1. Murat Kaya, Sabancı Üniversitesi 1 MS 401 Production and Service Systems Operations Spring 2009-2010 Aggregate Production Planning (APP) Slide Set #8

2. Murat Kaya, Sabancı Üniversitesi 2 APP Overview APP: A plan devised to determine companywide workforce and production levels –how many employees the firm should retain: hire/fire workers –quantity and mix of the products to be produced to meet demand for products, considering company strategy and the capacity constraints Considers “macro” production decisions

3. Murat Kaya, Sabancı Üniversitesi 3 Why APP? “APP is the top management’s handle on the business” –where critical trade-offs are resolved based on company strategy APP provides links from manufacturing to other functions –once APP is agreed on, the manufacturing’s duty is to “hit the schedule” Cost of not having an aggregate plan include –extra inventories –poor customer service –excess capacity –long lead times –panic operations –poor response to new opportunities

4. Murat Kaya, Sabancı Üniversitesi 4 Aggregation Managing groups of items rather than individual items –provides a big picture view –forecasts for aggregate units are more accurate Define the “aggregate unit of production” –should be commonly understood by the other functions APP is later disaggregated to individual items –results in the master production schedule (MPS) for each item

5. Murat Kaya, Sabancı Üniversitesi 5 Aggregate Units of Production: Example Model Number Worker-hours Price Percentage A55324.2285%32 K42424.9345%21 L98985.1395%17 L38005.2425%14 M26245.4525%10 M38805.8725%6 How do we define the aggregate unit to determine the workforce and production levels in the plant in this example? Aggregate unit: 1$ of output? NOT CONSISTENT Aggregate unit: A fictitious washing machine that requires.32*4.2+.21*4.9+.17*5.1+.14*5.2+.10*5.4+.06*5.8 = 4.856 hours of labour time

6. Murat Kaya, Sabancı Üniversitesi 6 A Sample Aggregation Scheme (Hax-Meal) 1.Items final products to be delivered to the customer SKU (stock-keeping unit) ex: an individual washing machine model 2.Families group of items that share a common manufacturing setup cost ex: all washing machines 3.Types group of families with production quantities that are determined by a single aggregate production plan ex: large home appliances (washing machines, dishwashers etc.)

7. Murat Kaya, Sabancı Üniversitesi 7 Hierarchy of Production Planning Decisions Copyright © 2001 by The McGraw-Hill Companies, Inc

8. Murat Kaya, Sabancı Üniversitesi 8 Primary Issues in APP Trade-off between –reacting quickly to anticipated changes in demand –retaining a stable workforce and/or production level Bottlenecks –where capacity restrictions occur Planning horizon –end-of horizon effect –rolling schedule –periods in which decisions are frozen Treatment of demand –assume deterministic demand to focus on the big picture D 1, D 2, …, D T

9. Murat Kaya, Sabancı Üniversitesi 9 Relevant Costs Smoothing costs –cost of changing the workforce –some components may be difficult to measure Holding costs –due to capital tied up in inventory Shortage costs Regular time costs –cost of producing one unit during regular working hours Overtime costs –cost of production beyond regular working hours Subcontracting costs –cost of production at a supplier or by some other firm Idle time costs

10. Murat Kaya, Sabancı Üniversitesi 10 Example: DensePack From Nahmias

11. Murat Kaya, Sabancı Üniversitesi 11 Problem Setup Currently (end of December) 300 workers employed Ending inventory in December: 500 units The firm would like to have 600 units at the end of June No backlogging, no overtime Forecast demand: MonthJanFebMarAprMayJun Demand 1280640900120020001400 c H : cost of hiring one worker: $500 c F : cost of firing one worker: $1000 c I : cost of holding one unit of inventory for one month: $80 (incurred at the end of each period) K = 0.14653 : number of aggrg. units produced by one worker per day

12. Murat Kaya, Sabancı Üniversitesi 12 Cumulative Net Demand MonthJanFebMarAprMayJun Demand 780640900120020002000 Cumulative78014202320352055207520 shortages not permitted

13. Murat Kaya, Sabancı Üniversitesi 13 Three Approaches 1.Chase strategy (zero inventory plan) 2.Constant workforce plan 3.A mixed strategy

14. Murat Kaya, Sabancı Üniversitesi 14 1) Chase Strategy (Zero Inventory Plan) Produce what is needed each month Keep zero inventory –inventory level may not be exactly zero due to integer num. of workers Hire and fire workers as needed –assuming sufficient labor pool exists –may not be possible in all countries unions, contracts etc –may lead to low morale and quality –may be suitable when low-skilled labor is required farming

15. Murat Kaya, Sabancı Üniversitesi 15 1) Chase Strategy

16. Murat Kaya, Sabancı Üniversitesi 16 1) Chase Strategy Total cost of hiring, firing and holding is (755)(500) + (145)(1000) + (30)(80) + (600)(80) = $572,000

17. Murat Kaya, Sabancı Üniversitesi 17 2) Constant Workforce Plan In the constant workforce plan, the goal is to eliminate completely the need for hiring and firing Calculate the minimum workforce required for each month to make sure that shortages do not occur –we use cumulative inventory values because inventory can be carried over

18. Murat Kaya, Sabancı Üniversitesi 18 2) Constant Workforce Plan The total (over periods) of the ending inventory levels is 5962+600=6562 Total cost of the plan: (6562)(80)+ (111)(500) =$580,460

19. Murat Kaya, Sabancı Üniversitesi 19 3) A Mixed Strategy Alternative Suppose we allow a single change in the workforce level –can we find a strategy that reduces inventory without permitting shortages? Other constraints can also be studied –for ex: limit on the production capacity of the plant: limit on slope

20. Murat Kaya, Sabancı Üniversitesi 20 Solution with Linear Programming

21. Murat Kaya, Sabancı Üniversitesi 21 Linear Programming Determine the values of “n” nonnegative decision variables in order to max/min a linear function of these variables subject to “m” linear constrains of these variables Can be solved efficiently using the Simplex algorithm

22. Murat Kaya, Sabancı Üniversitesi 22 Model Parameters c H Cost of hiring one worker c F Cost of firing one worker c I Cost of holding one unit of inventory for one period c R Cost of producing one unit on regular time c 0 Incremental cost of producing one unit on overtime c S Cost to subcontract one unit of production n t Number of production days in period t K Aggregate number of aggregate products produced per worker per day I 0 Initial inventory on hand at the start of the planning horizon W 0 Initial workforce at the start of the planning horizon D t Demand in period t (assumed to be known and deterministic) T Number of time periods (planning horizon) t Time period

23. Murat Kaya, Sabancı Üniversitesi 23 Decision Variables W t Workforce level (number of workers) in period t P t Production level in period t (regular and overtime) I t Inventory level in period t H t Number of workers hired in period t F t Number of workers fired in period t O t Overtime production in units U t Worker idle time in production units S t Number of units produced (procured) via subcontracting Thus, Kn t W t : the number of units produced by the entire workforce in period t O t = P t - Kn t W t or U t = Kn t W t -P t

24. Murat Kaya, Sabancı Üniversitesi 24 Problem Constraints

25. Murat Kaya, Sabancı Üniversitesi 25 The LP Formulation

26. Murat Kaya, Sabancı Üniversitesi 26 The DensePack Example W 0 =300 I 0 =500 I 6 =600 All decision variables >=0

27. Murat Kaya, Sabancı Üniversitesi 27 Aggregate Plan Obtained from LP The cost of this plan is only $379,500 –considerably less than the cost achieved with the chase strategy or the constant workforce plan