1. Production Planning & Scheduling in Large Corporations

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

4. Product Aggregation Schemes Items (or Stock Keeping Units - SKU’s): 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 type. 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. 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

7. 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

8. 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)

9. 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.

10. 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

11. 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

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

13. Technology Requirements Effective Data Collection and Maintenance/Data Integrity: There is a need for a monitoring tool that will provide a centralized, correct and efficient representation of the system status at any point in time. –Industry Solution: Manufacturing Execution Systems (MES) e.g., SAP, Oracle, PeopleSoft Efficient and Coherent Computerized Planning Tools: There is a need for a suite of computationally efficient planning tools that will effectively address the problems arising at the various levels of the decomposition framework, while maintaining plan consistency across the different levels. –Industry Solution: Production and Supply Chain Planning Software e.g., I 2 Technologies, BAAN, Manugistics

14. Aggregate Planning: Example (Adapted from Chase and Aquilano, “Fundamentals of Operations Management”, Irwin Pub., 1991)

15. Example: Introduction A vacuum cleaner manufacturer tries to “plan ahead” in order to effectively address the seasonal variation appearing in the annual demand of its products. A planning horizon of 6 months is used. The (aggregate) demand forecast for the next six months along the number of working days are as follows:

16. Example: Introduction (cont.) The associated cost break-down is as follows:

17. Example: Introduction (cont.) Starting and Operating Conditions:

18. The tabular approach: Computing net requirements

19. Plan 1: Demand Chasing Produce exactly the quantities required for each period through regular labor, by varying the workforce size.

20. Plan 1: Demand Chasing (cont.)

21. Plan 2: Minimum Production Workforce + Subcontracting Adjust the workforce so that the minimal monthly demand is met through regular labor. Subcontract all excess demand.

22. Plan 2: Minimum Production Workforce + Subcontracting

23. Plan 3: Anticipatory (Seasonal) Inventories + Backlogging Employ the minimal workforce level that can cover the total production requirements over the considered planning horizon, by working only regular hours. Take care of the demand fluctuations by building anticipatory inventories and/or backlogging excess demand.

24. Plan 3: Anticipatory (Seasonal) Inventories + Backlogging (cont.)

25. 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, 5*P t  WD t *W t +O t  t, I t  0.25*D t   = 0  t, P t, W t, O t, H t, F t, S t, I t, B t  0 ()

26. Proactive approaches to demand management 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)

27. Disaggregation and Master Production Scheduling (MPS)

28. The (Master) Production Scheduling Problem MPS Placed Orders Forecasted Demand Current and Planned Availability, eg., Initial Inventory, Initiated Production, Subcontracted quantities Master Production Schedule: When & How Much to produce for each product Capacity Consts. Company Policies Economic Considerations Product Charact. Planning Horizon Time unit Capacity Planning

29. (Typical) Analytical Approaches to MPS Recognizing that switching production from item to item (or family to family) requires significant set-up times, during which the effective productivity of the line is equal to zero, these (formal) approaches try to apportion the planned production capacity to the various items in a way that meets their effective demand while it minimizes the (long-run) number of set-ups. However, they tend to be technically cumbersome and/or limiting in terms of modeling capability, and therefore, not extensively used in practice. Example: –Textbook, Section 5.7.1

30. The Driving Logic behind the Empirical Approach DemandAvailability: Initial Inventory Position Scheduled Receipts due to initiated production or subcontracting Future inventories Net Requirements Lot Sizing Scheduled Releases Resource (Fermentor) Occupancy Product i Feasibility Testing Master Production Schedule Schedule Infeasibilities Revise Prod. Reqs Compute Future Inventory Positions

31. McGuinnes & Co. Microbrewery Case Study

32. Company Description One of the three largest microbreweries in Atlanta area Company started in 1995 A 12,000sq. ft. production facility and warehouse in the Chattahoochee Industrial Park The company is run by its owner, Mr. McGuinness Three full-time and two-part time employees, and occasionally hires part-time help Last year’s sales: > 35,000 cases => > $180,000 Average weekly sales: 500-800 cases

