System Optimization: Networks Introduction

Labor Planning for a Manufacturing Line Agenda • Introduction • Formulation of LP Model • Use and Demonstration of LP Model • LP Model Limitations TI Precision Thermostat Styles Weld contact to arm Weld contact to header Factory Flow Sort pins 40% Calibrate (3) Weld arm to header Vacuum bake and tig weld Laser weld 60% Disc assemble Leak check Hypot test (2) 25% Creep test (3) Temp check (5) Code Clean room 100K 15% 10% 40% Weld connector Wire leads (2) ( ) indicate # of workstations greater than 1 Clean room 100 25% Bend terminals 10% Tin dip 75% Inspection and write up QC Line History & Need For Model Line History • Line in existence since 1960’s • Wide range of skill leads to complex staffing pay (pay code, shift differential, clean room pay) • Some operators employed on line since 1960’s!! Consequently current work force is well cross trained but ‘top heavy’ and may not be ideal Current Need Model Addresses • Opportunities exist to manage and minimize labor cost on the production line given varying demand Higher paid, high experience workers Base pay, low experience workers Description of the LP Model 1st Shift Decision Variables Work Hours For Each Pay Code and Operation # of Shifts Operation 1.1 2.1 3.1 4.1 5.1 Sort Pins 7.73 0.00 0.00 0.00 0.00 Weld contact to Header 0.00 8.00 0.00 0.00 0.00 Weld contact to Arm 0.00 8.00 0.00 0.00 0.00 Weld Arm to Header 0.00 8.00 0.00 0.00 0.00 Disc Assemble 5.37 0.00 0.00 0.00 0.00 Calibrate 0.00 0.00 0.00 0.00 24.00 Laser Weld 0.00 0.00 8.00 0.00 0.00 Vacuum bake/tig weld 0.00 8.00 0.00 0.00 0.00 Leak check 0.00 8.00 0.00 0.00 0.00 Code 0.00 16.00 0.00 0.00 0.00 Temp Test 0.00 0.00 40.00 0.00 0.00 Creep Test 21.46 0.00 0.00 0.00 0.00 Hypot Test 16.00 0.00 0.00 0.00 0.00 Bend Terminals 8.00 0.00 0.00 0.00 0.00 Weld Wire Leads 0.00 3.22 0.00 0.00 0.00 Tin Dip 0.00 0.00 6.44 0.00 0.00 Weld Connector 0.00 8.00 0.00 0.00 0.00 Inspection/ Writeup 0.00 0.00 0.00 0.00 54.39 Shift 1 Shift 2 Shift 3 1 1 1 Description of the LP Model Constants/Inputs • • • • • • Number of days per month Demand Fraction Current work force Number of work stations Max capacity per hour per operation • Second and third shift fixed cost OPERATION F(fraction) A(#of stations) Units/hr Sort Pins 1 5 500 Weld contact to Header 1 1 180 Weld contact to Arm 1 1 180 Weld Arm to Header 1 1 180 Disc Assemble 1 1 720 Calibrate 1 3 120 Laser Weld 1 1 180 Vacuum bake/tig weld 0.4 1 60 Leak check 1 1 300 Code 1 2 120 Temp Test 1 5 60 Creep Test 1 3 180 Hypot Test 1 2 180 Bend Terminals 0.4 1 180 Weld Wire Leads 0.1 2 120 Tin Dip 0.1 1 60 Weld Connector 0.15 1 60 Inspection/ Writeup 1 5 60 Description of the LP Model Constraints • Labor demand per day • Machine capacity per shift • Number of workers for each shift • Work hours by each grade vs. the available number of work hours at each grade level • Non-negativity constraints for decision variables Objective Function To minimize the overall daily staffing cost of production. The cost is calculated by adding up the cost of labor on each operation per shift. Our Integer Model Foray • Disadvantage of LP Model: Fractional work hours (not standard 8 hr employee shift) • Modification of LP Model to create an Integer Model: Number of workers added as decision variables and they were forced to be integers • Disadvantage of the Integer Model: When demand increased (beyond 1-shift) model ran for too long without producing an optimal solution Supervisor Inputs Monthly Demand LP Model Current Workforce # of Work Days In Month Model Outputs Paycode Specific Staffing Hours: by-shift hours/location required by each paycode Operation Specific Staffing Hours: by-shift total hours of each shift on each individual operation. Overall Paycode Staffing Hours: total staffing hours for each paycode Overall Shift Staffing Hours: total staffing hours on each shift used by management & facilities to gauge level of operation for each shift. Daily and Monthly Staffing Costs: lowest cost per day/month for staffing given current factory constraints. Factory Manager Input/Output Interface Entered Data Inputs # Of Work Days In Month 22 Monthly Demand 45000 Existing Workforce Paycode 1 Paycode 2 Paycode 3 Paycode 4 Paycode 5 Head Count 0 0 5 5 7 Decision Variables Daily Paycode Specific Staffing Hours 1st Shift Staffing Avail Hours/Shift Operation 2nd Shift Staffing 3rd Shift Staffing Paycode 1 Paycode 2 Paycode 3 Paycode 4 Paycode 5 Paycode 1 Paycode 