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I am working on an LP problem where I have to model a constraint as:

"The total number of units of product A and B should be shipped in multiples of $1200$"

e.g. $700\text{(product A)} + 500\text{(product B)} = 1200\times1 = 1200$ or

$1800\text{(product A)} + 600\text{(product B)} = 1200\times2 = 2400$ or

$2000\text{(product A)} + 1600\text{(product B)} = 1200\times3 = 3600$

like that maximum shipment should be $6000$ units $(1200\times5)$, or I can say in other words as I can only ship $5$ batches of $1200$ units each.

Can somebody please help me to write such a constraint in algebraic form: $Xa + Xb = $?

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If $x_p$ denotes the quantity of product $p\in P$ that is shipped : \begin{align} \sum_{p\in P}x_p &= 1200 k \\ k &\in \mathbb{N} \\ x_p &\in \mathbb{R}^+ \end{align}

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  • $\begingroup$ @TheSimpliFire : just out of curiosity, why is better to write equations with \begin{align}, rather than with '$$' symbols ? $\endgroup$ – Kuifje Jan 20 '20 at 19:28
  • $\begingroup$ Well because it aligns equations together :) (note that $$ and \\ newline do not achieve this as there is no command to align $=$ and $\in$ in this case) $\endgroup$ – TheSimpliFire♦ Jan 21 '20 at 7:26

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