Models in Operation Research

-

Types of Operations Research Models

Operations Research (OR) models are idealized representations of real-life situations designed to analyze system behavior and improve performance. Examples include maps, activity charts, balance sheets, PERT networks, break-even equations, and economic ordering quantity equations.

Classification of Models

  • By Degree of Abstraction:
    • Mathematical Models: Utilize mathematical equations and algorithms to represent systems.
    • Language Models: Use descriptive or symbolic language to describe systems and processes.
  • By Function:
    • Descriptive Models: Describe the system as it is without suggesting improvements (e.g., economic models).
    • Predictive Models: Forecast future outcomes based on current data and trends (e.g., sales forecasting models).
    • Normative Models: Provide solutions to repetitive problems and suggest the best course of action (e.g., inventory models).
  • By Structure:
    • Physical Models: Tangible representations of systems (e.g., scale models of buildings).
    • Analogue (Graphical) Models: Use graphs and charts to represent systems (e.g., Gantt charts).
    • Symbolic or Mathematical Models: Use symbols and mathematical equations to represent systems (e.g., linear programming models).
  • By Nature of Environment:
    • Deterministic Models: Assume certainty in all aspects and parameters (e.g., transportation models).
    • Probabilistic Models: Incorporate uncertainty and probabilistic elements (e.g., queuing models).
  • By Time Horizon:
    • Static Models: Represent systems at a specific point in time (e.g., balance sheets).
    • Dynamic Models: Represent systems over a period of time, showing changes and evolution (e.g., simulation models).

Characteristics of a Good Model

  • Simple and Few Assumptions: Assumptions should be minimal and straightforward.
  • Few Variables: Models should have as few variables as possible to maintain simplicity.
  • Adaptability: Able to assimilate environmental changes without altering the framework.
  • Ease of Construction: Should be easy to construct and implement.

Constructing the Model

A mathematical model comprises equations that describe the system or problem. These include the objective function (e.g., cost or profit) and constraints (limitations on achieving the objectives). The general form is:

O = f(xi​,yi​)

where OOO is the objective function, xi​ are controllable variables, and yi​ are uncontrollable variables.

Simplification in OR Models

Simplifications should not significantly reduce accuracy. Common techniques include:

  • Omitting certain variables.
  • Aggregating variables.
  • Changing variables to constants or continuous forms.
  • Linearizing relationships between variables.
  • Modifying constraints.

Techniques of Operations Research

  • Inventory Control Models: Balance inventory costs (shortage, ordering, storage, interest) to decide how much to purchase, when to order, and whether to manufacture or purchase.
    • Example: Economic Order Quantity (EOQ) model.
  • Waiting Line Models: Minimize waiting and idle time costs.
    • Queuing Theory: Determines the number of service facilities and timing for servicing.
    • Sequencing Theory: Determines the sequence of servicing.
  • Replacement Models: Determine the optimal time for replacement or maintenance of items that become obsolete, inefficient, or uneconomical to repair.
  • Allocation Models: Optimize the allocation of limited resources to multiple activities.
    • Example: Resource allocation in project management.
  • Competitive Strategies: Efficiency of decisions depends on actions of others.
    • Example: Game theory in market pricing.
  • Linear Programming (LP) Technique: Solve problems with multiple variables under certain restrictions to maximize or minimize objectives like profit or costs.
    • Example: Production scheduling under capacity constraints.
  • Sequencing Models: Select the optimal sequence for performing a series of jobs to maximize efficiency.
  • Simulation Models: Study system behavior over time through experimentation.
  • Network Models: Plan, schedule, and control complex projects.
    • Example: PERT and CPM techniques.

Applications of Operations Research

  • Distribution or Transportation Problems: Optimize the distribution of products from warehouses to centers using linear programming.
  • Product Mix: Determine the best product mix to maximize profit or minimize costs with available resources.
  • Production Planning: Allocate jobs to machines to maximize production or minimize total production time.
  • Assignment of Personnel: Assign personnel to tasks based on aptitude to complete tasks in minimum time.
  • Agricultural Production: Maximize profit by optimizing the cultivation of crops with varying returns and cropping times.
  • Financial Applications:
    • Optimize investment portfolios for maximum return.
    • Decide financial mix strategies for projects, inventories, etc.

Operations Research uses various models and techniques to optimize decision-making, improve efficiency, and solve complex problems across different industries. By using these approaches, organizations can achieve better resource utilization, cost savings, and overall performance improvements.