1. Aggregate Planning Ash Soni ODT Department Kelley School of Business

2. What is Aggregate Planning Aggregate planning is a process by which a company determines levels of capacity, production, subcontracting, inventory, stock-outs and pricing over a specified time horizon. The objective is to satisfy demand in a way that maximizes profit or minimizes costs for the firm

3. Master Production Scheduling Material Requirements Planning Order Scheduling Weekly Workforce & Customer Scheduling Daily Workforce & Customer Scheduling Process Planning Strategic Capacity Planning Aggregate Planning Long-range Intermediate- range Short-range Manufacturing Services

4. Variables to be Determined Over the Planning Horizon Production Rate – No of units completed per time unit (such as week or per month) Workforce – No of workers/units needed for production Overtime – The amount of overtime production planned Machine Capacity Level Subcontracting – The subcontracted capacity required Backlog – Demand not satisfied but carried over to future periods beyond the planning horizon Inventory on Hand – Inventory carried over the various periods in the planning horizon

5. Formal Definition Given the demand forecasts for each period in the planning horizon, determine the production level, inventory level, and the capacity level for each period that maximizes the firm’s profit over the planning horizon

6. Information Required for an Aggregate Plan Demand Forecasts for each period in the planning period Production Costs Labor costs – Regular Time and Overtime ($/Hr) Cost of subcontracting production ($/Unit or $/Hr) Cost of changing production – cost of hiring/laying off workforce ($/Worker) and cost of adding or reducing machine capacity ($/Machine) Labor/Machine Hours required per unit

7. Information Required for an Aggregate Plan Cont’d 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

8. Some Key Determinations from Aggregate Planning Production quantity from regular time, overtime, and subcontracted time allows determination of number of workers and supplier purchase levels Inventory Held – Used to determine warehouse space required Backlogs/Stock-outs – Used to determine customer service levels Workers Hired/Laid Off – Used to determine labor issues Machine Capacity increase/decrease – Used to determine if new production equipment needs to be purchased

9. Aggregate Planning Strategies Trade-offs between three costs – capacity, inventory and backlogs Decrease in one cost usually results in an increase in the other two costs For example, to lower inventory costs, a planner must increase either capacity or backlogs or both This leads to trade-offs between capacity, inventory and backlogs.

10. Aggregate Planning Strategies Chase Strategy – Uses capacity as a lever. Production rate is synchronized with the demand rate by varying machine capacity or hiring and laying off workers. It can be used when the carrying cost of inventory is very high and costs to change levels of capacity and workforce are low.

11. Aggregate Planning Strategies Level Strategy – Using Inventory as a Lever. A stable machine capacity and workforce are used to maintain a constant output. Inventories or backlogs play a big role. It can used when inventory carrying costs and backlog costs are low.

12. Aggregate Planning Strategies Time Flexibility from Workforce or Capacity Strategy – Using utilization as a lever. May be used if there is excess machine capacity. Then workforce capacity can be kept stable but no. of hours worked is varied to synchronize production with demand. Results in lower inventory levels but the average utilization is lower

13. Example n Redwood Furniture Weekly Production

14. Mathematical Formulation XT - Number Of Tables XC - Number of Chairs Objective : Max 6 XT + 9 XC Subject to (Constraints) 30 XT + 20 XC <= 300 (Wood) 5 XT + 10 XC <= 110 (Labor) XT, XC >= 0 (Non-Negativity)

15. Red Tomato Inc. MonthDemand Forecast January1,600 February3,000 March3,200 April3,800 May2,200 June2,200

16. Red Tomato Inc. ItemCost Material Cost$10/Unit Inventory Holding Cost$2/Unit/Month Marginal Cost of Stock-out/Backlog$5/Unit/Month Hiring and Training Costs$300/Worker Layoff Cost$500/Worker Labor hours Required4 Hours/Unit Regular Time Cost$4/Hour Overtime Cost$6/Hour Cost of Subcontracting$30/Hour

17. Red Tomato – LP Formulation W t =Workforce size for month t, t=1,2 …..6 H t =No of employees hired at the beginning of month t, t=1,2 …..6 L t =No of employees laid off at the beginning of month t, t=1,2 …..6 P t =No of units produced in month t, t=1,2 …..6 I t =Inventory at the end of month t, t=1,2 …..6 S t =No of units stocked out/backlogged at the end of month t, t=1,2 …..6 C t = No of units subcontracted for month t, t=1,2 …..6 O t = No of overtime worked in month t, t=1,2 …..6

18. Red Tomato – LP Formulation Objective Function Regular time labor cost Overtime labor cost Cost of hiring and layoffs Cost of holding inventory Cost of stocking out Cost of subcontracting Material cost