The Aggregate Planning Problem in a Supply Chain

The objective of the aggregate plan is to satisfy demand in a way that maximizes profit for the firm. We can state the aggregate planning problem formally as follows:

Given the demand forecast for each period in the planning horizon, determine the produc­tion level, inventory level, capacity level (internal and outsourced), and any backlogs (unmet demand) for each period that maximize the firm’s profit over the planning horizon. 

To create an aggregate plan, a company must specify the planning horizon. A planning horizon is the time period over which the aggregate plan is to produce a solution—usually between 3 and 18 months. A company must also specify the duration of each period within the planning horizon (e.g., weeks, months, or quarters). In general, aggregate planning takes place over months or quarters. Next, a company specifies key information required to produce an aggregate plan and to make the decisions for which the aggregate plan will develop recommen­dations. In this section, this information and the recommendations are specified for a generic aggregate planning problem. The model we propose in the next section is flexible enough to accommodate situation-specific requirements.

An aggregate planner requires the following information:

• Aggregate demand forecast F_t for each Period t in a planning horizon that extends over T periods
• Production costs
  • Labor costs: regular time ($/hour), and overtime costs ($/hour)
  • Cost of subcontracting production ($/unit or $/hour)
  • Cost of changing capacity; specifically, cost of hiring/laying off workforce ($/worker) and cost of adding or reducing machine capacity ($/machine)
• Labor/machine hours required per unit
• Inventory holding cost ($/unit/period)
• Stockout or backlog cost ($/unit/period)
• Constraints
  • Limits on overtime
  • Limits on layoffs
  • Limits on capital available
  • Limits on stockouts and backlogs
  • Constraints from suppliers to the enterprise

Using this information, a company makes the following determinations through aggregate planning:

• Production quantity from regular time, overtime, and subcontracted time: used to determine number of workers and supplier purchase levels
• Inventory held: used to determine the warehouse space and working capital required
• Backlog/stockout quantity: used to determine customer service levels
• Workforce hired/laid off:  used to determine any labor issues likely to be encountered
• Machine capacity increase/decrease:  used to determine whether new production equip­-ment should be purchased or available equipment idled

The quality of an aggregate plan has a significant impact on the profitability of a firm. A poor aggregate plan can result in lost sales and lost profits if the available inventory and capacity are unable to meet demand. A poor aggregate plan may also result in a large amount of excess inven­tory and capacity, thereby raising costs. Therefore, aggregate planning is an important tool to optimally match supply and demand.

1. Identifying Aggregate Units of Production

An important first step in aggregate planning is the identification of a suitable aggregate unit of production. When planning is done at the aggregate level, it is important that the aggregate unit be identified in a way that when the final production schedule is built (this has to be at the disag­gregate product level), the results of the aggregate plan reflect approximately what can be accom­plished in practice. Given that the bottleneck is likely to be the most constraining area in any manufacturing facility, it is important to focus on the bottleneck when selecting the aggregate unit and identifying capacity as well as production times. When evaluating production times, it is also important to account for activities—such as setups and maintenance—that use up capacity but do not result in any production. Otherwise, the aggregate plan will overestimate the produc­tion capacity available, resulting in a plan that cannot be implemented in practice. We now dis­cuss a simple approach that can be used to identify aggregate units and also to evaluate costs, revenues, and times for this aggregate unit.

Consider, for example, Red Tomato Tools, a small manufacturer of gardening equipment with manufacturing facilities in Mexico. The company makes six product families at its manu­facturing plant. The costs, revenues, production times, setup times, and historical batch sizes of production for each family are as shown in Table 8-1.

In Table 8-1 (see spreadsheet Chapter8-Table 8-1), the net production time per unit is obtained by adding the changeover time allocated to each unit and the production time (setup time/batch size + production time). Thus, the net production time/unit for Family A is obtained as 8/50 + 5.60 = 5.76 hours.

A simple approach to defining the aggregate unit is based on the weighted average of the percentage of sales represented by each family. Such an approach is meaningful if management is relatively confident of the mix of sales and all the product families use roughly the same set of resources at a plant. Taking this approach, the material cost per aggregate unit is obtained as (15 X 0.10) + (7 X 0.25) + (9 X 0.20) + (12 X 0.10) + (9 X 0.20) + (13 X 0.15) = $10. Using a similar evaluation, we obtain that the revenue per aggregate unit = $40 and the net production time per aggregate unit = 4.00 hours.

Other potential aggregate units could be tons of output (likely to be suitable for continuous flows, such as gasoline or paper) or dollars of sales. For example, a paper mill might produce papers of different thickness and quality. If tons of output is used as the aggregate unit, all capac­ity, cost, and revenue calculations should account for the product mix.

Source: Chopra Sunil, Meindl Peter (2014), Supply Chain Management: Strategy, Planning, and Operation, Pearson; 6th edition.