8/2/2019 Assignment PMOR
1/14
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
8/2/2019 Assignment PMOR
2/14
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
2
8/2/2019 Assignment PMOR
3/14
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:
3
8/2/2019 Assignment PMOR
4/14
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.
4
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
8/2/2019 Assignment PMOR
5/14
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
8/2/2019 Assignment PMOR
6/14
WinQSB:
Below information was entered to the program:
And the optimal solution was provided:
Range of optimality
6
8/2/2019 Assignment PMOR
7/14
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
7
8/2/2019 Assignment PMOR
8/14
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.
8
8/2/2019 Assignment PMOR
9/14
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:
9
8/2/2019 Assignment PMOR
10/14
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):
10
8/2/2019 Assignment PMOR
11/14
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:
11
8/2/2019 Assignment PMOR
12/14
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.
12
8/2/2019 Assignment PMOR
13/14
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
13
8/2/2019 Assignment PMOR
14/14
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.
14