Question

Given a certain forecast, aggregate planning is to determine operational parameters over a specified time horizon, such as production rate, workforce size, machine capacity
level, inventory, etc.
a) The fundamental trade-offs in aggregate planning are among capacity (regular time, overtime, subcontracted), inventory and backlog/lost sales because of delay. Briefly explain the three strategies that are most widely used in aggregate planning.
[6]
b) A gardening tool company aims to establish an aggregate plan to minimise its operation cost in the next month, in terms of units of production, units of subcontracted, number of overtime hours, and inventory (at the end of the next month). Formulate a mathematical optimisation problem for this company by using the information below. You may wish to define extra variables as necessary.
 Workforce. The company pays a monthly cost of £1000 for each of the W workers, and decides not to hire or to lay off any workers in the month. Each worker can produce 40 units per month on regular time.
 Overtime. Overtime labour cost is £12 per hour per worker. Every four hours of overtime per worker can produce one unit. No one can work more than 10 hours of overtime each month.
 Inventory. At the beginning of the month the inventory is 1000 units. The inventory cost for a certain month is calculated from the average at the beginning and the end of that month. The actual cost is £2 per unit per month. The company decides that at the end of next month the inventory must be more than 500 units.
 Production. Production cost is £10 per unit.
 Subcontract. Subcontracted production cost is £30 per unit.
 Demand. The demand for the next month has been forecasted to be 1500 units.

Answer 1

Aggregate Planning Strategies

There are three types of aggregate planning strategies available for organization to choose from. They are as follows.

Level Strategy

As the name suggests, level strategy looks to maintain a steady production rate and workforce level. In this strategy, organization requires a robust forecast demand as to increase or decrease production in anticipation of lower or higher customer demand. Advantage of level strategy is steady workforce. Disadvantage of level strategy is high inventory and increase back logs.

Chase Strategy

As the name suggests, chase strategy looks to dynamically match demand with production. Advantage of chase strategy is lower inventory levels and back logs. Disadvantage is lower productivity, quality and depressed work force.

Hybrid Strategy

As the name suggests, hybrid strategy looks to balance between level strategy and chase strategy.

1. Change inventory levels

• Increase in low periods to meet high demand later

• Costs: storage, insurance, handling, obsolescence, and capital investment

• Shortages may mean lost sales

2. Varying workforce size by hiring or layoffs

• Training and separation costs for hiring and laying off workers

• New workers may have lower productivity

• Laying off workers may lower morale and productivity

3. Varying production rates through overtime or idle time

• May be difficult to meet large increases in demand

• Overtime can be costly and may drive down productivity

• Absorbing idle time may be difficult

4. Subcontracting

• Meet peak demand, may be costly

• Assuring quality and timely delivery may be difficult

• Exposes your customers to a possible competitor

5. Using part-time workers

• Useful for filling unskilled or low skilled positions

• WORKFORCE = 1000*40 = 40000
• OVERTIME = 12 *10 =120
• INVENTORY = 1000/500 = 2
• PRODUCTION = 10
• SUBCONTRACTED PRODUCTION = 30
• DEMAND = 1500

THEREFORE COST = 40000+120+2+10+30+1500

= 41662