How to Optimize Workforce Planning Over Three Years with Hiring, Training, and Layoffs

Problem Description

A company is changing its business model, which will alter employee demand. Purchasing new machines will reduce the need for unskilled labor while increasing demand for semi‑skilled and skilled workers. An anticipated economic slowdown and lower sales forecasts will further reduce demand for all categories.

Projected workforce demand for the next three years:

Year 1: Unskilled 1000, Semi‑skilled 1400, Skilled 1000

Year 2: Unskilled 500, Semi‑skilled 2000, Skilled 1500

Year 3: Unskilled 0, Semi‑skilled 2500, Skilled 2000

The company must each year decide on hiring, retraining, layoffs (redundancy), and the mix of part‑time versus full‑time staff. All employees have already completed at least one year of service.

Hiring

External hiring limits per year are 500 unskilled, 800 semi‑skilled, and 500 skilled workers.

Retraining

Up to 200 unskilled workers can be retrained to semi‑skilled each year at a cost of $400 per worker. Semi‑skilled workers can be upgraded to skilled, but not exceeding 25% of the current skilled workforce, at $500 per worker. Additionally, 50% of demoted employees will leave the company, increasing attrition.

Layoffs

Severance payments are $200 per unskilled worker and $500 per semi‑skilled or skilled worker.

Redundancy

The company may have at most 150 redundant workers per year, each incurring additional annual costs of $1500 (unskilled), $2000 (semi‑skilled), or $3000 (skilled).

Part‑time Workers

Up to 50 employees per skill level can be assigned to part‑time work. Annual cost per part‑time employee is $500 (unskilled) and $400 (semi‑skilled and skilled). Part‑time productivity is half that of full‑time staff.

Mathematical Model

Sets and Indices

t: set of years

s: set of skill levels (Unskilled, Semi‑skilled, Skilled)

Parameters

rookie_attrition_s: attrition rate for employees in their first year

veteran_attrition_s: attrition rate for employees beyond the first year

demotion_attrition: attrition rate for demoted employees

parttime_productivity: productivity factor of part‑time workers relative to full‑time

max_train_unskilled: maximum number of unskilled workers that can be trained per year

max_train_semiskilled: maximum number of semi‑skilled workers that can be trained per year

max_parttime_s: maximum number of part‑time workers per skill level per year

max_redundancy: maximum allowed redundant workers per year

hire_limit_s: external hiring limit for each skill level

train_cost_unskilled_to_semiskilled

train_cost_semiskilled_to_skilled

layoff_cost_s

parttime_cost_s

redundancy_cost_s

initial_workforce_s: current number of employees per skill level

Decision Variables

hire_{t,s}: number of full‑time hires of skill level s in year t

parttime_{t,s}: number of part‑time hires of skill level s in year t

train_{t,from,to}: number of workers retrained from skill level ‘from’ to ‘to’ in year t

layoff_{t,s}: number of workers of skill level s laid off in year t

redundancy_{t,s}: number of redundant workers of skill level s in year t

Objective Functions

Minimize total number of layoffs over the planning horizon.

Minimize total cost of retraining, part‑time staffing, layoffs, and redundancy.

Constraints

Initial Balance: Workforce_{t,s} equals previous year workforce plus hires, promotions, demotions (after attrition), minus layoffs and skill changes.

Quantity Balance: Workforce_{t,s} = (1‑veteran_attrition_s)·Workforce_{t‑1,s} + (1‑rookie_attrition_s)·hire_{t,s} + Σ_{s' < s}[(1‑veteran_attrition_{s'})·train_{t,s',s} – train_{t,s,s'}] + Σ_{s' > s}[(1‑demotion_attrition)·train_{t,s',s} – train_{t,s,s'}] – layoff_{t,s} ∀ t>1, s

Training Limits: Trained unskilled workers each year ≤ max_train_unskilled; trained semi‑skilled workers each year ≤ max_train_semiskilled.

Redundancy Limit: Redundant workers each year ≤ max_redundancy.

Demand Satisfaction: Available workforce (full‑time + part‑time + redundancy) must meet required headcount for each skill level each year.

Reference: H. Paul Williams, Model Building in Mathematical Programming, 5th edition (pp. 255‑256, 354‑356).