Operations Research :- Unit V Integer Programming Problem and Project Management

Unit VI Decision Theory and Sensitivity Analysis

Syllabus:

Decision making under certainty, uncertainty and risk, sensitivity analysis, Goal programming formulation and algorithms – The weights method, The preemptive method.

6.1 Decision making under certainty, uncertainty and risk

6.2 Sensitivity analysis     

Change in objective function co-efficients and effect on optimal solution

Table 5.11: Sensitivity Analysis Table Output

6.3 Goal programming formulation and algorithms – The weights method, The preemptive method.

Generally speaking, the objective of a business organization is to maximize profits and to minimize

expenditure, loss and wastage. However, a company may not always attempt at profit maximization

only. At times, a necessity may arise to pay attention to other objectives also. We describe some

such situations in the sequel.

A manufacturing organization may like to ensure uninterrupted supply of its products even if it

means additional expenditure for the procurement of raw materials or personal delivery of goods

during truckers’ strike, etc. with the objective of assuring the good will of the customers.

A company may be interested in the full utilization of the capacity of the machines and therefore

mechanics may be recruited for attending to break downs of the machines even though the

occurrence of such break downs may be very rare.

A company, driven by social consciousness, may spend a portion of its profits on the maintenance of

trees, parks, public roads, etc. to ensure the safety of the environment, with the objective earning the

support of the society.

Another organization may have the objective of establishing brand name by providing high quality

products to the consumers and for this purpose it may introduce rigorous measures of quality checks

even though it may involve an increased expenditure.

While all the sales persons in a company are formally trained and highly experienced, the

management may still pursue a policy to depute them for periodical training in reputed institutes so

as to maximize their capability, without minding the extra expenditure incurred for their training.

A travel agency may be interested to ensure customer satisfaction of the highest order and as a

consequence it may come forward to operate bus services even to remote places at the normal rates,

so as to retain the customers in its fold.

A bank may offer services beyond normal working hours or on holidays even if it means payment of

overtime to the staff, in order to adhere to the policy of customer satisfaction on priority basis.

A business organization may accord priority for the welfare of the employees and so a major part of

the earnings may be apportioned on employee welfare measures.

A garment designer would like to be always known for the latest fashion and hence may spend more

money on fashion design but sell the products at the normal rates, so as to earn the maximum

reputation.

A newspaper may be interested in earning the unique distinction of ‘Reporter of Remote Rural

Areas’ and so it may spend more money on journalists and advanced technology for communication.

The above typical instances go to show that the top level management of a business organization

may embark upon different goals in addition to profit maximization. Such goals may be necessitated

by external events or through internal discussion. At times, one such goal may be in conflict with

another goal.

‘Goal programming’ seeks to deal with the process of decision making in a situation of multiple

goals set forth by a business organization. A management may accord equal priority to different

goals or sometimes a hierarchy of goals may be prescribed on their importance. One has to strive to

achieve the goals in accordance with the priorities specified by the management. Sometimes the

goals may be classified as higher level goals and lower level goals as perceived by the

management and one would be interested in first achieving the higher order goals and afterwards

considering lower order goals.

Some of the goals that may be preferred by a business organization are : maximum customer

satisfaction, maximum good will of the customers, maximum utilization of the machine capacity,

maximum reliability of the products, maximum support of the society, maximum utilization of the

work force, maximum welfare of the employees, etc.

Since different goals of an organization are based on different units, the goal programming has a

multi-dimensional objective function. This is in contrast with a linear programming problem in

which the objective function is uni-dimensional.

Given a goal of an organization, one has to determine the conditions under which there will be

under-achievement and over-achievement of the goal. The ideal situation will be the one with neither

under-achievement nor over-achievement of the goal.

interested to find out the optimal production of tables and chairs so as to have a maximum profit of Rs.

4000. Formulate a goal programming problem for this situation.