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Constraints of case study exercise

Continue the case study of the Capacitated Plant Location model of a car manufacture. You are given four Pandas data frames demand, var_cost, fix_cost, and cap containing the regional demand (thous. of cars), variable production costs (thous. $US), fixed production costs (thous. $US), and production capacity (thous. of cars). Two python lists loc, and size have also been created, containing the different locations, and the two types of plant capacities. All these variables have been printed to the console for your viewing. The code to initialize the decision variables, define them and create the objective function has been completed for you.

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Supply Chain Analytics in Python

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# Initialize, Define Decision Vars., and Objective Function
model = LpProblem("Capacitated Plant Location Model", LpMinimize)
loc = ['USA', 'Germany', 'Japan', 'Brazil', 'India']
size = ['Low_Cap','High_Cap']
x = LpVariable.dicts("production_", [(i,j) for i in loc for j in loc],
                     lowBound=0, upBound=None, cat='Continuous')
y = LpVariable.dicts("plant_", 
                     [(i,s) for s in size for i in loc], cat='Binary')
model += (lpSum([fix_cost.loc[i,s] * y[(i,s)] for s in size for i in loc])
          + lpSum([var_cost.loc[i,j] * x[(i,j)] for i in loc for j in loc]))

# Define the constraints
for j in loc:
    model += lpSum([____ for i in ____]) ____ demand.loc[____,'Dmd']
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