# Linear Programming

## Linear Programming

### Meaning

In many business situations, resources are limited, and demand for them is great. The resources may be time, money or materials and the limitations are known as constraints. Linear Programming is a technique that is useful for allocating scarce resources among competing demands. Linear programming is a mathematical technique designed to help managers find an optimal decision chosen from a large number of possible decisions. Prof. G.B. Dantzig is one of the pioneers in formulating the procedure of Linear Programming.
A linear programming model consists of two important ingredients:

1. Objective function

The company must define the specific objective to be achieved.

2. Constraints

Constraints are in the form of restrictions on the availability of resources or meeting minimum requirements.

As the name linear programming indicates, both the objective function and constraints must be in linear form.

### Definition:

Linear programming is a mathematical technique designed to help operations managers plan and make decisions relative to the trade-offs necessary to allocate resources.

### Uses and applications of Linear Programming

Linear Programming supplies valuable information for proper planning and control of operations by evaluating an optimum combination of several factors (variables) involved in the phenomenon under known constraints e.g.
Many problems in operations management have been modeled as LP problems. The following list identifies some problems that can be solved with LP:

1. Aggregate planning
• Production or operations

Finding the least cost production schedule, taking into account inventory, hiring and layoff, overtime and outsourcing costs, subject to various capacity and policy constraints, scheduling flights.

• Blending

Selecting the least cost mi of ingredients for manufactured products, blending gasoline

• Staffing

Finding the optimal manpower allocation.

1. Distribution
• Shipping

Determining a least cost shipping pattern from plants to distribution  centers or from warehouses to distributors.

1. Location
• Warehouses orplants

Selecting the best warehouse location to minimize shipping costs.

1. Scheduling
• Shifts

Finding the least cost assignment of workers to shifts, subject to varying demand

• Jobs

Scheduling jobs to machines.
Linear Programming gives solution to such situations providing a clear and sound understating of the complex phenomenon to the executive by formulating the

1. Objective to be pursued
2. The various restrictions present
3. The various alternative courses of actions and relationship between them, if any
4. The contribution of each alternative action towards the accomplishment of the objectives.

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