Introduction

Use CPLEX to solve cutting stock problem by Column Generation

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Model

RMP

Formula

$$min \sum_{j=1}^n x_j$$

$$s.t. \sum_{j=1}^n a_{ij}x_j \ge demand_i \forall i$$

Explain

• a pattern will use a whole stock.
• $x_j$ is the time that $pattern_j$ used
• $a_ij$ is how much item used in $pattern_j$ of item $i$
• $demand_i$ is the demand of item $i$

Sub Problem