## The municipalitys problem

On a terrain of one point four hectares, a housing association wants to build a number of housing complexes and service units (e.g. shops, social-cultural buildings) within sixteen months. A housing complex takes one thousand square metres, and a service unit takes two thousand square metres. The areas mentioned include park and traffic infrastructure. The construction time of a service unit is one month, that of a housing complex is two months. A service unit costs five million euros, a housing complex costs eight million euros. A budget of eighty million euros is available for the whole project. The terrain need not be built up completely. From a poll amongst potential residents, it is apparent that the occupants' appreciation for the new neighbourhood is in the ratio of five housing complexes to three service units. The council has decided to maximise the compliance with this appreciation ratio for the future residents.

Once again, we use the modelling ABC to build the model. Define the Adjustable cells

 A B C D E F 1 Endogenous variables N HOUS N SERV 2 Outcome 0 0

In this case the Adjustable cells are the number of houses and service units. The cells B2 and C2 are the adjustables.

Define the best cell

 A B C D E F 1 Endogenous variables N HOUS N SERV 2 Outcome 0 0 3 4 Objective function 5 3 0

The Best cell would be the total compliance given the numbers of houses and service units. Cell D4 is the cell that needs to be maximised. Cell D4 must be the outcome of B4 times B2 plus the outcome of C4 times C2.

Define the constraints that have to be met

 A B C D E F 1 Endogenous variables N HOUS N SERV 2 Outcome 0 0 3 4 Objective function 5 3 0 5 required available 6 Max. area 1 2 0 < = 14 7 Max. time 2 1 0 < = 16 8 Max. money 8 5 0 < = 80

The Constraints are the restrictions in time, area, and money.

The model is now ready to be solved. Figure 1.5 shows a screenshot of the solved model with the result: building 6 housing complexes and 4 service units yields the highest resident's compliance, of 42. [O e_lp-2.xls]

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