Machine Scheduling - Handbook

Type: LP (Linear Programming)

This handbook explains the Machine Scheduling sample problem in the LP Black Box platform.

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The Problem

Scenario

A factory has 2 machines (M1, M2) that can produce two products (A, B). Each machine-product combination has different efficiency.

Machine-Product	Profit per Unit ($)	Time per Unit (hrs)
Machine 1 → A	10	2
Machine 1 → B	8	1
Machine 2 → A	12	1
Machine 2 → B	6	2

Each machine has 40 hours available.

Your Goal

Maximize total profit by deciding how much of each product to produce on each machine.

The Variables

Variable	Meaning
M1_A	Units of A produced on Machine 1
M1_B	Units of B produced on Machine 1
M2_A	Units of A produced on Machine 2
M2_B	Units of B produced on Machine 2

The Constraints

1. Machine 1 Time: Cannot exceed 40 hours

   Formula: 2×M1_A + 1×M1_B ≤ 40

2. Machine 2 Time: Cannot exceed 40 hours

   Formula: 1×M2_A + 2×M2_B ≤ 40

3. Product A Demand: Must produce at least 20 units total

   Formula: M1_A + M2_A ≥ 20

4. Product B Demand: Must produce at least 15 units total

   Formula: M1_B + M2_B ≥ 15

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How to Use

Step 1: Load the Sample

Select Machine Scheduling from the dropdown.

Step 2: Solve

The solver determines how to allocate production across machines to maximize profit while meeting demand.

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Try It Yourself

• Increase Machine 1 time to 50 hours
• Add a constraint that M2 must produce at least 10 of Product A

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This demonstrates multi-machine production scheduling with constraints.