Projects / How many workers to hire and when, for a factory with seasonal demand

How many workers to hire and when, for a factory with seasonal demand

Course project, Michigan Ross MBA. Integer program for a 12-month production plan, in Excel Solver and Python. Not client or employer work.

ExcelPython
Excel modelMonthly plan with costs, and three strategiesPython modelInteger program for the three strategies
SituationA factory has 160 workers and makes one product. The demand forecast for the next 12 months is known.
ComplicationDemand in the peak month is three times the demand in the low months. The factory can hire, lay off, use overtime or build inventory, and each of the four has a cost.
QuestionWhich mix of the four gives the lowest cost for the year?
AnswerA mixed plan of hires, overtime and inventory costs $6.22M for the year, 8% less than a level workforce.

Four costs make the total; the plan trades inventory and overtime against changes in the workforce

  • Cost for the year$6.22M in the answer
    • Regular labor
      • Workers each monthThe lever: 160 at the start, 237 at the peak
      • SalaryFixed: $2,400 a month
    • Changes in the workforce
      • Hires and layoffsThe lever. $1,800 for a hire, $1,200 for a layoff

        Is one workforce size all year cheaper?

        No. A level workforce costs 8% more.

    • Overtime
      • Workers on overtimeThe lever. $3,300 for a worker-month

        When does overtime pay?

        At the peak only. Two months of the year.

      • CapacityThe limit: one overtime shift for each worker; 13,000 units a month
    • Inventory
      • Units held at month endThe lever. $8 for a unit-month

        Is a plan with no inventory cheaper?

        No. Production that follows demand costs 2% more.

Lever what the decision changes Limit what the answer must respect Fixed outside the decision

Lowest cost for the year

$6.22M

8% below a level workforce, 2% below production that follows demand

Workforce

160 to 237

hire before the peak, then reduce in steps to 140

Overtime

2 months

Aug and Sep only; inventory takes the rest of the peak

The mixed plan costs 8% less than a level workforce and 2% less than production that follows demand

Build inventory before the summer, then use overtime for the last part of the peak

The lowest-cost plan, by month (units and workers)
JanFebMarAprMayJunJulAugSepOctNovDec
Demand4,4004,4006,0008,0006,60011,80013,00011,20010,8007,6006,0005,600
Production6,4006,4006,4006,4009,4009,4809,48011,20010,8007,6006,0005,600
Inventory at month end2,2404,2404,6403,0405,8403,520000000
Workers160160160160235237237237237190150140
Hires0000752000000
Layoffs000000000474010
Workers on overtime00000004333000

One worker makes 40 units a month for $2,400. A hire costs $1,800, a layoff $1,200, a worker-month of overtime $3,300, and one unit in inventory $8 a month. The plant makes 13,000 units a month at most.

The model

Decision

For each of 12 months: hires, layoffs, workers on overtime. 36 whole-number variables.

Objective

The lowest total of salaries, hire and layoff costs, overtime and inventory cost.

Constraints

Demand is met each month from production and inventory. Production is inside plant capacity. Each worker does one overtime shift at most.

  • Salaries are 85% to 90% of the cost in each strategy. The strategies differ in how they pay for the peak: inventory ($600k in the level plan) or overtime ($412k when production follows demand).
  • The mixed plan pays $188k for inventory and $251k for overtime, plus $255k to change the workforce.
  • The whole-number plan costs only $160 more than the plan with fractions of a worker, so the rounding has no practical effect.
  • The plan uses one demand forecast. A plan for use must be tested against a high and a low forecast.