Problem 1 – Customer Projections [50 marks]
The MPS Group has recently opened a new mall in Ramsgate, Kent. The number of daily visitors in the first 4 weeks since the opening are recorded in the sheet MallVisitors of the Excel file MPSGroupMall.xlms available on Moodle.
a) Develop a forecasting model to predict the daily number of visitors in week 5. [20]
b) Write a short report that includes the following: [30]
a. A discussion of the data series characteristics
b. An interpretation of the results produced by the selected forecasting method
c. An evaluation of the forecasting error(s)
d. A chart displaying the forecasted data
Problem 2 – Staff Scheduling [50 marks]
Mark Shennon, the general manager of the new MPS Group Mall, is trying to ensure that enough support staff are available to clean the mall before it opens each day. The mall operates seven days a week and the cleaning staff work between 12:30am and 8:30am each night. Based on the projected mall traffic data for the upcoming week, Marks estimates that the number of cleaning staff required each day will be as shown in the Table 1 below.
Table 1: Cleaning Staff Requirement Data
Day of week Number of Staff Required
Monday 22
Tuesday 13
Wednesday 15
Thursday 20
Friday 18
Saturday 23
Sunday 27
Mark can use the work schedules shown in Table 2 for the cleaning staff. The wages for each schedule are also shown in Table 2. In order to be perceived as a fair employer, Marks want to ensure that at least 75% of the workers have two consecutive days off and that at least 50% of the workers have at least one weekend day off. How should Mark schedule his cleaning staff in order to meet the mall’s requirements at minimum cost?
Table 2: Schedule and Cost Data
Work Schedule Wages per Week
WS1. Saturday and Sunday off £350
WS2. Saturday and Tuesday off £375
WS3. Tuesday and Wednesday off £400
WS4. Monday and Thursday off £425
WS5. Tuesday and Friday off £425
WS6. Thursday and Friday off £400
WS7. Sunday and Thursday off £375
WS8. Sunday and Wednesday off £375
a) Develop a model to determine Mark’s optimal cleaning staff schedule. [20]
b) Write a report which includes a discussion on the following. [30]
i. A schedule showing the recommended number of staff working on each day and the corresponding total wages. Interpret the results of the model.
ii. A discussion for the optimality ranges of the objective coefficients. What do the ranges indicate about how sensitive the recommended solution is to the weekly work schedule wages?
iii. The impact of including the two additional requirements that allow Mark to be perceived as a fair employer. Should Mark reconsider these? Or at least one of these?
iv. Mark would like to consider an alternative model that minimises the number of staff who do not have a weekend day off. In this case, the 50% requirement in the original model can be removed. Mark wants to ensure that the cost of the new solution does not exceed £14,000. Compare this solution with the ones analysed in i) and iii). Which one is better? Why?
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