Chase Manhattan Bank By South Group

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Chase Manhattan BankBy South Group

• Case Chase has labor planning problems that
  address staffing needs over a specific time
  period.
• Goals To minimize total daily personal cost
  within the corporate policies and constrains

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Chase Manhattan BankBy South Group

• To solve the issues, we let
• F0 Number of full-time tellers who dont work
  over time
• F1 Number of full-time tellers who work 1 hr
  over time
• F2 Number of full-time tellers who work 2 hr
  over time
• A PT tellers who work 4 hrs from 9am to 1pm
• B PT tellers who work 5 hrs from 9am to 2 pm
• C PT tellers who work 6 hrs from 9am to 3 pm
• D PT tellers who work 6 hrs from 9am to 4 pm

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Chase Manhattan BankBy South Group

• E PT tellers who work 4 hrs from 10 am to 2 pm
• F PT tellers who work 5 hrs from 10 am to 3 pm
• G PT tellers who work 6 hrs from 10 am to 4 pm
• H PT tellers who work 7 hrs from 10 am to 5 pm
• I PT tellers who work 4 hrs from 11 am to 3 pm
• J PT tellers who work 5 hrs from 11 am to 4 pm
• K PT tellers who work 6 hrs from 11 am to 5 pm
• L PT tellers who work 7 hrs from 11 am to 6 pm
• M PT tellers who work 4 hrs from 12 pm to 4 pm

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Chase Manhattan BankBy South Group

• N PT tellers who work 5 hrs from 12 pm to 5 pm
• O PT tellers who work 6 hrs from 12 pm to 6 pm
• P PT tellers who work 7 hrs from 12 pm to 7 pm
• Q PT tellers who work 4 hrs from 1 pm to 5 pm
• R PT tellers who work 5 hrs from 1 pm to 6 pm
• S PT tellers who work 6 hrs from 1 pm to 7 pm
• T PT tellers who work 4 hrs from 2 pm to 6 pm
• U PT tellers who work 5 hrs from 2 pm to 7 pm
• V PT tellers who work 4 hrs from 3 pm to 7 pm

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Chase Manhattan BankBy South Group

• Objective
• Minimize (10.11)(7)F0
• (10.11)(7)8.08F1
• (10.11)(7)(8.08)(2)F2
• (7.82)(4)AEIMQTV
• (7.82)(5)BEJNRU
• (7.82)(6)CGKOS
• (7.82)(7)DHLP

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Chase Manhattan BankBy South Group

• Subjects
• 9-10am (F0F1F2)ABCD gt14
• 10-11am (F0F1F2)ABCDEFGH
  gt25
• 11-12pm
• 0.5(F0F1F2)ABCDEFGHIJK
  L gt26
• 12-1pm
• 0.5(F0F1F2)ABCDEFGHIJKLMONPgt
  38
• 1-2pm
• (F0F1F2)BCDEFGHIJKLMNO
  PQRS gt55

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Chase Manhattan BankBy South Group

• 2-3pm
• (F0F1F2)CDFGHIJKLMNOPQRSTU
  gt60
• 3-4pm
• (F0F1F2)DGHJKLMNOPQRSTUV gt51
• 4-5pm
• (F0F1F2)HKLMNOPQRSTUV
  gt29
• 5-6pm ( F1F2)LOPSTUV
  gt14
• 6-7pm ( F1F2)PSUV
  gt9
• 4(AEIMQTV)5(BFJNRU)6(CGKOS)7(DH
  LP)
  
  
• 
  
  lt 40(321)

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Chase Manhattan BankBy South Group

• Start QM for Windows
• Select Module Menu
• Select Linear Programming Menu
• Select File Menu
• Select New
• Define Data set for Linear Program

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Chase Manhattan BankBy South Group

• Fill in data grid with problem data
• Solve the problem by clicking the solve button

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Chase Manhattan BankBy South Group

• The solution can be viewed in the data grid

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Chase Manhattan BankBy South Group

• Use Excel Solver to solve the question
• Step 1
• Start Excel and create a new worksheet
• Step 2
• Enter Headings, variables, and coefficients for
  the objective function
• Step 3
• Enter cells where values of variables will be
  located, this is where solver will put the
  solution
• Step 4
• Write formula to compute left side constraints

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Chase Manhattan BankBy South Group

• Step 5
• Enter right side constraints
• The spread Sheet is now ready to run solver

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Chase Manhattan BankBy South Group

• Step 6
• Click on Tools
• then Solver
• Step 7
• Fill in Solver Parameters to match your Spread
  Sheet layout

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Chase Manhattan BankBy South Group

• Step 8
• Set Solver Options as follows
• Step 9
• Solve the problem and Keep solver Values

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Chase Manhattan BankBy South Group

• Step 10
• Review answer

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Chase Manhattan BankBy South Group

• DISCUSSION QUESTION
• What is the minimum-cost schedule for the bank?
• By utilizing QM for Windows and Excel Solver, we
  obtain the minimum-cost schedule for the bank is
  3,026.65

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Chase Manhattan BankBy South Group

• DISCUSSION QUESTION
• 2. What are the limitations of the model used to
  answer question 1?
• The model used to solve the problem suffers from
  the limitation that there are several optimal
  outcomes and a different answer may be obtained
  depending on the sequence in which the
  constraints are answered.

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Chase Manhattan BankBy South Group

• DISCUSSION QUESTION
• 3. Costs might be reduced by relaxing the
  constraint that no more than 40 of the days
  requirement be met by part-timers. Would
  changing the 40 to a higher value significantly
  reduce costs?
• Yes, changing the 40 to a higher value would
  significantly reduce costs. We provide the
  sensitivity analysis as follows

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Chase Manhattan BankBy South Group

• Changing to 60
• Cost 2,485.83
• Changing to 80
• Cost 2,382.08
• As the percentage
• increases, the cost
• decreases.