How to apply math.ceil function to the part of objective function in python pulp

Question

Am trying to apply the math.ceil function on one part of the objective function in python-pulp. But, Am getting

"TypeError: must be real number, not LpAffineExpression" error.

Following is the example.

models = [A, B, C, D, E]
modelCost = {A: 10, B: 15, C: 20, D: 25, E: 30}
TotalModelsCost = pulp.lpSum([(model*modelCost[model]) for model in models])
OverHeadCost = (math.ceil(pulp.lpSum([model for model in models])/4))*100

prob += TotalModelsCost + OverHeadCost

How to apply the ceil function to OverHeadCost ?

Answer 1

Create a new decision variable called, say, OverHeadCostCeil , which is a general integer (not binary) variable:

OverHeadCostCeil = pulp.LpVariable('OverHeadCostCeil', 0, None, LpInteger)

Require OverHeadCostCeil >= OverHeadCost via a constraint:

prob += OverHeadCostCeil >= OverHeadCost

Replace term in objective function:

prob += TotalModelsCost + OverHeadCostCeil

Then solve. Note that you need to use a solver that can handle general integer variables.