Integer Programming Problem and Gomory’s All-I.P.P. Method for Solving the I.P.P. Problem from MB0032 MBA Assignment

This is the most probable assignment question of Operation Research for MB0032 SMU MBA. The question is “What do you understand by the Integer Programming Problem? Describe the Gomory’s All-I.P.P. method for solving the I.P.P. problem.” You already have taken many solved assignments from SMU MBA MB002 such as - classification of Operations Research models, Matrix Minimum Method and Penalty Cost Method or Big-M Method for Solving LPP.

An integer programming problem can be described as follows:

Determine the value of unknowns X1, X2, …, Xn

So as to optimize z = C1X1 + C2X2 + … CnXn

Subject to the constraints

ai1 X1 + ai2 X2 + … + ain Xn = bi, i = 1,2, …, m

and xj ≥ 0 j = 1, 2, …, n

where xj being an integral value for j = 1, 2, …, k ≤ n.

If all the variables are constrained to take only integral value i.e. k = n, it is called an all (or pure) integer programming problem. In case only some of the variables are restricted to take integral value of rest (n – k) variables are free to take any one negative values, then the problem is known as mixed integer programming problem.

Gomory’s All – IPP Method:

An optimum solution to an I. P. P. is first obtained by using simplex method ignoring the restriction of integral values. In the optimum solution if all the variables have integer values, the current solution will be the desired optimum integer solution. Otherwise the given IPP is modified by inserting a new constraint called Gomory’s or secondary constraint which represents necessary condition for integrability and eliminates some non integer solution without losing any integral solution.

After adding the secondary constraint, the problem is then solved by dual simplex method to get an optimum integral solution. If all the values of the variables in this solution are integers, an optimum inter-solution is obtained, otherwise another new constrained is added to the modified L P P and the procedure is repeated.

An optimum integer solution will be reached eventually after introducing enough new constraints to eliminate all the superior non integer solutions. The construction of additional constraints, called secondary or Gomory’s constraints is so very important that it needs special attention.

Matrix Minimum Method and The Initial Basic Feasible Solution In The Transportation Problem for MB0032 Assignment

This question comes from Operation Research assignment of MB0032 for SMU MBA. The question is “Describe the Matrix Minimum method of finding the initial basic feasible solution in the transportation problem.” From the SMU MBA MB002 assignment I already have shared about classification of Operations Research models and Penalty Cost Method or Big-M Method for Solving LPP.

Matrix Minimum Method:

Step 1: Determine the smallest cost in the cost matrix of the transportation table. Let it be Cij, Allocate Xij = min (aj, bj) in the cell (i, j).

Step 2: If Xij = aj cross off the ith row of the transportation table and decrease bj by ai go to step 3.

If xij = bj cross off the ith column of the transportation table and decrease ai by bj go to step 3.

If Xij = ai = bj crosss off either the ith row or the ith column but not both.

Step 3: Repeat steps 1 and 2 for the resulting reduced transportation table until all the rim requirements are satisfied whenever the minimum cost is not unique make an arbitrary choice among the minima.

The Initial Basic Feasible Solution:

Let us consider a T.P involving m-origins and n-destinations. Since the sum of origin capacities equals the sum of destination requirements, a feasible solution always exists. Any feasible solution satisfying m+n -1 of the m+n constraints is a redundant one and hence can be deleted. This also means that a feasible solution to a T.P can have at the most only m + n -1 strictly positive component, otherwise the solution will degenerate.

It is always possible to assign an initial feasible solution to a T.P. in such a manner that the rim requirements are satisfied. This can be achieved either by inspection or by following some simple rules. We begin by imagining that the transportation table is blank i.e. initially all Xij = o. The simplest procedures for initial allocation discussed in the following section.

Penalty Cost Method or Big-M Method for Solving LPP for MBA MB0032 Assignment

Write the question from Operation Research assignment of MB0032 for SMU MBA. The question is “Describe the Penalty Cost method (Big M Method) for solving L.P.P.” From the SMU MBA MB002 assignment you already have gotten classification of Operations Research models.

Consider a L.P.P. when at least one of the constraints is of the type ≥ or =. While expressing in the standard form, add a non negative variable to each of such constraints. These variables are called artificial variables. Their addition causes violation of the corresponding constraints, since they are added to only one side of an equation, the new system is equivalent to the old system of constraints if and only if the artificial variables are zero. To guarantee such assignments in the optimal solution, artificial variables are incorporated into the objective function with large positive coefficients in a minimization program or very large negative coefficients in a maximization program. These coefficients are denoted by ± M.

