1. Production Planning & Scheduling in Large Corporations

2. The role of aggregate planning and scheduling in the broader picture (borrowed from Heizer and Render)

3. 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)

4. Aggregate Planning

5. 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 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.

6. 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

7. 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

8. 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

9. 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)

10. 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.

11. 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

12. 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

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

14. A prototype problem Forecasted demand: Jan: 1280 Feb: 640 Mar: 900 Apr: 1200 May:2000 Jun: 1400 On-hand Inventory: 500 Required on-hand Inventory at end of June: 600 Current Workforce Level: 300 Worker prod.capacity: 0.14653 units/day Working days per month Jan: 20 Feb: 24 Mar: 18 Apr: 26 May: 22 Jun: 15 Cost structure: Inv. holding cost: $80/unit x month Hiring cost: $500/worker Firing cost: $1000/worker

15. A prototype problem (cont.) Net predicted demand: Jan: 780 Feb: 640 Mar: 900 Apr: 1200 May: 2000 Jun: 2000 Forecasted demand: Jan: 1280 Feb: 640 Mar: 900 Apr: 1200 May:2000 Jun: 1400 On-hand Inventory: 500 Required on-hand Inventory at end of June: 600

16. An LP formulation for the prototype problem Problem Parameters D t = Forecasted demand for period t d t = working days at period t c = daily worker capacity W 0 =Initial workforce level I 0 = Current on-hand inventory C H = Hiring cost per worker C F = Firing cost per worker C I = Inventory holding cost per unit per period Problem Decision Variables H t = Workers hired at period t F t = Workers fired at period t W t = Workforce level at period t P t = Level of production at period t I t = Inventory at the end of period t

17. An LP formulation for the prototype problem s.t.

18. Optimal Plan for the considered example Fire 27 workers in January Hire 465 workers in May Produce at full (labor) capacity every month Resulting total cost: $379320.900

19. 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

20. 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.

21. 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)

22. Disaggregation and Master Production Scheduling (MPS)

23. 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

24. MPS Example: 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:

25. Example: Implementing the Empirical Approach in Excel

26. 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

27. Problem Decision Variables: Scheduled Releases

28. Testing the Schedule Feasibility

29. Fixing the Original Schedule

30. Infeasible Production Requirements

31. A feasible schedule with spoilage effects

32. 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

33. 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

34. Materials Requirements Planning (MRP)

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

36. Example: The (complete) MRP Explosion Calculus 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

37. 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

38. (borrowed from Heizer and Render)

39. 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

40. Lot Sizing If affordable, a lot-for-lot (L4L) policy will incur the lowest inventory holding costs and it will maintain a smoother production flow. Possible reasons for departure from a L4L policy: –High set up times and costs => need for serial process batching to control the capacity losses –Processes that require a large production volume in order to maintain a high utilization (e.g., fermentors, furnaces, etc.) => need for parallel process batching Selection of a pertinent process batch size –It must be large enough to maintain feasibility of the production requirements –It must control the incurred inventory holding costs, and/or part delays (this is a measure of disruption to the production flow caused by batching) Move or transfer batches: The quantities in which parts are moved between the successive processing stations. –They should be as small as possible to maintain a smooth process flow

41. Some Lot Sizing Methods employed in the traditional MRP framework Main focus: Balance set-up and holding costs Wagner-Whitin Algorithm for dynamic Lot Sizing Economic Order Quantity (EOQ): Compute a lot size using the EOQ formula with the demand rate D set equal to the average of the net requirements 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.

42. (borrowed from Heizer and Render) Pegging and Bottom-up Replanning

43. Finite-Capacity Planning & Scheduling in the MRP II / ERP context: Load Reports (Example) Available resource time Periods123 4567 8 50 100 150

44. Finite-Capacity Planning & Scheduling in the MRP II / ERP context: More Systematic Approaches Bottleneck-based scheduling in a cellular manufacturing context (Goldratt’s Theory of Constraints approach): –Each part (family) has its own production cell with a well-defined bottleneck resource. –Production is scheduled on the bottleneck resource and the schedule for the other resources are organized around this schedule by taking into consideration the expected lead times. –Typically, a “cushion” of extra workload is maintained at the bottleneck in order to prevent its starvation, in case of any disruptions in the upstream processes. –If the bottleneck supports the production of more than one part types, a “single- machine” scheduling problem arises naturally. This is addressed by selecting an appropriate dispatching rule. Earliest Due Date (EDD) => minimizes maximum lateness (tardiness) Least slack (LS), where slack = difference between job due date and expected completion time => tend to reduce average tardiness Shortest Processing Time (SPT) => minimizes average flowtime at the bottleneck, and (by Little’s law) average WIP Other heuristics addressing different problem variations including weighted performance measures, non-zero release times, etc.

45. Finite-Capacity Planning & Scheduling in the MRP II / ERP context: More Systematic Approaches (cont.) Cases where the previous approach is not effective: –There are more than one capacity-constrained resource –Bottlenecks are shifting depending on the product mix –There are operations involving parallel process batching –Process routes are non-linear (e.g., due to routing flexibility, re-entrance, extensive need for rework) Remark: The semiconductor manufacturing operational context is a typical example of all of the above. A more global view of the system operations is necessary in order to support effective and efficient scheduling. Possible approaches –Employ a set of pertinently selected dispatching rules at the different (critical) resources, and assess its efficacy through simulation (possibly maintain a bank of such rules for different operational conditions – meta-heuristics) –Generate efficient (not necessarily optimal) global schedules by employing an approach that searches for such a schedule in the space of feasible schedules

46. Shop floor-level Production Control / Scheduling

47. 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.

48. Example W_q W_2W_i W_M W_1 J_1 J_2 J_N

49. A modeling abstraction 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.

50. 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 alternatives 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)

51. 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)

52. Performance Criteria

53. Example

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

55. Schedule Performance Evaluation

56. 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 for job j) –Critical ratios, defined as (d_j-current time)/rem. proc. time for job j

57. Some Limitations of MRP-based Planning The employment of fixed nominal lead times –This problem is mitigated in case of a stable operational environment where past experience and / or approximate formal models can provide insight for setting lead times –Lead time assessment is also facilitated by a well-structured, cellular shop- floor Lack of an inherent mechanism for detecting and managing shop-floor congestion – a purely “Push” approach –However, it is possible to combine the planning visibility offered by the MRP explosion calculus with more sophisticated production control mechanisms that take advantage of the existing technology of Manufacturing Execution Systems (MES). Possible system nervousness due to re-planning and the applied lot sizing policies –Potential remedies Firm planned orders MPS Frozen Zone and Time Fences L4L planning whenever possible

58. Reading Assignment From your textbook: Chapter 3: Sections 3.1-3.6, 3.10 Chapter 7: Sections 7.1-7.3, 7.5-7.8 Chapter 8: 8.1-8.6, 8.11, 8.12