ESLARP East St. Louis Action Research Project
University of Illinois at Urbana-Champaign


Low Cost Rental Multifamily Housing Development in East St. Louis, Illinois

Multi-layered Mixed Integer Quadratic Programming

Project report for UP485, December, 1994.

Instructor: Professor Kieran Donaghy
Department of Urban and Regional Planning


Emily Stern
Sandeep Kumar

Department of Urban and Regional Planning
University of Illinois at Urbana-Champaign

Purpose of the Study

The purpose of this study is to minimize the deviation of the present worth of the income and subsidies for a new housing development in East St. Louis, Illinois from the costs associated with constructing and operating the development. In other words, the planning dilemma, taken from the perspective of a non-profit housing development corporation, is to propose a housing development project that achieves the lowest rents possible when supplemented with federal housing subsidies to just cover the costs associated with the development, with minimal profits to the organization. This planning objective must be accomplished in a manner which complies with designated overall planning criteria, conforms to physical constraints on development, and, in addition, meets certain requirements to qualify for federal subsidy programs which are needed help ease the financial burden on the future occupants of the units.

Background and Rationale for the Proposed Housing Development

East St. Louis is a city plagued by many social ills, which, taken cumulatively, have shaped the dire circumstances that define the citys housing market today. The city, characterized by a deteriorating and diminishing housing stock, lost over 17% of its housing supply between 1980 and 1990 (East St. Louis CHAS, 1994). In addition, marginal income levels of current residents have precluded them from registering sufficient demand in the housing market to spur private, for-profit housing investment in the city. The 1989 median household and family income levels for all of East St. Louis were $12,627 and $15,975 respectively. These figures lie in contrast to median household and family income levels in St. Clair County, which were $26,813 and $31,939 respectively in 1989 (East St. Louis CHAS, 1994). In fact, the only significant private housing investment occurring in East St. Louis today is the result of a housing market underworld comprised of several area realtors using unscrupulous business practices to manipulate housing purchase agreements called installment land contracts which, in many cases, ultimately prevent residents from gaining title to the properties. These alternative housing finance instruments, were, until the recent passage of an ordinance in East St. Louis, largely unregulated and frequently abused in the city (University of Illinois, Dept. of Urban and Regional Planning, UP378 Report, 1994). The objective of forestalling this continual downspiral of the East St. Louis housing market through the development of new, affordable units is a primary rationale for the proposed housing development.

The vital need for new housing initiatives in East St. Louis is made doubly poignant when the plight of current residents is considered and the loss of potential market demand for housing in the city is weighed. Specifically, many residents of the city are trapped in substandard housing and are subjected to conditions of overcrowding. In fact, East St. Louis reports the highest degree of overcrowding among larger cities in Illinois. In 1990, overcrowding occurred in 8% of owner-occupied units and 14.7% of rental units in the city according to HUD standards (East St. Louis CHAS, 1994). Compounding the housing dilemma for the city is the rapidly hemorrhaging market of potential home buyers and renters in East St. Louis, evidenced by a 25% drop in the citys population between 1980 and 1990 (East St. Louis CHAS, 1994). This massive outmigration is one symptom of the menacing housing problems East St. Louis faces, manifested in the decision of many residents to leave the city and its associated social ills. Finally, new job opportunities emerging in the city in municipal government and commercial enterprises have spawned another source of housing demand which may be potentially lost if no new housing initiatives are taken in the city. In light of these facts, preserving the community of East St. Louis and growing the population of the city in a revitalizing manner are additional goals in proposing this non-profit housing development initiative.

Description of the Proposed Development and Planning Assumptions

For our designated project area we have chosen a largely vacant tract of land of approximately 114,080 sq. ft. in the Winstanley-Industry Park neighborhood of East St. Louis (See Maps 1 and 2). By selecting an existing vacant site we accomplish dual goals of minimizing demolition and clearance costs and avoiding the displacement of current residents. Our selection of a project site in this particular neighborhood was also motivated by the presence of a strong neighborhood organization in this area which could serve as a necessary catalyst in garnering community input and support for this endeavor. In addition, this project would contribute to ongoing stabilization efforts which have been concentrated in this neighborhood.

