Staff Scheduling at USPS Mail Processing & Distribution Centers A Case Study Using Integer Programming

General Observation Companies and organizations that build, or make use of the latest technology in their business practices, rarely make use of the latest technology in planning and scheduling!

Service Area in City

Processing & Distribution Center

USPS Scheduling Problem Equipment scheduler Staff scheduler facility configuration Mail arrival profiles & volume Worker demand Union rules & local policies Flow patterns & Weekly staff assignments

Staff Planning and Scheduling Long-term planning: Fix size and composition of permanent workforce Mid-term scheduling: Determine days off and shift assignments Short-term scheduling: Overtime, individual tasks, requests, part-timers Real-time control: Emergencies, absenteeism, and other disruptions

Long-Term Staff Scheduling Categories Full-Time Regulars, Part-Time Regulars Part-Time Flexibles Goal : Minimize labor costs Skills (15 Categories)   Input Data Labor Requirements (1/2 hour increments) Labor Costs by Worker Type

Model Components for Long-Term Staff Scheduling Operations analysis (simulation) optimal amount Determine of equipment Daily mail arrivals Mail flow configuration Machine parameters Work rules Labor ratio Days off Shifts Equipment counts Equipment schedules Tours Personnel scheduling (optimization)

Computational Flow Input data Optimization engine Initial output Post-processing Weekly schedules Microsoft Excel Spreadsheets CPLEX Days-off scheduling (Visual Basic) FT, PT (Visual Basic) OPL Studio (ILOG) Staff levels and shifts (FT, PT) Breaks (OPL Studio) Modeling language

Shift Optimization Model Minimize (Full time costs + Part time costs) Subject to 1. Cover all time periods during the week 2. Ensure sufficient lunch breaks are assigned 3. Adhere to days off requirements 4. Meet other labor rules and policies

Portion of IP Model

Size of Typical Staff Planning Model Number of Constraints = 1100 Number of Integer Variables = 1500 Number of Logic Variables = 336 Solution Times: seconds  years

Post-Processors Days-Off Scheduling Greedy algorithm for assigning days off Small integer program for 2-days off in a row Lunch Break Assignments Transportation problem Greedy algorithm Task Assignments Multi-commodity network flow problem Tabu search

Modeling Issues Time to run, # of runs, how often Users and their skills GUI sophistication Training requirements Version control Help desk availability

Who Is The Customer ? USPS Headquarters Contracting Officer Facility Managers Facility Industrial Engineers Information Technology Manager

Everybody Wants Something More Headquarters Headquarters – Implementation in 9 months system-wide Contracting Officer Contracting Officer – Statement of Work is just a starting point (don’t expect any more money, though, for additional work) Plant Manager Plant Manager – More modeling features IT Manager IT Manager – It will take years to provide the data you want

Model “Creep” 10-hour shifts, 4-day a week schedules Some schedules 2 days off in row, others not necessary Worker assignments during the day At least “X” workers per shift No more than 1 shift every “Y” hours

Implementation Prototype written in OPL Studio to demonstrate concepts Web Access – Java CPLEX is optimization engine 1600 variables (all integers) 1500 constraints Two Test Sites – Dallas and Philadelphia

SOS Menu

Workstation Sets

Output Report

Number of constraints Number of variables Total cost per week Number of full-timers Number of part-timers % 2 days off in a row Baseline model $96, Ratio 3: $95, Ratio 5: $97, Consecutive off-days $103, hr/6 day workers $95, Variable start time $95, Part-time flexible $94, Computational Results

Parametric Analysis

Benefits of Flexibility

Observations and Lessons The Customer is Not Always Right Sometimes a Good Product will Sell Itself but it Pays to Have a Champion Don’t Expect the Customer to Understand his Business from Your Point of View Data are Always a Problem

Observations and Lessons (cont.) Do not Try to Explain Optimization to Anyone Who Does not Have an Advanced Degree Nobody Reads Manuals so Make Sure the Interfaces are Simple and Clear However, Don’t Underestimate the Intuition of the Customer

Skill Categories  