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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?

Orders and Lead Time

Rodrigo de Azevedo
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Vinay
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  • Are lead times constant, or are they also variables? – prubin Sep 23 '17 at 22:56
  • The lead times are constant for this problem. The reason I varied them a bit is because I was looking for an answer which is generic and not specifically designed for lead times 0,1 and 2 for air, land sea respectively. – Vinay Sep 24 '17 at 04:16
  • I figured this problem(https://drive.google.com/open?id=0B74iryIUAeIwT0lTUjhoazJEX2M) but I have a feeling I may have complicated it a bit. I welcome any solutions better than mine. – Vinay Sep 24 '17 at 04:25

1 Answers1

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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 $\sum_m \sum_{t : t + \ell_{m t} = \tau} x_{m, t}$.

prubin
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