We have developed a proposal for a planned unit development (PUD) for this site which will contain a mixture of multi-family and single-family units and associated parking areas, open space and commercial activities. The rental units will combine 1-BR, 2-BR, and 3-BR units. The 1-BRs will be targeted toward elderly residents, the only segment of the population in East St. Louis to be increasing in absolute numbers. Between 1980 and 1990, the number of persons in East St. Louis age 65 years and older increased by about 23% (East St. Louis CHAS, 1994). Many of these individuals currently live in 2- and 3-BR single-family houses (East St. Louis CHAS, 1994) and could benefit from a more communal, assisted-living environment. Many of the 2- and 3-BR units would be targeted toward female-headed households. It was noted that these households grew significantly in relative numbers over the previous few decades. In 1990, female-headed households comprised over 30% of the households in East St. Louis, compared to only 11% in the rest of St. Clair County (Cestero, Gerich, Goodrich, Salgado, 1993). We have proposed to build about three times as many 2-BR units as 1-BR units and about two times as many 3-BR units as 1-BR units to accommodate some of the many households and families who are presently living in conditions of overcrowding in the city.

The single-family units will combine 2-BR, 3-BR, and 4-BR units. Some of these will be targeted toward large-female headed households who currently may be living in structures unsuitable for their size. Another primary target group for these units will be the families of new East St. Louis employees, who, in the absence of other quality housing options, may follow the path of so many before them and choose to live outside the city.


For the purposes our project, we have selected a scaled-down area on our project site from which to develop a micro-model of our proposed housing development (See Map 3). We have divided the area into fifteen equally-sized parcels of 1600 sq. ft. each to facilitate the modeling of the spatial configuration of the units. The proposed activities considered for the project site in the model include multi-family housing and associated parking and open space areas. In the case of our non-profit housing development initiative, the objective function is to minimize the balance of the projects income and costs. In other words, the goal of the housing development corporation is to take in sufficient income from the project to just cover the costs of building and operating the development, without additional profits. The income from the development is considered to be the present value of the rents received over the life of the project, supplemented with federal housing subsidies in the form HOME program funds and Low Income Housing Tax Credits. The projects costs are comprised of construction costs, the present value of maintenance costs and property taxes over the life of the project, and the cost of the land. The implicit goal in this analysis is, through supplemental income and zero-balance financing, to create housing that is affordable and attainable for many residents in East St. Louis.

The heart of our planning model includes four layers of analysis. The first is the parcel number (i) which can assume an integer value between 1 and 15 (our total number of parcels). We also differentiate in our model between the different types of units (j) with 1, 2, or 3 bedrooms. For each unit and rent variable, we specify whether it corresponds to High rents or Low HOME rents under the HOME program (k = H, L). Finally, for each variable we also distinguish between units and associated rents that qualify for tax credits (l = 1) and those which do not qualify for tax credits (l = 0). This multi-layered approach has given us sixteen possible variables for each variable type (Rijkl, Xijkl, Sijkl, Tijkl), starting at the parcel level (i) and moving on to the type of unit (j), to describing which category of qualifying HOME rents are satisfied (k), and lastly, whether or not the unit/rent meets tax credit qualifications (l). This systematic progression to the different variable types is displayed in diagram 1.

The constraints in our model are both physical and financial in nature. The physical criteria governing the number and types of units include: an overriding spatial constraint for the entire project area; a spatial constraint on the multi-family units; a spatial constraint on the parking area; a minimum number of units; contiguity constraints for the configuration of the units; and constraints on the relative proportions of different types of units. The financial limitations determining the level of subsidies and the rents include: limits on the amounts of HOME funds and tax credits available; rent limits under the HOME program (2 sets of rent limits--high and low) and rent limits to receive tax credits; and required percentages of units with specified rent levels under both HOME and the Tax Credit program to receive funding. A crucial financial constraint under which we are operating is that our balance must be greater than zero. That is to say, while our primary objective is to minimize the difference between the income from and the costs of the project, we cannot accept a negative balance where costs exceed income. The details of these constraints and the objective function, along with their operational forms, are presented in the subsequent section on methodology.

