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Workforce Reallocation Throughput Stability: A Simulated Operations Case Study

Abstract

This case study evaluates two staffing designs in a fulfillment context: 4 workers x 10-hour shifts versus 6 workers x 6-7-hour shifts. Using simulated order-level logic derived from non-proprietary records, we model demand timing, packaging-time variability, fatigue effects, backlog carry-over, and labor cost. Under the configured assumptions, the 6-worker short-shift model delivers higher per-person hourly efficiency and lower labor cost with substantially reduced backlog pressure.

1. Background

Operational instability in fulfillment environments is often caused by mismatch between demand timing and effective labor capacity. Even when total staffing appears adequate, long-shift fatigue and late-day backlog accumulation can reduce throughput stability and increase cost.

This study reconstructs a practical staffing comparison in a simulation-safe format for portfolio publication.

2. Research Objective

Compare whether a reallocated staffing model (6x6-7) outperforms a long-shift model (4x10) on:

  • Per-person hourly productivity
  • Backlog stability
  • Labor cost efficiency

3. Data and Scope

3.1 Source Data

  • Input file: Simulated_Case_Study.csv
  • Core fields used:
    • Create Time
    • Product Size (cm) L * W * H

3.2 Operation-Day Definition

For day D (from Jan 2 onward), demand window is:

  • Start: D-1 09:00:00
  • End: D 08:59:59

Simulation window: Jan 2 to Jan 31 (30 operation days).

4. Methodology

4.1 Demand Mapping

Orders are mapped to operation days by Create Time:

  • if time >= 09:00, assign to next day
  • else assign to same day

4.2 Volume Derivation

For each record:

  • Parse L, W, H from size field
  • Compute Total Volume = L * W * H

4.3 Stochastic Packaging-Time Model

Per-order processing seconds are randomly generated by volume bucket:

  • <= 250: 8-14 sec
  • 251-500: 10-15 sec
  • 501-1000: 12-16 sec
  • 1001-2000: 13-18 sec (bridge assumption)
  • > 2000: 15-20 sec

A fixed random seed is used for reproducibility.

4.4 Staffing Models

Model A: 4 workers x 10 hours

  • Daily threshold: 2000 orders
  • Fatigue mechanism after hour 6:
    • Late-shift slowdown factor sampled from 1.3-1.4
    • Effective capacity reduced in hours 7-10

Model B: 6 workers x 6-7 hours

  • Daily threshold: 3500 orders
  • Shift length sampled uniformly between 6.0 and 7.0 hours
  • No additional post-6h fatigue penalty in this setup

4.5 Backlog Logic

If daily demand exceeds threshold, overflow moves to next day backlog.

Backlog propagation:

  • total_demand_orders = backlog_start + incoming_orders

4.6 Cost Model

Hourly wage is fixed at $18 per person-hour.

  • daily_labor_cost = workers * shift_hours * 18

5. Results

Source: data/processed/staff_allocation_efficiency_summary.csv

Metric 4 workers x 10h 6 workers x 6-7h
Avg orders/person/hour 32.6308 33.7127
Avg daily processed orders 1305.2333 1305.2333
Avg backlog end orders 269.5 29.0
Days with backlog 8 1
Total labor cost 21600.0 20836.8941
Avg daily labor cost 720.0 694.5631
Labor cost per processed order 0.5516 0.5321

5.1 Directional Effects

  • Per-person hourly efficiency: +3.32% for 6x6-7
  • Total labor cost: -3.53%
  • Cost per processed order: -3.54%
  • Average backlog: substantially lower for 6x6-7

6. Discussion

The short-shift, higher-headcount model improves both efficiency and cost outcomes under this setup. The fatigue mechanism in long shifts and lower backlog threshold in Model A jointly increase pressure and reduce stability.

This suggests that workforce-hour redistribution can be more impactful than simply extending shift duration.

7. Limitations

  • This is a simulation-oriented case, not a production replay.
  • Processing-time buckets are randomized and assumption-driven.
  • One bridge assumption is introduced for volume 1001-2000.
  • Results are directional and should be validated in live operations.

8. Conclusion

For this case-study configuration, 6 workers x 6-7 hours outperforms 4 workers x 10 hours on per-person efficiency, labor cost, and backlog stability while maintaining equivalent total processed volume.

9. Reproducibility

Run:

python3 src/hourly_peak_avg.py
python3 src/daily_orders_9am_window.py
python3 src/staff_allocation_efficiency.py
python3 src/plot_hourly_peak_svg.py
python3 src/plot_daily_orders_line_svg.py
python3 src/plot_staff_allocation_comparison_svg.py

Generated outputs:

  • Tables: data/processed/*.csv
  • Figures: images/*.svg

10. Figure Index

  • Figure 1: images/jan_hourly_average_orders.svg
  • Figure 2: images/jan_daily_orders_with_peak.svg
  • Figure 3: images/staff_allocation_comparison.svg