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Selecting Day Care Facilities for Twin Rivers

You have been hired by the executives of City of Twin Rivers to conduct analyses in support of their “Care for our Children” program.

The city council of Twin Rivers recently passed a resolution to fund much needed child care facilities for the city. A total of ?850,000 has been made available to buy or lease child care sites throughout the city. An initial survey of the requirements for city-supported facilities has already been conducted and that data will form the basis of the sitting and facility selection analysis process. That initial survey indicated the need for facilities providing four categories of child care: infant care, pre-school care, after school care, and drop-in care. The survey indicated the following minimum requirements for each category of child care. Naturally, a goal of this program is not only to try and cover these minimum requirements, but also to try and maximize the total number of child care slots created.

Category    Requirements*
Infant care    200
Pre-school care    250
After-school care    325
Drop-in care    150
*all requirements are in terms of available slots
Various sites have been identified and these sites are either for lease or for sale. The leased sites require no additional modification at city expense. All modification expenses are borne by the site owner. The sites for sale will require some level of renovation and these renovation costs have been rolled into the purchase cost for the site. Additionally, some types of maintenance on leased sites will be borne by the owner reducing the expected maintenance costs the city must cover. The sites and the pertinent information about those sites is summarized in the table below. Note that all costs are in ?1000s. Each site was also assessed regarding the relative “safety” of the site. Safety issues included such things as parking, condition of the grounds, and condition of the structure. A safety index was used with each site rated as 1 for acceptably safe, 2 for marginally safe, and 3 for marginally safe given some modifications. Any sites surveyed found unacceptable in the safety department were dropped from further consideration.

Child Slots Supported
Infant    Pre-school    After    Drop-in    Type of    Cost of    Maintenance    Index of
Facility    Care    Care    school care    Care    Facility    Facility    Cost    Facility
1    50    —    75    50    RENT    ?145.00    ?11.98    1
2    40    —    75    60    RENT    ?146.00    ?12.03    2
3    —    70    75    30    RENT    ?139.50    ?11.71    2
4    75    40    —    30    RENT    ?136.50    ?11.56    1
5    50    —    —    75    BUY    ?125.00    ?26.98    1
6    —    90    —    75    BUY    ?156.50    ?60.56    3
7    25    —    80    40    BUY    ?115.50    ?42.51    2
8    —    85    100    —    RENT    ?137.25    ?11.59    2
9    85    50    75    —    BUY    ?169.00    ?61.18    3
10    100    75    75    —    BUY    ?203.75    ?30.92    1
11    60    —    —    75    RENT    ?134.00    ?11.43    3
12    40    40    40    40    RENT    ?139.00    ?11.68    2
13    —    85    —    65    BUY    ?142.25    ?43.84    2
14    75    85    75    —    BUY    ?189.75    ?30.22    1
15    65    —    75    30    BUY    ?138.50    ?43.66    2

These new facilities will require staffing. The city council would like insight into the number of new staff required and the subsequent annual personnel budget to accommodate these new positions. Medical, administration, and of course providers are required for the facilities. The desired level of staffing is based on a projected child-to-staff ratio. For planning purposes, a Created Slot-to-Staff ratio can be employed.

Ratios Refer to Child-to-Staff Ratio
Type of
Personnel    Annual Cost
of Position    Overall
Ratio    Infant
Ratio    Pre-School
Ratio    After-School
Ratio    Drop-In
Medical    ?16,000    40:1
Administration    ?25,000    80:1
Providers    ?13,000        3:1    6:1    15:1    7:1
Maintainers**    ?21,000
** One maintainer per facility.

Although the city council has agreed to fund this project for approximately ?850,000, reasonable targets for maintenance and personnel costs, and safety index levels must be established. The city council members would not only like recommendations on site selection that account for all the goals established for this project, they would like a summary breakout of the personnel requirements and costs associated with the recommended options.    (Case study adapted from Ragsdale (2014))

(a)    Formulate and implement appropriate multiple objective linear programming and goal programming optimization model(s) to provide a recommendations for the ?Care for our Children? programme using appropriate software.

(b)    Critically evaluate the ethical implications of the recommendation(s) you have made above in the context of the literature on ethical decision making with suggestions for justifiable changes to the original recommendation(s).

11.  Assessment criteria

The attached assessment grid will be used in marking your work

12. Special instructions

Your attention is drawn to the University Regulations for Assessment Section 7

Careful referencing of sources is vital when making use of the work of others.  You are expected to employ the referencing conventions recommended in the Field/Course.  These conventions apply to information taken from internet sources, as well as books, journals and lectures.  These are some of the points you should check before submitting your work:

?    are all direct quotations, from both primary and secondary sources, suitably acknowledged (placed in quotation marks or indented)?
?    have you provided full details of the source of the quotation, according to the referencing convention used in the Field?
?    have you acknowledged the source of ideas not your own, even if you are not quoting directly from the source?
?    have you avoided close paraphrase from sources? (Check that you are not presenting other people?s words or phrasing as if they are your own.)
?    if you have worked closely with others in preparing for this assessment, is the material you are presenting sufficiently your own?


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