33. Company Products Pale Ale: The oldest company product. Since May 2000, this product is also offered in the NY and Boston areas, through a major national distributor. Product monthly sales over the last four years (1997-2000) in cases of beer:

34. Company Products Stout: A rather new product, offered only in the last 14 months. Monthly sales in cases for the last 14 months:

35. Company Products Winter Ale: A seasonal beer, offered primarily during the winter period (from October to April). Product monthly sales over the last 4 years:

36. Company Products Summer Brew: A seasonal beer offered primarily during the summer season. A new product offered over the last two years. Product monthly sales in cases over the last two years:

37. Company Products Octoberfest: An “image promoter” for the company, offered once a year, during the Octoberfest season. The product is delivered to the company distributors and the local restaurants only once a year, in late September or early October. Product annual sales in cases for the last four years:

38. Company Operations Mashing (1 mashing tun) Boiling (1 brew kettle) Fermentation (3 40-barrel ferm. tanks) Filtering (1 filter tank) Bottling (1 bottling station) Grain cracking (1 milling machine) Fermentation Times:

39. Company Challenges Company production scheduled by its owner, in an ad-hoc fashion Sustained growth strains the company production capacity There is a dire need for a systematic methodology that will allow the company and its owner to –foresee the expected production requirements over a certain planning horizon; –organize appropriately its production activity based on the forecasted demand; –systematically manage its growth by adjusting appropriately its capacity. Eventually, this methodology should be offered to the company in a set of user-friendly tools.

40. Example: Implementing the Empirical Approach in Excel

41. Computing Inventory Positions and Net Requirements Net Requirement: NR i = abs(min{0, IP i }) Inventory Position: IP i = max{IP i-1,0}+ SR i +BNR i -D i (Material Balance Equation) i DiDi IP i (IP i-1 ) + SR i +BNR i

42. Problem Decision Variables: Scheduled Releases

43. Testing the Schedule Feasibility

44. Fixing the Original Schedule

45. Infeasible Production Requirements

46. Advantages and Disadvantages of the Empirical Approach Advantages: –Easy to present and motivate –Provides clear visibility to the problems and their underlying causes –Supports effective and efficient “what-if” analysis –Provides modeling flexibility Disadvantages –No guarantee for optimality or exhaustive search for a feasible solution –Hard to trace for more complex production environments

47. Modeling the Inventory Spoilage

48. A feasible schedule with spoilage effects

49. Computing Spoilage and Modified Inventory Position Spoilage: SP i = max{0, IP i-1 -  SR i-1 +SR i-2 +…+SR i-sl+1 ) -  BNR i-1 +BNR i-2 +…+BNR i-sl+1 )} Inventory Position: IP i = max{IP i-1,0}+ SR i +BNR i -D i -SP i (Material Balance Equation) i DiDi IP i (IP i-1 ) + SR i +BNR i SP i

50. Materials Requirements Planning (MRP)

51. The “MRP Explosion” Calculus BOM MRP MPS Current Availabilities Planned Order Releases Priority Planning Lead Times Lot Sizing Policies

52. Example: The (complete) MRP Explosion Calculus (J. Heizer and B. Render “Operations Management”, 6th Ed. Prentice Hall) Item BOM: Alpha C(2)D(2) B(1)C(1) E(1) F(1) Item Levels: Level 0: Alpha Level 1: B Level 2: C, D Level 3: E, F

53. The “MRP Explosion” Calculus Level 0 Level 1 Level 2 Level N Initial Inventories Scheduled Receipts External Demand Capacity Planning Planned Order Releases Gross Requirements

