Step 1 – Definition and Identification of problem –
It is impossible to obtain ‘Right answers from wrong problem’. In formulating the problem, objectives, alternative course of action, constraints and effect of the system under study must be well established.
Step -2- Constructing a mathematical model –
The next step is to construct a mathematical model of the problem with following basic elements :-
Decision or controllable variables and parameters or uncontrollable variables : A controllable variable is one that can be directly controlled by the decision maker. The value of these variables are to be determined. Uncontrollable variables are those which are not under direct control of decision maker. Ex govt. policy, increasing prices.
Constraints or restriction– The model must include constraints in order to check physical limitation of the system.
Objective function : i.e mathematical expression of profit or cost for a particular operation.
Ex. : Two products P1 and P2 Two machines M1 M2
one unit of P1 requires 3 hours on M1 and 1 hour on M2
one unit of P2 requires 2 hours on M1 and 2 hour on M2
No of hours available per week on M1 and M2 are 60 & 40. Profit contribution of P1 and P2 are Rs. 60 and Rs. 50 per unit. desired to maximize profit. Draft a mathematical model.
→ x1 and x2 = controllable variable whose values are to be determined, profits per unit, cost/unit amount of resources are all uncontrollable.
Equation (i) = objective function (ii) and (iii) are constraints
Step 3 – Deriving a solution –
The next step is to obtain a solution i.e. determination of those values of the decision variables that optimize the given objective (maximization of profit and minimization of cost).
Step 4- Testing the model and the solution –
It involves testing of the model used. A model is valid if it can provide a reliable prediction of system’s performance. A good operation research analyst continuously tries to update his model.
Step 5- Implementation and control
The next step is implementing the solution derived. Explanation of the solution be made in terms of procedure used in actual system. After applying the solution, observe response of the system. A control over the solution is established by proper feedback.
