Question: Your boss needs your help in figuring out the constraints so that she can complete an aggregate plan using linear programming. She sells the product
Your boss needs your help in figuring out the constraints so that she can complete an aggregate plan using linear programming. She sells the product for $50 per unit. She wants to minimize costs. She is forecasting demand for next year as:
| Jan | 1500 |
| Feb | 1700 |
| Mar | 1900 |
| Apr | 2100 |
| May | 2300 |
| Jun | 2500 |
| Jul | 2700 |
| Aug | 3100 |
| Sep | 2600 |
| Oct | 2300 |
| Nov | 1900 |
| Dec | 1700 |
Her costs are:
| Materials (per unit) | $ 28 |
| Inventory holding (per unit per month) | $ 6 |
| Marginal cost of stockout (per unit per month) | $ 5 |
| Hiring & training (per worker) | $ 150 |
| Layoff (per worker) | $ 300 |
| Regular time (per hour) | $ 15 |
| Overtime (per hour) | $ 22 |
| Subcontracting (per unit) | $ 30 |
Your boss knows this information about labor:
| Beginning workforce | 65 |
| Working days in a month | 20 |
| Worker productive time (hours per day) | 7 |
| Maximum overtime (hours) | 15 |
| Labor hours required (per unit) | 4 |
Finally, here is what your boss wants for inventory management:
| Beginning | 1500 |
| Ending | 500 |
| Stockout at the end of June | 0 |
Here are things your boss wants you to figure out:
- What is the worker pay per month (per worker)? And what does each worker produce per month?
- Workforce for the period (Wt) equals Workforce at the beginning plus the number of employees hired for the period (Ht) minus the number of employees laid-off for the period (Lt). How would you write the constraint so that the workforce constraint equals zero?
- Capacity for the period (Pt) is the amount produced less than or equal to the amount produced by all workers during normal time plus the amount produced during overtime. What is the constraint so that the production is greater than or equal to zero?
- Overtime for the period (Ot) is less than or equal to the maximum overtime per worker times the number of workers per period. What is the constraint so that overtime is greater than or equal to zero?
- Inventory for the period (It) is the beginning inventory minus the beginning stockout plus the production for the period (Pt) plus subcontracting for the period (Ct) which equals the demand for the period (Dt) plus the ending inventory (It) minus the ending stockout (St). How would you write the constraint for the demand for the period (Dt)?
Bonus question: What is the total revenue for the year?
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