I have order quantities as decision variables. How do I write constraints adding up the orders with different lead times and arriving in a single period?
2026-03-27 02:39:50.1774579190
How to write constraints for this tricky LP or MIP program?
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Let $m$ denote the transportation mode (air, sea or land), $t$ the time the order is placed, and $x_{mt}$ the amount shipped via mode $m$ at time $t$. Let $\ell_{mt}$ be the lead time for an order shipped at time $t$ via mode $m$. Importantly, I'm assuming lead times are parameters rather than variables. Then the total quantity due for delivery in period $\tau$ is $\sum_m \sum_{t : t + \ell_{m t} = \tau} x_{m, t}$.