# Modify a model

##

Modify a model

**Examples:**diet, feasopt, fixanddive, lpmod, sensitivity, workforce3, workforce4

This section considers model modification. Modification can take many forms, including adding constraints or variables, deleting constraints or variables, modifying constraint and variable attributes, changing constraint coefficients, etc. Here is a sample of some types of model modification.

diet

This example builds a linear model that solves the classic diet problem: to find the minimum cost diet that satisfies a set of daily nutritional requirements. Once the model has been formulated and solved, the example adds an additional constraint to limit the number of servings of dairy products, and solves the model again. Let's focus on the model modification.

Adding constraints to a model that has already been solved is no different from adding constraints when constructing an initial model. In Python, we can introduce a limit of 6 dairy servings through the following constraint:

m.addConstr(buy[7] + buy[8] <= 6, "limit_dairy")For linear models, the previously computed solution can be used as an efficient

*warm start*for the modified model. The Gurobi solver retains the previous solution, so the next

`optimize`

call automatically starts from the previous solution.
lpmod

Changing a variable bound is also straightforward. The
`lpmod`

example changes a single variable bound, then
re-solves the model
in two different ways. A variable bound can be changed by modifying
the `UB`

or `LB`

attribute of the variable. In C:

error = GRBsetdblattrelement(model, GRB_DBL_ATTR_UB, var, 0.0);In Python:

minVar.ub = 0The model is re-solved simply by calling the

`optimize`

method
again. For a continuous model, this starts the optimization from the
previous solution. To illustrate the difference when solving the
model from an initial, unsolved state, the `lpmod`

example calls
the `reset`

function. In C:
error = GRBresetmodel(model);In C++, Java, and Python:

m.reset()In C#:

m.Reset()When we call the optimize method after resetting the model, optimization starts from scratch. Although the difference in computation time is insignificant for this tiny example, the warm start can make a big difference for larger models.

fixanddive

The `fixanddive`

example provides another example of bound
modification. In this case, we repeatedly modify a set of variable
bounds, utilizing warm starts each time. In C, variables are fixed
as follows:

for (j = 0; j < nfix; ++j) { fixval = floor(fractional[j].X + 0.5); error = GRBsetdblattrelement(model, "LB", fractional[j].index, fixval); if (error) goto QUIT; error = GRBsetdblattrelement(model, "UB", fractional[j].index, fixval); if (error) goto QUIT; }In Python, they are fixed as follows:

for i in range(nfix): v = fractional[i] fixval = int(v.x + 0.5) v.lb = fixval v.ub = fixvalAgain, the subsequent call to

`optimize`

starts from the
previous solution.
sensitivity

The `sensitivity`

example computes the amount by which the
optimal objective changes if each binary variable is fixed at either 0
or 1. For each binary variable, the example creates and solves a copy
of the model with new upper and lower bounds. This example is a MIP,
so Gurobi can not make use of advanced start information. As a
result, the model is solved from scratch after each bound
modification.

feasopt

The last modification example we consider is `feasopt`

, which
adds variables to existing constraints and also changes the
optimization objective. Setting the objective to zero is
straightforward: simply call `setObjective`

with a zero
argument:

m.setObjective(0)Adding new variables is somewhat more complex. In the example, we want to add artificial variable(s) to each constraint in order to allow the constraint to be relaxed. We use two artificial variables for equality constraints and one for all other constraints. The Python code for adding a single artificial variable to constraint

`c`

is:
feasModel.addVar(obj=1.0, name="ArtP_" + c.Constrname, column=Column([1], [c]))We use the

`column`

argument of the `addVar`

method to
specify the set of constraints in which the new variable participates,
as well as the associated coefficients. In this example, the new
variable only participates in the constraint to be relaxed. Default
values are used here for all variables attributes except the objective
and the variable name.