Planning Technique and Linear

This document provides study material on planning technique and linear programming. It includes information on origin, production, constraints, and objective. It also discusses the minimum value of the objective function and the optimum mix method. Additionally, it covers AOA, shortest completion time, and achieving completion time goals.

Planning technique and linear
programming

Table of Contents
PART A...........................................................................................................................................4
PART B...........................................................................................................................................5
PART C...........................................................................................................................................6

PART A
Origin UK
Netherland
s Spain Italy Poland
Production
capacity
Denmark 6 5 9 5 4 15000
Greece 3 2 3 4 2 18000
Norway 4 5 7 4 4 7000
France 2 4 3 2 3 10000
Dummy 0 0 0 0 0 10000
Forecasted demand 8000 12000 20000 15000 5000 60000
Constraints:
6x1 + 5x2 + 9x3 + 5x4 + 4x5 ≤ 15,000
3x1 + 2x2 + 3x3 + 4x4 + 2x5 ≤ 18,000
4x1 + 5x2 + 7x3 + 4x4 + 4x5 ≤ 7,000
2x1 + 4x2 + 3x3 + 2x4 + 3x5 ≤ 10,000
0x1 + 0x2 + 0x3 + 0x4 + 0x5 ≤ 10,000
Objective:
Max z = 8000x1 + 12000x2 + 20000x3 + 15000x4 + 5000x5

PART B
a.
The minimum value of the objective function Z=160 occurs at the extreme point (0, 20).
Hence, the optimal solution to the given LP problem is: x1=0, x2=20 and min Z=160.
The minimum cost will be achieved when only MODEL B table type is used; and minimum cost
could be 160.

b.
For identifying optimum solution; values have been put in the solver function of excel.
Constraints have been defined separately; and then the value of objectivity has been entered
manually; final the optimum answer found which is =
c.
The optimum mix method is used to identify the best solution for given equation. The solution
found from the method gives optimum way to solve given problem. It helps in identifying the
value of variables to find the solution in both maximizing or minimizing value. In the above
problem the main objective is to find optimum solution to minimize the overall cost of the table
manufacturing. There are two options available Table A and Table B model. The solution
suggests that only Table B should be used at the unit of 20 to give minimum cost of 160; below
this company cannot achieve with given constraints.
PART C
1. AOA
2. Shortest completion
Shortest completion time = 15 Weeks

Critical Path = B + D + F + H + I/K + L =30 Weeks
Once all activities are arranged in logical order and relationships are set, the logic diagram is
ready for the calculation process. TT and FF indicate where to place float values. ES, EF, LS, LF
and the Duration indicate where to place their respective values.
The first step in the computer cycle is the name Pass Forward. In the next step, the Early Start
and Early Finish scores for each action are determined, along with the overall project length. To
encourage counting of plans, "end of day" documentation is used for both early start and late
start results. Thus, the start of the group is the "end of day zero". At the end of the day, the rough
circle begins with zeroing at the Early Start (ES) position in the main activity.
The absolute float shows the difference between the most precise date the action can start and the
latest date the action will start before the end date is postponed. All outgoing buoys can be
determined as the difference between Late End and Early End, as ES short LS and LF less EF
measure the same number.
The Free Float, in any case, is the amount of time the action can be postponed before any other
material is canceled. Ambitious start / end times are used to create the Free Float image.
Therefore, in essential terms, the end date (Early Completion) of the movement and the
organized start (Early Start) of the following exercises are compared, activity C has a three-day
mark before the start of activity E is postponed.
Once the float values are confirmed, the baseline exercise line is identified. This stable line of
basic exercises is called the essential route. The basic exercises are the ones that do not shave
any huts. Note that the sum of the basic operating hours equals the total length of the company
(determined in the next step). This confirms how the delay (or extra time added at the end of the
action) will delay any basic action in the deployment date. While not a feature of the model,
more than one finger schedule or set of exercises can make up the basic method. See Link 6 for a
picture of a PC-made CPM plan.
One or two routine checks are to be carried out to help gauge whether the manual calculation
was performed accurately. First, the promotion of a free full-float move may be more prevalent
or the equivalent of a free shipping. Or again, all in all, Free Float can be no more than your
Total Float inspiration. Second, the necessary path should be stable from the main task in the

schedule to the final move. Third, negative numbers should not be displayed for a particular
value.
Timetables are used as on-board tools to broadcast workgroups, determine start / end dates for
exercises and monitor the progress of almost any type of campaign. With the growing interest in
development project leaders, a number of organizations are hiring people who have not received
proper home management. Similarly, PCs and registration programming have become relatively
inexpensive and CPM programming has melted away many “chimes and whistles” that can
confuse young venture capital managers with a chance that they may not understand the basic
ideas about recording calculations.
3.
Yes, 40 week completion time goal can be achieved; as now total time taken by the company to
complete the whole task is only 30 weeks. Thus company can easily attain the goal of 40 weeks.
The critical path for the company is 30 weeks which is maximum time taken by the company to
complete the task. On the other hand 15 weeks is the minimum time taken by the company to
complete the same task? It is also recommended to the company to make relation between
predecessor and successor activities. For instance, company hasn’t made any relationship after
task A, and E.