Question

Each certified instructor puts in 480 hours per quarter regular time and can work an additional 120 hours overtime. Regular-time wages and benefits cost Carlton $7,200 per employee per quarter for regular time worked up to 480 hours, with an overtime cost of $20 per hour. Unused regular time for certified instructors is paid at $15 per hour. There is no cost for unused overtime capacity The cost of hiring, training, and certifying a new employee is $10,000. Layoff costs are $4,000 per employee. Currently, eight employees work in this capacity Round up the workforce numbers for your calculation uarter 4 Demand 4,200 6,400 3,000 4,800 4,400 6,240 3,600 4,800 A) Find a staffing plan using the level strategy that allows for no delay in service. It should rely only on overtime and the minimum amount of undertime necessary. What is the total cost of this plan? B) Use a chase strategy that varies the workforce level without using overtime or undertime. What is the total cost of this plan? C) Proposer plan and calculate its total cost.

Answer 1

A) Staffing plan based on level strategy is following:

B C D E F G HIJK N O SSolver Parameters 1 Level strategy CostCategory cate 2 Quarter 3 Demand (hours 4 Regular time 5 Overtime 6 Service Dela 7 Undertime 8 Overtime capacity remaining 1320200 1320 1320 1320360 1320 1320 8480 9 #of employees 10 Hired 11 Fired 12 13 8 Total 4200 6400 3000 4800 4400624036004800 37440 4200 5280 3000 4800 4400 5280 3600 4800 35360 0 2080 SMS14 Set Objective: To: ○ Max ⓔMlin O value of: By Changing Variable Cells: 0 0 1120 0 960 41,600 Subject to the Constraints: 0 2280 480880 0 1680 480 6880 633,600 30,000 SCS10 SJS11 integer SDS10 SIS11 0 10000 Reset All Total Cost 705 200Make Unconstrained Variables Non-Negative 15 16 17 18 19 20 21 22 Golf Camp 23 24 Select a Solving Method: Simplex LP Options Solving Method Select the IPOPT Nonlinear engine for Solver Problems that are smooth nonlinear.Select the LP Simplex engine for linear Solver Problems. Solve

EXCEL FORMULAS:

Cell	Formula	Copy to
C6	=C3-SUM(C4:C5)	C6:J6
C7	=480*C9-C4	C7:J7
C8	=120*C9-C5	C8:J8
C9	=B9+C10-C11	C9:J9
K3	=SUM(C3:J3)	K3:K11
M5	=K5*L5	M5:M11
M14	=SUM(M3:M11)

B) Staffing plan based on Chase strategy is following:

B C D E FG HIJK N O 1 Chase strategy 2 Quarter S Solver Parameters Cost/Category 8 Total SMS14 3 Demand (hours 4 Regular time 5 Overtime 6 Service Dela Set Objective To: Max Min By Changing Variable Cells: 4200 6400 3000 4800 4400 62403600480037440 4200 6400 3000 4800 4400 6240 3600 480037440 Value Of: o 0,0 SCS4 SJS5,SCS10 SIS11 Subject to the Constraints Undertime 120 320 1800 0 400 0 1200 0 0 3840 8 Overtime capacity remaining 1080 1680 1200 1200 1200 15601200 1200 10320 # of employees 14 10 10 13 10 7200619,200 90,000 28,000 SC$10 SJS11-integer Change 10 Hired 11 Fired 10000 Delete Reset All 14 Total Cost 737 Make Unconstrained Variables Non-Negative 16 17 Select a Solving Method: Simplex LP Options Solving Method Select the IPOPT Nonlinea nonlinear.Select the LP Simplex engine for linear Solver Problems. r engine for Solver Problems that are smooth 20 Solve 22 Golf Camp 23 24 25

C) Better plan based on Mixed strategy is following:

B C D EF G HIJK 1Mixed strategy CostCategory SSolver Parameters 2 Quarter 8 Total 4200 6400 3000 4800 440062403600480037440 4200 5280 3000 4800 4400 5280 3600 4320 34880 480 2560 SM$14 Set Objective: To: Max Min By Changing Variable Cells: 3 Demand (hours 4 Regular time 5 Overtime 6 Service Dela 7 Undertime 8 Overtime capacity remaining 1080200 1200 1200 1200 360 1080 6006920 9 #of emplo s 10 Hired 11 Fired 12 13 Value of: o 1120 960 51,200 SCS4 SIS5,SCS10 SJS11 120 0 1800 0 0 3040 Subject to the Constraints: SCS6:SJS6-0 10 10 10 7200 568,800 40,000 12,000 10000 SC$10:SJS11 integer Delete Reset All Total Cost 672,000 Make Unconstrained Variables Non-Negative Select a Solving Method: Simplex LP Options Solving Method Select the IPOPT Nonlinear engine for Solver Problems that are smooth nonlinear.Select the LP Simplex engine for linear Solver Problems. 20 21 22 Golf Camp 23 24 Solve