Optimización y simulación [DOI-IMAT-314] Course Materials & Test Answers | sifo.comillas.edu

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We can force the vegetarian pizza and the histamine-free pizza to be different with:

$V_{j} + Y_{j} = 1 \forall j$ V_{j} + Y_{j} = 1 \forall j

We can force that one pizza is histamine free with:

$\sum_{j}V_{j} = 1$ \sum_{j}V_{j} = 1

$\sum_{i} h_{i}*X_{i,j} \leq 6 - 6V_{j} \forall j$ \sum_{i} h_{i}*X_{i,j} \leq 6 - 6V_{j} \forall j

We can force that two pizzas do not share more than 2 ingredients with:

new variable $W_{i,j,k}$ W_{i,j,k} if two pizzas j and k share an ingredient i (0,1)

$X_{i,j} + X_{i,k} \leq 1 + W_{i,j,k}$ X_{i,j} + X_{i,k} \leq 1 + W_{i,j,k}

$\sum_{i} W_{i,j,k} \leq 2 \forall j, k>j$ \sum_{i} W_{i,j,k} \leq 2 \forall j, k>j

We can force that any ingredient is not on two or more pizzas with:

$\sum_{i} X_{i,j} \leq 2 \forall j$ \sum_{i} X_{i,j} \leq 2 \forall j

We can for that at least half of the ingredients are vegetarian with:

$\sum_{i} (1-v_{i})X_{i,j} \leq 0.5 \sum_{i} X_{i,j}$ \sum_{i} (1-v_{i})X_{i,j} \leq 0.5 \sum_{i} X_{i,j}

We can force that two pizzas do not share more than 2 ingredients with:

new variable $W_{i,j,k}$ W_{i,j,k} if two pizzas j and k share an ingredient i (0,1)

$X_{i,j} + X_{i,k} \geq W_{i,j,k}$ X_{i,j} + X_{i,k} \geq W_{i,j,k}

$\sum_{i} W_{i,j,k} \leq 2 \forall j, k>j$ \sum_{i} W_{i,j,k} \leq 2 \forall j, k>j

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