55. Capacity Planning (Example) Available labor hours Periods123 4567 8 50 100 150

56. Computing the item Scheduled Releases Synthesizing item demand series Projecting Inv. Positions and Net Reqs. Lot Sizing Time- Phasing Parent Sched. Rel. Item External Demand Gross Reqs Scheduled Receipts Initial Inventory Safety Stock Requirements Net Reqs Lot Sizing Policy Planned Order Receipts Lead Time Planned Order Releases

57. Some Lot Sizing Heuristics Economic Order Quantity (EOQ): Compute a lot size using the EOQ formula with the demand rate D set equal to the average of the demand values observed over the considered planning horizon. Periodic Order Quantity (POQ): Compute T = round(EOQ/D), and every time you schedule a new lot, size it to cover the net requirements for the subsequent T periods. Silver-Meal (SM): Every time you start a new lot, keep adding the net requirements of the subsequent periods, as long as the average (setup plus holding) cost per period decreases. Least Unit Cost (LUC): Every time you start a new lot, keep adding the net requirements of the subsequent periods, as long as the average (setup plus holding) cost per unit decreases. Part Period Balancing (PPB): Every time you start a new lot, add a number of subsequent periods such that the total holding cost matches the lot set up cost as much as possible.

58. Shop floor-level Production Control / Scheduling

59. General Problem Definition Determine the timing of –the releases of the various production lots on the shop-floor and –the allocation to them of the system resources required for the execution of their various operations so that the production plans decided at the tactical planning - i.e., MPS & MRP - level are observed as close as possible.

60. A modeling absrtaction M: number of machine types / workstations. N: number of jobs to be scheduled. Job routing: an ordered list / sequence of machines that a job needs to visit in order to be completed. Operation: a single processing step executed during the job visit to a machine. P_j: the set of operations in the routing of job j. t_kj: the processing time for the k-th operation of job j. d_j: due date for job j. r_j: the release date of job j, i.e., the date at which the material required for starting the job processing will be available.

61. Example W_q W_2W_i W_M W_1 J_1 J_2 J_N

62. Problem variations Based on job routing: –job shop: each job has an arbitrary route –flow shop: all jobs have the same route, but different operational processing times –re-entrant flow shop: some machine(s) is visited more than once by the same job –flexible job shop / flow shop: each operation has a number of machine alteratives for its execution Based on the operational processing times: –deterministic: the various processing times are known exactly –stochastic: the processing times are known only in distribution Based on the possibility of pre-emption: –pre-emptive: the execution of a job on a machine can be interrupted upon the arrival of a new job –non-preemptive: each machine must complete its currently running job before switching to another one. Based on the considered performance objective(s)

63. Performance-related job and schedule attributes job completion time: C_j schedule makespan: max_j C_j job lateness: L_j = C_j - d_j (notice that, by definition, job lateness can be either positive or negative - in which case that the job is finished earlier than its due date) job tardiness: T_j = max (0, L_j) = [L_j]+ job flow time: F_j =C_j - r_j (i.e., the amount of time the job spends on the shop-floor) job tardy index: TI_j = 1 if job is tardy; 0 otherwise. Number of tardy jobs: NT job importance weight: w_j (the higher the weight, the more important the job)

64. Performance Criteria

65. Example

66. A feasible schedule and its Gantt Chart 1 2 3 4 5 5101520 Machine Time Job 1Job 2Job 3Job 4Job 5

67. Schedule Performance Evaluation

68. Solution Approaches Analytical (Mixed Integer Programming) formulations: Notoriously difficult to solve even for relatively small configurations Heuristics: In the scheduling literature, the applied heuristics are known as dispatching rules, and they determine the sequencing of the various jobs waiting upon the different machines, based upon job attributes like –the required processing times –due dates –priority weights –slack times, defined as d_j - (current time + total remaining processing time) –etc.

69. Course Objectives Demonstrate the combinatorial nature of the problem and the sources of the problem complexity, by investigating the single-machine scheduling problem. Introduce some basic dispatching rules used in practice, and discuss the motivational logic behind them.