2 Paycode 3 Paycode 4 Paycode 5 Paycode 1 Paycode 2 Paycode 3 Paycode 4 Paycode 5 Sort Pins 40 4.09 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Weld contact to Header 8 0.00 0.00 0.00 0.00 8.00 0.00 0.41 0.00 0.00 2.95 0.00 0.00 0.00 0.00 0.00 Weld contact to Arm 8 0.00 8.00 0.00 0.00 0.00 0.00 3.36 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Weld Arm to Header 8 0.00 0.00 0.00 0.00 8.00 0.00 3.36 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Disc Assemble 8 2.84 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Calibrate 24 0.00 0.00 0.00 0.00 17.45 0.00 0.00 0.00 0.00 16.64 0.00 0.00 0.00 0.00 0.00 Laser Weld 7 0.00 0.00 0.00 4.05 2.95 0.00 0.00 2.50 1.86 0.00 0.00 0.00 0.00 0.00 0.00 Vacuum bake/tig weld 8 0.00 8.00 0.00 0.00 0.00 0.00 5.64 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Leak check 8 0.00 6.82 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Code 16 0.00 16.00 0.00 0.00 0.00 0.00 1.05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 34.09 Temp Test 40 0.00 Creep Test 24 11.36 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Hypot Test 16 11.36 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Bend Terminals 8 4.55 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Weld Wire Leads 16 0.00 6.82 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Tin Dip 8 0.00 0.00 3.41 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Weld Connector 8 0.00 8.00 0.00 0.00 0.00 0.00 2.23 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 40 0.00 0.00 0.00 34.09 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 34.20 53.64 37.50 38.14 36.41 0.00 16.05 2.50 1.86 19.59 0.00 0.00 0.00 0.00 0.00 Inspection/ Writeup Totals Per Day Daily Operation Specific Staffing Hours Operation Avail Hours/Shift Shift 1 Shift 2 Shift 3 Outputs Staffing Cost Sort Pins 40 4.09 0.00 0.00 Weld contact to Header 8 8.00 3.36 0.00 Daily Weld contact to Arm 8 8.00 3.36 0.00 Monthly $3,589 $78,968 Weld Arm to Header 8 8.00 3.36 0.00 Disc Assemble 8 2.84 0.00 0.00 Daily Shift Staffing Hours Calibrate 24 17.45 16.64 0.00 Laser Weld 7 7.00 4.36 0.00 Shift 1 199.89 Vacuum bake/tig weld 8 8.00 5.64 0.00 Leak check 8 6.82 0.00 0.00 Shift 2 40.00 Shift 3 0.00 Daily Overall Paycode Staffing Hours Code 16 16.00 1.05 0.00 Temp Test 40 34.09 0.00 0.00 Paycode 1 Paycode 2 Paycode 3 Paycode 4 Paycode 5 Creep Test 24 11.36 0.00 0.00 34.20 69.68 40.00 40.00 56.00 Hypot Test 16 11.36 0.00 0.00 Bend Terminals 8 4.55 0.00 0.00 Weld Wire Leads 16 6.82 0.00 0.00 Tin Dip 8 3.41 0.00 0.00 Weld Connector 8 8.00 2.23 0.00 Inspection/ Writeup 40 34.09 0.00 0.00 Denotes No Work Required Given Current Demand Denotes Paycode Does Not Having Training To Complete Operation Run LP Model Strategic Uses Determining a “Target” Workforce • How many permanent staff in the face of varying demand • Cost of holding too many workers vs. cost of hiring $5,000.00 $4,500.00 $4,000.00 $3,500.00 $3,000.00 $2,500.00 $2,000.00 $1,500.00 $1,000.00 $500.00 $- Small staff Medium Staff 2 2 0 75 0 32 3 0 75 0 0 0 00 50 0 0 Large Staff 50 1 0 00 No current staff 0 Labor Cost (daily) Labor Cost with Varying Demand 42 Demand (monthly) 5 0 00 0 6 0 00 0 Strategic Uses Daily Operation Specific Staffing Hours Understanding the Bottleneck • The machine that is most constrained causes more shifts • New capital investment vs. working another shift Operation Avail Hours/Shift Shift 1 Shift 2 Shift 3 Sort Pins 40 5.45 0.00 0.00 Weld contact to Header 8 8.00 7.15 0.00 Weld contact to Arm 8 8.00 7.15 0.00 Weld Arm to Header 8 8.00 7.15 0.00 Disc Assemble 8 3.79 0.00 0.00 Calibrate 24 24.00 21.45 0.00 Laser Weld 7 7.00 7.00 1.15 Vacuum bake/tig weld 8 8.00 8.00 2.18 Leak check 8 8.00 1.09 0.00 Code 16 16.00 6.73 0.00 Temp Test 40 40.00 5.45 0.00 Creep Test 24 15.15 0.00 0.00 Hypot Test 16 15.15 0.00 0.00 Bend Terminals 8 6.06 0.00 0.00 Weld Wire Leads 16 9.09 0.00 0.00 Tin Dip 8 4.55 0.00 0.00 Weld Connector 8 8.00 5.64 0.00 Inspection/ Writeup 40 40.00 5.45 0.00 Model Limitations • Idealized plant view • No variation in machine rates • No defects • No machine downtime • Idealized worker view • No vacations, breaks, or sick time • Assumed all workers work at same rate • Forecasts hours not complete 8 hr shifts • Limited staff planning tool • Not a per-worker scheduling tool • Does not address soft-concerns Conclusions • Useful part of the “toolkit” for a manager • Interpretation of the results is required • LP models can get complex really fast