Whenever artificial variables are part of the initial solution Xo, the last row of simplex table will contain the penalty cost M. The following modifications are made in the simplex method to minimize the error of incorporating the penalty cost in the object function. This method is called Big M-method to penalty cost method.

1. The last row of the simplex table is decomposed into two rows, the first of which involves those terms not containing M, while the second involves those containing M.

2. The step 1 of the simplex method is applied to the last row created in the above modification and followed by steps 2,3 and 4 until this row contains no negative elements. Then step 1 of simplex algorithm is applied to those elements next to the last row that are positioned over zero in the last row.

3. Whenever an artificial variable ceases to be basic, it is removed from the first column of the table as a result of step 4, it is also deleted from the top row of the table as is the entire column under it.

4. The last row is removed from the table whenever it contains all zones.

5. If non-zero artificial variables are present in the final basic set, then the program has no solution. In contrast, zero valued artificial variables in the final solution may exist when one or more of the original constraints equations are redundant.

Classification of OR Models and Operation Research Problem Solving for MB0032 Assignment

The question is related to Operation Research assignment of MB0032 for SMU MBA. The question is “Describe the broad classification of Operations Research models in details. Name the different steps needed in OR approach of problem solving?” However, we already have solved significance of reviewing ROI.

A model is a representation of the reality. It is an idealized representation or abstraction of a real life system. A model is helpful in decision making as it provides a simplified description of complexities and uncertainties of a problem in logical structure.

A) Physical Model: It includes all form of diagrams, graphs and charts. They are designed to deal with specific problems. They bring out significant factors and inter-relationship in pictorial firm so as to facilitate analysis.

B) Mathematical Model: It is known as symbolic models also. It employs a set of mathematical symbols to represent the decision variable of the system.

C) By Nature of Environment: We have 1) Deterministic model in which every thing is defined and the results are certain. Eg: EOQ model 2) Probabilistic Models in which the input and output variables follow a probability distribution. Eg: Games Theory.

D) By the extent of Generality: The two models belonging to this class are 1) General models can be applied in general and does not pertain to one problem only. Eg: Linear programming 2) Specific model is applicable under specific condition only. Eg: Sales response curve or equation as a function of advertising is applicable in the marketing function alone.

Methodology of Operations Research:

The basic dominate characteristic feature of operations research is that it employs mathematical representations or model to analyze problems. This distinctive approach represents an adaptation of the scientific methodology used by the physical sciences. The scientific method translates a real given problem into a mathematical representation which is solved and transformed into the original context. The OR approach problem solving consists of the following steps:

Definition of the Problem

Construction of the Model

Solution of the Model

Validation of the Model

Implementation of the Final Result

Meaning of Baseline and Reviewing Process of Baseline from MB0033 Assignment

The question is the part of Project Management of MB0033 assignment of SMU MBA. It is – “What is meant by baseline? How is it reviewed?” You already have gotten many assignments in this category such as - Deming’s philosophy relevant to Project Management, How can risks be prioritized in a Project Management, Main Considerations in Planning P2M, significance of reviewing ROI and Introduction to ScMo Supply Chain Monitoring. Now, you will get a new assignment about “What is meant by baseline? How is it reviewed?”

The Baseline created can be used to compare the original project plan with actual events and achievements. This will display the days required for each task and project phase. For actual operating instruction phase refer the Microsoft project user handbook.

After creating a baseline, if the project has begun, it is necessary to enter actual dates that tasks are being completed and the resource utilization used to complete them. Again review different views and the cost and summary tables before proceeding to the next section. Return to the entry view of the Gantt chart before proceeding.

At times people and equipment can become assigned more work then they can complete in normal working hours. This is called over allocation. Project can test for this condition and reschedule (or level) their workload to accommodate completing tasks during a normal day.

After a baseline has been established and the project has begun, it is desirable to determine if task are being accomplished on time and/or if cost over runs are occurring.

Project has many different built-in reports and has the capability building custom reports and exporting data to other MS office applications for integration into other reporting venues.

Significance of Reviewing ROI and Explain Return on Investment for MB0033 MBA Assignment

It is the question of Project Management of MB0033 assignment of SMU MBA. The question is – “What is the significance of reviewing ROI? Explain in detail.” We already have discussed on many assignments in this category such as - Deming’s philosophy relevant to Project Management, How can risks be prioritized in a Project Management and Introduction to ScMo Supply Chain Monitoring. Now, I am going to present my theory on ROI (Return on Investment) for MB0033 MBA assignment of SMU.

