1. Aggregate Planning

2. Dealing with the Problem Complexity through Decomposition Aggregate Planning Master Production Scheduling Materials Requirement Planning Aggregate Unit Demand End Item (SKU) Demand Corporate Strategy Capacity and Aggregate Production Plans SKU-level Production Plans Manufacturing and Procurement lead times Component Production lots and due dates Part process plans (Plan. Hor.: 1 year, Time Unit: 1 month) (Plan. Hor.: a few months, Time Unit: 1 week) Shop floor-level Production Control (Plan. Hor.: a day or a shift, Time Unit: real-time)

3. Aggregate Planning Problem Aggregate Planning Aggregate Unit Demand Aggregate Unit Availability (Current Inventory Position) Aggregate Production Plan Required Production Capacity Aggr. Unit Production Reqs Corporate Strategy Aggregate Production Plan: Aggregate Production levels Aggregate Inventory levels Aggregate Backorder levels Production Capacity Plan: Workforce level(s) Overtime level(s) Subcontracted Quantities

4. Product Aggregation Schemes Items (or Stock Keeping Units - SKUs): The final products delivered to the (downstream) customers Families: Group of items that share a common manufacturing setup cost; i.e., they have similar production requirements. Aggregate Unit: A fictitious item representing an entire product family. Aggregate Unit Production Requirements: The amount of (labor) time required for the production of one aggregate unit. This is computed by appropriately averaging the (labor) time requirements over the entire set of items represented by the aggregate unit. Aggregate Unit Demand: The cumulative demand for the entire set of items represented by the aggregate unit. Remark: Being the cumulate of a number of independent demand series, the demand for the aggregate unit is a more robust estimate than its constituent components.

5. Computing the Aggregate Unit Production Requirements Aggregate unit labor time = (.32)(4.2)+(.21)(4.9)+(.17)(5.1)+(.14)(5.2)+ (.10)(5.4)+(.06)(5.8) = 4.856 hrs

6. Pure Aggregate Planning Strategies 1. Demand Chasing: Vary the Workforce Level D(t)P(t) = D(t) W(t) PCWCHCFC D(t): Aggregate demand series P(t): Aggregate production levels W(t): Required Workforce levels Costs Involved: PC: Production Costs fixed (setup, overhead) variable (materials, consumables, etc.) WC: Regular labor costs HC: Hiring costs: e.g., advertising, interviewing, training FC: Firing costs: e.g., compensation, social cost

7. Pure Aggregate Planning Strategies 2. Varying Production Capacity with Constant Workforce: D(t)P(t) O(t) PCWCOCUC U(t) S(t) SC W = constant S(t): Subcontracted quantities O(t): Overtime levels U(t): Undertime levels Costs involved: PC, WC: as before SC: subcontracting costs: e.g., purchasing, transport, quality, etc. OC: overtime costs: incremental cost of producing one unit in overtime (UC: undertime costs: this is hidden in WC)

8. Pure Aggregate Planning Strategies 3. Accumulating (Seasonal) Inventories: D(t)P(t) I(t)PCWCIC W(t), O(t), U(t), S(t) = constant I(t): Accumulated Inventory levels Costs involved: PC, WC: as before IC: inventory holding costs: e.g., interest lost, storage space, pilferage, obsolescence, etc.

9. Pure Aggregate Planning Strategies 4. Backlogging: D(t)P(t) B(t) PCWCBC W(t), O(t), U(t), S(t) = constant B(t): Accumulated Backlog levels Costs involved: PC, WC: as before BC: backlog (handling) costs: e.g., expediting costs, penalties, lost sales (eventually), customer dissatisfaction

10. Typical Aggregate Planning Strategy A mixture of the previously discussed pure options: D PCWCHCFCOCUCSCICBC P W H F O U S I B + Additional constraints arising from the company strategy; e.g., maximal allowed subcontracting maximal allowed workforce variation in two consecutive periods maximal allowed overtime safety stocks etc. Io Wo

11. Solution Approaches Graphical Approaches: Spreadsheet-based simulation Analytical Approaches: Mathematical (mainly linear programming) Programming formulations

12. Analytical Approach: A Linear Programming Formulation min TC = t ( PC t *P t +WC t *W t +OC t *O t +HC t *H t +FC t *F t + SC t *S t +IC t *I t +BC t *B t ) s.t. t, P t +I t-1 +S t = (D t -B t )+B t-1 +I t t, W t = W t-1 +H t -F t t, (u_l_r)*P t s_d) w_d) t *W t +O t t, P t, W t, O t, H t, F t, S t, I t, B t 0 ( )Any additional policy constraints Prod. Capacity: Material Balance: Workforce Balance: Var. sign restrictions: Time unit: month / unit_labor_req. /shift_duration (in hours) / (working_days) for month t

13. Demand (vs. Capacity) Options or Proactive Approaches to Aggregate Planning Influencing demand variation so that it aligns to available production capacity: –advertising –promotional plans –pricing (e.g., airline and hotel weekend discounts, telecommunication companies weekend rates) Counter-seasonal product (and service) mixing: Develop a product mix with antithetic (seasonal) trends that level the cumulative required production capacity. –(e.g., lawn mowers and snow blowers) => The outcome of this type of planning is communicated to the overall aggregate planning procedure as (expected) changes in the demand forecast.