers and Facility:

There is no need of increasing the number of employees and Facility, because the dual

price of both is equal to zero.

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Reduced cost

The reduced cost of the variable indicates the index of the cost which has been decreased incomparison with cost which firstly was in the business plan.

As the model shows, the reduced cost of Pick ups and Vans are the same, equal to zero. So,

there is no point for Bay City from decreasing the costs. Costs of both will stay still the same,

24000 for Pick ups and 60000 for Vans.

Slack or Surplus

Slack or surplus associates level of the output. Any changes in automatically changes the

optimal solution. It is preferably to be zero. Only in this case there wont be any extra or lack of

output.

Capacity and workers:

Numbers of employees and capacity are on their optimal, because there is no any slack or

surplus. Both of them are zero.

Facility:

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Surplus of companys facility is 16. This means that company is not doing its best in

utilizing resources connected to facility.

Alternatives

Alternative 1(A):

The range of capacity when only Pick ups are chosen is from zero to 40. The minimum

numbers of employees and Pick ups that can be utilized are the same, 36. Allowable maximum of

Pick up trucks is 8 units. However, the solution is feasible and can be used by the company.

Alternative 1(B):

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Output

The solution when only moving Vans are purchased is infeasible. Both, minimum and

maximum numbers of the capacity are negative. Range between minimum and maximum number

of employees is also too big and shadow price for each worker is 9000, which makes this solution

infeasible.

Alternative 2:

This part of the case will analyze the alternatives when company purchases the same

number of both trucks.

Input:

Output:

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The output shows that there is no optimal solution, it is infeasible. First of all, the capacity

is negative. Secondly, four extra workers should be hired, but dual price of one extra employee is

too big. It would cost the company a lot.

Alternative 3:

Purchasing the minimum total number of trucks

Input

Solution

This alternative has optimal solution. The optimal minimum for Pick ups is 16 and its half

8 is optimal minimum for moving Vans. So, minimum for both is 24. The unit cost is equal to

one for both types of trucks. In this case company will invest 864000.

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3.4 Choosing the best alternative.

As it known from above outputs of the WinQSB program, two of four solutions are

infeasible. So, the best alternative will be chosen from other two ones. Two feasible solutions were

provided by the program when only Pick ups were chosen and when the total minimum of both

trucks was analyzing. If compare these two alternatives, the best one is purchasing the minimum

total number of trucks. Because, unit cost of both trucks is only one. When at the same time, if

only Pick ups are chosen, unit cost for them is 24000 and 60000 for Vans. Furthermore, in case of

alternative number three, costs can be reduced, which is also may be profitable for Bay City.

Recommendations and Conclusion

It is recommended by the author of the current paper to purchase 16 units of Pick ups and 8

units of moving Vans as it is shown in optimal solution of alternative number three. It is

recommended because prices of purchase can be decreased according to the solution. Furthermore,

16 and 8 are the minimum total numbers of trucks which can be increased, what leads to

enlargement of income and level of output.

In conclusion it can be said that, there are number of optimal solutions for Bay City movers

provided by Linear Programming. All of tem ensures further existence in the market. But, some of

them are better than other ones. So, it is crucial for the company to make a correct choice in

choosing the optimal solution.

References

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Anderson, D., Sweeney D., Williams, T., and Kipp, M. (2008), An Introduction to Management Science,

Quantitative Approaches To Decision Making, Thomson learning, Canada

Lawrence, J. A. J. and Pasternack, B. A. (2002), Applied Management Science, Modeling,

Spreadsheet Analysis, and Communication for Decision Making (Second Edition), John Wiley &

Sons, Inc., U.S.A.

Taylor D. and Pacelli M, Mathematics and Politics: strategy, voting, power and proof, 2nd edition,

Springer Science + Business Media LLC, 2010.

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