Operations Research Cheatsheet

Cheatsheet Content

1.3 Phases of OR Approach to Problem Solving Phase 1: Make a Decision Determine the operation. Establish the operation's aims and values. Determine appropriate measurements of effectiveness. Formulate challenges connected to the objectives. Phase 2: Research Stage Operations and data collection. Better understanding of problems, hypothesis, and model formulation. Observation and experimentation to test the hypothesis with additional data. Analysis of the available data and hypothesis verification using pre-established effectiveness measures. Predictions of various results from the hypothesis. Examination of other methodologies and generalization of different outcomes. Phase 3: Action Phase Implement the chosen solution. Affect the operation in which the problem originated. Methodology of Operation Research General approach to solve a problem in operations research: Step 1: Define and Identify the Issue Obtaining "Right solutions from the wrong issue" is impossible. Goals, alternative courses of action, limitations, and impact of the system under investigation must all be adequately defined when articulating the issue. Step 2: Develop a Mathematical Model Create a mathematical model of the issue using essential parts: Decision variables and parameters: Uncontrolled variables. Controllable variable: One that the decision maker has direct influence over. Uncontrollable variables: Those that are outside the decision maker's direct control. Constraints or restrictions: In order to assess the system's physical limitations, the model must incorporate constraints. A mathematical statement of profit or cost for a certain process is known as the objective function. Example: $P_1$ and $P_2$ are two different types of people. There are two machines, $M_2$ and $M_3$. $P_1$ units need 3 hours on $M_1$ and 1 hour on $M_2$. $P_2$ units need 2 hours on $M_1$ and 2 hours on $M_2$. $M_1$ is available for 60 hours, $M_2$ for 40 hours. Objective: Maximize profit. Let $x_1$ be the number of $P_1$ units, $x_2$ be the number of $P_2$ units. Objective Function: Maximize $P = x_1 + x_2$ (assuming unit profit is 1 for both). Subject to constraints: $3x_1 + 2x_2 \le 60$ ($M_1$ constraint) $1x_1 + 2x_2 \le 40$ ($M_2$ constraint) $x_1, x_2 \ge 0$ (non-negativity constraint) Profits per unit/cost per unit quantity of resources are all uncontrolled variables. $x_1$ and $x_2$ are controllable variables. Profit is objective function. Constraints (ii) and (iii) in equation 1 = objective function. Step 3: Come up with a Solution The first solution is the first solution, which entails determining values of the decision variables best meet the stated goal (maximization of profit and minimization of cost). It means to put the model and solution to the test. It entails putting the model to the test. A model is valid if it can accurately anticipate the performance of a system. A competent operation research analyst strives to always keep the model as simple. Step 4: Control and Implementation The next stage is to put the solution into action. The answer should be explained in terms of the system's operation. A user must understand the system's behaviour after implementing the solution. Proper feedback establishes control over the solution. Methodology of Operations Research (Detailed Steps) Step 1: Formulate the Problem The OR team should explicitly outline the management challenge and then translate it into a research topic during this phase. The OR team conducts a detailed study of organizational structure and function, communication, and control systems. The output of this stage is a clear statement of the goals and objectives, alternative courses of action, and any restrictions or constraints. Step 2: Analysis and Problem Definition To gain a better understanding of the problem, the researcher should further analyse the problem and characterise it in more precise words. All aspects that impact the difficulty should be included in the analysis, and the analyst should make every effort to ensure appropriate comprehension and their contribution to the problem's best solution. Assume a manager discusses the sales decline issue to the operations researcher. Now, the operations researcher examines the pricing and promotions of the company's items. He realises that the fundamental issue involves the pricing of its items and the many amount of money that was spent. The media that was utilised. The sale's schedule. Alternatively, any combination of the above. Step 3: Collecting the data that the old adage requires "Garbage in, garbage out" goes the old adage. It implies that if the data is not accurate or complete, the model created from the data will be useless. The information might come from a primary or secondary source. This implies that the researchers need to undertake new study or consult historical documents in order to model. Step 4: Produce a mathematical process The next step is to attempt to explain the important characteristics of the system under investigation using a mathematical model. A mathematical model may have the following general form: $E = f(X_i, Y_j)$ $E$: Objectives or dependent variables (e.g., total sales, cost, profit). $X_i$: Controllable variables (e.g., number of units produced, amount of advertisement). $Y_j$: Uncontrollable variables (e.g., demand, competitor's actions, economic conditions). Step 5: From Manipulation of the Mathematical Model, the Solution The goal is to discover the values of controllable variables that maximize the different mathematical strategies for arriving at such answers. The best solution is one that is both practical and mathematically sound. The problem's origins might be traced to a different location. As a result, it's a good idea to perform sensitivity analysis. Mission Statement: Precise organisation of the problem. Alternative paths of action that may solve the issue. The results are available to decision-makers. Step 6: Evaluation of the Model The correctness of the model and its assumptions must be checked during this stage. Finding must be compared to real-time data to evaluate how the model reacts to changes. For the sake of abstraction and simplicity, the inclusion of certain inconvenient variables in the model and the removal of some non-essential variables may be necessary. Due to these simplifications, the model's output cannot be directly applied. Step 7: Setting Up Controls over the Solution Complex models of particular issues generate decision ties, which may be utilised in the future. It is critical to be able to predict the effects of future changes in the environment on the solution values. This necessitates the introduction of controls into the model in order for it to remain useful even when some parameters become obsolete. For example, if the model predicts future sales, and there is a significant change in current sales, the solution should be re-evaluated. Without controls, the model solution will be ineffective for future values. A conscious control mechanism must be devoted to indicate the action to be detected a significant change in the solution. Step 8: Putting the Solution into Place This is unquestionably the most crucial stage of the research, since operations research is essentially about taking action. After deciding on an operationally viable solution, the next stage is to put that solution into practice. Solutions that seem possible on paper may clash significantly with the "real-world" circumstances. Most of the OR proposals are never implemented because they are impracticable in nature. If an OR system is fully static, and it is vital to constantly monitor the environment in which the solution will be used. If the answer is not put in place, it is a solution ineffective. It's critical to make sure that any solution you put in place is examined on a regular basis.