Why is an equality constraint used for the demand requirement in the production problem?

Conditions

• The problem involves fulfilling a specific customer order.
• The order quantity is fixed and must be met exactly.
• Overproduction or underproduction is not allowed or desired.

Reasoning, step by step

1. Identify the total demand quantity from the problem statement.
2. Recognize that the demand must be met exactly, not just at least or at most.
3. Sum the production variables $X_i$ for all machines.
4. Set the sum equal to the demand quantity: $\sum X_i = \text{Demand}$.

Example

The company receives an order to supply 1000 units. The constraint is written as $X_1 + X_2 + X_3 = 1000$. This ensures that the total production is exactly 1000 units.

Common misconceptions

• Using $\ge$ because it is safer to produce more.
• Using $\le$ to avoid excess inventory.
• Thinking that equality constraints are harder to solve than inequalities in this context.

Watch the explanation

Explore next

• How do you formulate the total cost objective function for the three-machine production problem?
• What are the capacity constraints for the machines?
• Why must capacity constraints be linked to binary variables?