There are three basic programming tools necessary for this analysis. The overall model is a quadratic programming problem, with the objective function containing the product of two variables, Rijkl (rents) and Xijkl (# of units) which are subject to linear constraints. The model also contains elements of integer programming. In the land use contiguity constraints, integer variables (0,1) are used to set up certain requirements for the configuration and adjacency of activities. Also, for the rent constraints there are certain ranges of rents defined by the relative criteria for the two federal subsidy programs within which the associated units would qualify for HOME funds but not for tax credits. By setting up integer constraints for these variables, if the program finds that it is not optimal to support rents within these ranges, these rents become zero and no units are supported with these rents. Finally, general integer programming methods are used to define the variables for the numbers of units Xijkl which must assume real, integer values
(1, 2, ...., n).


Multilayered Mixed Integer Quadratic Programming

Objective Function:

Minimize Balance = Income -Cost

Income = Present value of rent stream + Home Subsidies + Tax credit subsidies


i = parcel #; i = 1,2....15
j = unit type # of bedrooms; j= 1,2,3
k = Qualifying unit under HOME subsidy program
H= High HOME Rent
L = Low HOME Rent
l = Eligibility for Tax Credit Subsidy program
1 = Yes
0 = No

Notes: Present Worth Factor = 12.4
for n=30 years and interest rate=.07

Cost = construction cost + present value of maintenance cost + present value of property tax + land value

Present Value of maintenance cost = (12.4)(.05) (Construction Cost)

Land cost= $2,160

Cijkl= construction cost of each type j unit inclusive of building and associated costs of providing landscaping and parking requirements.
where Ci1kl= $20,450 (37*400 + 19*160 + 3*870)
Ci2kl= $28,610 (37*600 + 19*200 + 3*870)
Ci3kl= $36,770 (37*800 + 19*240 + 3*870)
Construction cost = $37/sq.ft
Parking cost = $19/sq.ft.
Landscaping cost = $3/sq.ft.
(Source: Means Building Construction Manual, 93).
Maintenance Cost per year= 5% of original construction cost
Property tax rate = 13.5% (St. Clair County Clerks Office)
Assessed Value = 1/3 of total value of property including land and structure (Koenig, 89)
Land Cost = $.09/sq.ft. ($1,000 per 75* 150 lot size; Koenig, 89)
Total land cost = 15parcels*1600 sq. ft. * .09 = $2,160

Constraint Functions:

To keep objective function positive:

Balance >= 0

For Spatial Configuration

1. Total Area of multifamily units in each parcel <= area of the parcel
Allowable Height of the structure
2 floors on parcels 10 and 18
1 floor on parcel 11
< img src="images/image6">

where Aj= area of each type j unit
A1= 400 sq.ft.
A2= 600 sq.ft.
A3= 800 sq.ft.
(Sources: Koenig, 89; DeChiara, 76)

2. Total sum of Parking area associated with each unit <= 3200sq.ft.

where Pj = Area of Parking for type j unit
i = 10, 11, 18
P1=160 sq.ft.
P2=200 sq.ft.
P3=240 sq.ft.
(Source: DeChiara, 76)

3. Total Number of units >=10

where i = 10, 11, 18

4. Proportions of units:

a) total 2 bed room units should be more than or equal to 3 times of 1 bed room units
b) total 3 bedroom units should be more than or equal to 2 times of 1 bed room units

where i= 10, 11, 18

5. Overriding Spatial Constraint: Total sum of the floor area, open space and parking associated with each unit <= land available for first phase development.

