Project. Workforce Planning Mexico City Bank of Commerce and Industry is a busy
ID: 3314062 • Letter: P
Question
Project. Workforce Planning Mexico City Bank of Commerce and Industry is a busy bank that needs different number of tellers depending on the time of day due to different number of customers needed service. The table below indicates the number of workers needed at arious hours that the bank is open. Full-time Employee.s The bank currently has employed 14 full-time tellers that work from 9 a.m. to 5 #of Tellers Needed Time Period .1m. Part-time Employee: The bank plans to hire Part-time Employees to cover the additional tellers needed. Many people are available for part-time employees. A part-time employee will work exactly 4 hours per day, but can be scheduled to start at any time between 9 a.m. and 1 p.m. Hourly pay - Each full-timer will be paid $120 per day (S15 per hour) in salary and am.-10 am 10 am-II a.m I am.-Noon 10 12 14 16 18 16 14 oon-I p.m p.m.-2 p.m. 2 p.m.-3 p.m. Part-timers will be paid $40 per 4-hour shift ($10 per hour) on averagep.m benefits on average Lunch time Full-timers are divided into 2 groups for 1 hour lunch time. (The 1t group Full timers eat between 11-noon., and the rest (2d group) of the Full-timers eat between noon-1pm.) There is no lunch time for part timers Corporate policy The bank limits part-time hours to a maximum of 40% of the day's total required labor hours * The bank may not use all Full Time Employees currently hired. The unused full time Employees can be 4p.m.-5 p.m relocated to another department at a relocation cost S10 each during the planning periods. The bank would like to set a labor hiring schedule (full time and part time) and Full timer employee's lunch schedule that would minimize its total workforce related costs. Use Linear Programming we are learning to help the bank make the best decision Tasks: Part I. You need to do the followings i) Formulate the problem into a Linear Programming model. i) Solve the Linear Programming using Excel a. Summarize the optimal decision on the number of Full time employees to use and the number of part time employees to hire starting at different hours between 9:00m00pm, and the full timer lunch schedule that minimize the total costs. Part II. Use the Answer Report and Sensitivity Report from the solver outputs to answer the following questions (Important: It is required that we support our answers to the questions by referring to the Exact Place in the Answer Report and Sensitivity Reports. It is not allowed to answer the questions by re-solving the LP models with updated parameters again and again) i) If the per pay for the Full-time employee is Reduced by $10, will the optimal decision remain same? What will be the corresponding optimal total costs now? Explain. ii) Will the optimal total costs change if the pay for the Full-time employee is Reduced by $75 a day? Explain. iii) iv) v) If the required number of employees in period 10:00-11:00am is Increased to 14, what will be the optimal total costs? Do you think the optimal decision on Full-time and Part-time employees will change? If the required number of employees in period 11:00-12:00am is Increased by 2, what will be the optimal total costs? Do you think the optimal decision on Full-time and Part-time employees will change? If the required number of employees in period 11:00-12:00am is changed to 11, what can you say about the optimal total costs, and optimal decision on Full and Part time employees? Page 2Explanation / Answer
Formulate
Let us consider xi and yi be the number of full time and part time employess working at the ith time period.
Hence, x9 + y9 >= 10
x9 + y9 + y10>= 12 , there is no change for full time employees
x9 + y9 + y10 + y11 -l1 >= 14 , where l1 is full time employees out for lunch
x9 + y9 + y10 + y11 + y12 -l2 >= 16 , where l2 is full time employees out for lunch
x9 + y10 + y11 + y12 + y1 >= 18 , part time employees started at 9 am are now completed with the shift
x9 + y11 + y12 + y1 >= 16 , no part time employee starts after 1 as to complete 4 hours
x9 + y12 + y1 >= 14
x9 + y12 + y1 >= 10
l1 + l2 = 14
x9 = 14
To minimize the empolyee cost,
f(x) = 120 * 14 + 40* (y9 + y10 + y11 + y12 + y1)
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