pg. 1Business IT and Logistics—OMGT2287 Supply Chain Modelling and DesignAssessment 2: Case StudyDetailsThe childcare centre is a non-profit community and has been in the business for over 20 years. It is inMelbourne managed by a local university to provide high quality care for children of university staff andstudents. Its aim is to provide a safe, supportive environment for children to meet the needs of childrenand families.The centre has four floors with five rooms. Rooms 1–3 are for children under the age of 3. Room 4 ismainly for children at the age of 3 but this room has some 4-year-old children mixed in due to atransition to a kindergarten. Room 5 is mainly for children at the age of 4. However, some 5-year-oldchildren still attend because they are waiting for a term to open in a kindergarten. According to theAssistant Coordinator, the current numbers of children attending each day in each room and themaximum room capacities are summarised in the table below: Room 1Room 2Room 3Room 4Room 5Max Capacity1216161622Age (years)< 3< 3< 33–44+Monday101413916Tuesday111014158Wednesday78161320Thursday912121018Friday1211101617 According to the National Quality Framework (NQF), the minimum ratio of educators to children is 1:4 for0–35 months and 1:11 for 36+ months. Although the NQF ratios are calculated across the service, and notby individual rooms, for practical and safety reasons, the centre calculates the ratio on a room-by-roombasis.Generally, there are two levels of qualifications required to work as educators: Certificate III and Diploma.To comply with the NQF and to offer high quality care, in each room, the centre requires one educatormust have a Diploma qualification for every three educators. For example, if Room 1 requires 3 educators,one of them must have a Diploma (i.e. as a room leader) and the other two may have either a Diploma ora Certificate III qualification. However, if Room 1 requires 4 educators, two of them must have a Diplomaqualification as a minimum.pg. 2The centre has 16 permanent educators which are summarised in the table below: EducatorQualificationWorking TimeWorking Day1Diploma09:30–18:00Mon–Fri2Certificate III09:00–16:30Mon–Fri3Certificate III10:00–17:30Mon–Fri4Diploma07:30–16:00Mon–Thu5Certificate III10:00–17:30Mon–Fri6Diploma07:30–16:00Mon–Fri7Diploma09:30–18:00Mon–Fri8Certificate III10:00–17:30Mon–Fri9Certificate III09:00–16:30Mon–Fri10Diploma07:30–16:00Tue–Fri11Diploma09:30–18:00Mon–Fri12Certificate III09:30–16:30Mon–Fri13Certificate III09:00–17:30Mon–Fri14Diploma07:30–16:00Mon–Fri15Diploma09:30–18:00Tue–Fri16Certificate III09:30–17:00Mon–Fri In addition, the centre has a contract with the agency. If the centre requires additional qualifiededucators, either Certificate III or Diploma, they can contact the agency for an arrangement. The agencyeducators are paid only when needed, and there is no on-going cost required. Currently, the centre hasbooked eight educators on standby through the agency. The centre, however, can ask the agency toprovide more educators if needed.The centre pays the wages to the permanent educators according to the Children’s Services Award 2010.The wages depend on the experience and qualifications of the educators which are summarised below: LevelExperienceHourly Rate3.1On commencement$23.093.2After 1 year$23.893.3After 2 years$24.644.1On commencement$27.214.2After 1 year$27.624.3After 2 years$28.03 Level-3 employees are Certificate-III qualified educators, and Level-4 employees are Diploma qualifiededucators. All permanent educators in this centre have more than two years of experience working in thisindustry. The hourly wage to hire an agency educator, whether Certificate III or Diploma, is $52.67; andthey will always work for the full eight hours.Since one of the duties of educators is to engage and familiar with children, when they are assigned tosupervise one room, they will stay in the same room for the whole day and week. The centre opens at06:30 and closes at 18:30. Due to the availability of the permanent educators, the centre also hires casualeducators to cover for the permanent ones during the opening time, lunch break, and closing time, whichare approximately a few hours per day. As a result, the management has decided to ignore the workingtime of each permanent educator and focus on the main problem which is how to schedule thepermanent educators for the whole week. To simplify the problem, the centre does not group childrenfrom different rooms into a single room when there are only few of them present (i.e. in the earlypg. 3morning and in the evening). The centre also assumes that all children are present for the whole day.With all the details above, the Centre Manager, Margaret Hunt, wants to create a roster for the educatorswith a minimum-cost plan. She wants the plan that (1) each permanent educator will be given a job to doand (2) in case that there are insufficient educators, an agency educator will be given a job:a. Formulate and implement the mathematical model to solve this problemb. How much will it cost for the plan?c. Which educator will be assigned to which room?d. Is there any available place for a new child to attend? Which room? Which day?e. If Educators 4 and 10 are going to be on paid leave next week, what is a new minimum-cost planthat the manager should adopt?Guidelines: Report Structure1. Cover pagea) Report’s titleb) Names and student IDs2. Problem formulation (please ensure that all mathematical symbols are correct and consistent)a) Define decision variables with a measurement unit (e.g. pallets, kg, or km)pg. 4b) Provide an objective function and constraints and clearly show how you formulate themwith an explanation what each equation meansc) Ensure that decision variables and each equation are linked back to the data3. Problem solving (i.e. process of how you find the solution step-by-step)a) Explain how you implement the model in the Excel spreadsheet• Explain how you implement each equation in the model using what functions in Excel(e.g. SUMPRODUCT) and where you place it on the spreadsheet (e.g. at Cell B2). Ifconstraints are of the same kind and implemented in the same way, you just need toexplain the first one and summarise therest.b) Explain how you set up Solver in Excelc) Do not forget to submit the Excel spreadsheet together with the Word report4. Discussiona) Discuss the optimal solution based on the results that you findb) If you conduct sensitivity analysis, the results should be presented here.5. Recommendationsa) List and discuss what action should be taken based on the discussion.• For example, the results may suggest that the optimal solution for the productionproblem is to make 3 units of X and 4 units of Y. In addition, sensitivity analysisindicates that an increase of each Resource A can increase the profit by $5, up to themaximum of 100 units of Resource A. Your first recommendation can be to produce 3units of X and 4 units of Y, and the second recommendation is to procure additional100 units of Resource A.6. Presentationa) Discussion and explanation are succinctb) There is a link between each section. And when the report is read, the reader should notfeel jumpy (i.e. some important information is omitted).c) Cross-referencing and citations are correct, if anyd) All headings and sections are in placee) Images or figures are clearf) The writing is readable. You may use Flesch–Kincaid readability tests to evaluate your report.
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