6. Minimum number of each type of unit on each parcel >=1

where i = 10, 11, 18

7. Land use contiguity and built form:

a) Units on parcels 10 and 11 must exist together
b) Units on parcels 10 and 18 must exist together
c) 2 contiguous parcels must have parking

Land use:
(IX10jkl- IX11jkl) = 0
(IX10jkl- IX11jkl) = 0
(IX10jkl- IX11jkl) = 0
(IX10jkl- IX18jkl) = 0
(IX10jkl- IX18jkl) = 0

PX9 - PX17=0
PX9- PX1 = 0

where IX and PXs are integer variables having values 0,1

For Financial restraints

8. HOME subsidy:

Total amount of HOME subsidies:

Notes: Subsidy Limit for 1 bed room unit = $62,086
for 2 bed room unit = $75,496
for 3 bed room unit = $97,666
(Source: Rich Koenig, Illinois Housing Development Authority, Chicago)

9. Tax Credit subsidy:

Total amount of tax credit should be 91% of the present value of the construction cost of unit types j =1,2,3 with qualifying tax credit rents (l=1)

10. Rent constraints:

where Rijkl = Rent limits for each unit type j= 1,2,3 to qualify for subsidy under HOME for High rent units (H) and low rent units (L) either accompanied with Tax credits for that unit (l=1) or not meeting the rent limits for the tax credit (l=0)
and IRijkl are integer variables having values 0,1.


Requirements to qualify for
HOME subsidy:
a) up to 80% of the units of the development can have high HOME rents
Rent for one bed room unit (Ri1Hl)<= $361
Rent for two bed room unit (Ri2Hl)<= $468
Rent for three bed room unit (Ri3Hl)<= $609
b) at least 20% of the units of the development can have low HOME rents
Rent for one bed room unit (Ri1Ll)<= $361
Rent for two bed room unit (Ri2Ll)<= $468
Rent for three bed room unit (Ri3Ll)<= $580
(Source: Rich Koenig, Illinois Housing Development Authority, Chicago)

Tax credit subsidy:
Rent limit for one bed room unit <= $355
Rent limit for two bed room unit <= $434
Rent limit for three bed room unit <= $502
(Source: Guggenheim, J; Tax Credits for Low Income Housing, 1992)

11. HOME units % requirements:


While this model has not yet been solved and its potential results remain questionable, it does present an interesting attempt at merging spatial and financial considerations in a model which tries to capture the ideal relationship between rents, numbers and types of units, and subsidies to achieve a supplemental income, zero-balance housing development which is capable of providing affordable housing options to existing and new residents of East St. Louis, Illinois.


1. Koenig, R; The feasibility of building new affordable housing in the low income inner city neighborhood of Emerson Park, Masters Project, Dept. of Urban and Regional Planning, University of Illinois at Urbana-Champaign, 1991.

2. Means Building Construction Cost Data, 1993.

3. Dechiara, Joseph & Koppelman, Lee; Manual of Housing Planning and Design Criteria, Prentice-Hall, Inc., New York, 1975.

4. Guggenheim, Joseph; Tax Credits for Low Income Housing, Simon Publications, Glen echo, Maryland, 1992.

5. ------; Comprehensive Housing Affordibility Strategy 1994-1998, East St. Louis, Illinois, 1994.

6. Community Development Workshop, Dept. of Urban & Regional Planning; Installment Land Contracts in East St. Louis: Analysis and Solutions, workshop report, Dept. of Urban & Regional Planning, University of Illinois at Urbana-Champaign.

7. Winstanley/Industry Park Neighborhood Five year Neighborhood Demonstration Area Strategic Community Stabilization Plan, a report by The Winstanley Industry Park Organization, Inc. and Department of Urban and Regional Planning, University of Illinois at Urbana-Champaign, 1993.


1. Rich Koenig, Illinois Housing Development Authority, Chicago.

2. St. Clair County Clerks Office.

Document author(s) : Emily Stern, Sandeep Kumar
HTML by : Sandeep Kumar
Last modified: April 2, 1996


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