Return on Investment (ROI) is the calculated benefit that an organization is projected to receive in return for investing money (resources) in a project within the context of the review process. The investment would be in an information system development or enhancement project. ROI information is used to assess the status of the business viability of the project at key check points throughout the project’s life-cycle.

ROI may include the benefits associated with improved mission performance, reduced cast, increased quality, speed, or flexibility, and increased customer and employee satisfaction. ROI should reflect such risk factors as the project’s technical complexity. The agency’s management capacity, the likelihood of cost overruns, and the consequences of under – or non-performance where appropriate, ROI should be reflect actual returns observed through pilot projects and prototypes.

ROI should be quantified in terms of dollors and should include a calculation of the break-even point (BEP) which is the date when the investment begins to generate a positive return. ROI should be re-calculated at every major checkpoint of a project to see if the BEP is still on schedule, based on project spending and accomplishments to date. If the project is behind schedule or over budget, the BEP may move out in time; if the project is ahead of or under budget the BEP may occur earlier. In either case, the information is important for decision-making based on the value of the investment throughout the project life-cycle.

Any project that has developed a business case is expected to fresh the ROI at each key project decision point (i.e. stage exist) or at least yearly.

Main Considerations in Planning P2M MBA MB0033 Assignment of SMU

The question has been taken from Project Management of MB0033 assignment of SMU MBA. The question is – “What are the main considerations in planning P2M? Give relevant examples.” There are already many assignments in this category - Deming’s philosophy relevant to Project Management, How can risks be prioritized in a Project Management and Introduction to ScMo Supply Chain Monitoring.

Some of the considerations for effective program management are given below:

Focusing on the various strategic initiatives taken up for multiple projects and the issues related to benefits and risks.

Bringing about the attention of management to a defined set of benefits, which are understood immediately, which are understood immediately, which are managed thought the implementation and at completion.

Helping to management to set priorities, choosing options and allocate resources.

Setting up mechanisms to measure and ensure that the projects making contributions for realizing expected business benefits.

Leading the organization on the path of ‘where it’ and ‘where it wants to be’. Ensuring that the effects of the programme driven changes are coordinated, the transitions are successfully managed. The operations are effective and efficient.

The objective sought to be achieved and the methods which are adopted and the activities that are going to be undertaken i.e. the process include the following steps.

Preparing and maintaining a set of activities and the workflow that is to be followed and identifying business areas responsible for different stage in the above:

The marketing sure that the priorities that the above generate are relevant and the projects are run on the basis of their impact on the business in a whole:

The Process has to incorporate all the important aspects which are to be addressed during implementation and management of the projects. It is important to identify all factors and incorporate resources – men, material, technology and time, so that their provision can be planned.

How Can Risks Be Prioritized In A Project Management? MB0033 Assignment of MBA for SMU

This is Project Management question of MB0033 assignment of SMU MBA. The question is – “How can risks be prioritized in a Project Management? Give any suitable example.” In this category, we already have discussed about Deming’s philosophy relevant to Project Management.

To identify risks, we must first define risk. Risks are potential problems, ones that are not guaranteed to occur. When people performing risk identification they often start by listing known problems. Known problems are not risks. During risk identification, you might notice some problems. If so, just move them to a problem list and concentrate on future potential problems.

Risk identification can be done using a brainstorming session. The brainstorm typically takes 13-30 minutes. Be sure to invite anyone who can help you think risks. Invite the project team, customer, people who have been a similar projects, and experts in the subject area of the project, limit the group size to nine people. In the brainstorming session, people call out potential problems that they think could hurt the project. New ideas are generated based on the items on the brainstorm list. A project manager can also use the process to refer to a database of risk obtained from past.

The information obtained from such databases can help the project manager to evaluate and asses the nature of the risk and its impact on he project. Also to a great extent the judgment of the project manager based upon his post experience comes very handy in dealing with risks. Another important method is to generate alternative solution or methodology to deal with risk. Generate solution by means of group review meetings or a brainstorm session.

During the brainstorm, consider the following items:

Selection of weak areas in a project, such as unknown technology being used or to be used:

Things, that is critical or extremely important to the effort, such as the timely delivery of a vendor’s database software, creation of translators, or a user interface that meets the customer needs.