1. Production Planning & Scheduling in Large Corporations

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

6. Aggregate Planning Problem
Aggr. Unit
Production Reqs
Corporate Strategy
Aggregate
Unit Demand
Aggregate Production Plan
Aggregate Planning
Aggregate
Unit Availability
(Current Inventory
Position)
Required
Production Capacity
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) PC WC HC FC
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: PC SC WC OC UC
D(t)
P(t)
S(t)
O(t)
U(t)
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) PC WC IC
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: PC WC BC
D(t)
P(t)
B(t)
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: PC WC HC FC OC UC SC IC BC P W D H F O Io U S I Wo 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.

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., I2 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 = St ( PCt*Pt+WCt*Wt+OCt*Ot+HCt*Ht+FCt*Ft+
SCt*St+ICt*It+BCt*Bt )
s.t.
t, Pt+It-1+St = (Dt-Bt)+Bt-1+It
t, Wt = Wt-1+Ht-Ft
t, 5*Pt  8*WDt*Wt+Ot (
t, It  0.25*Dt )
B6= 0
t, Pt, Wt, Ot, Ht, Ft, St, It, Bt  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
Capacity
Consts.
Company
Policies
Product
Charact.
Economic
Considerations
Placed Orders
MPS
Master Production
Schedule:
When & How Much
to produce for each
product
Forecasted Demand
Current and Planned
Availability, eg.,
Initial Inventory,
Initiated Production,
Subcontracted quantities
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
Initial Inventory Position
Scheduled Receipts due to initiated production or subcontracting
Demand
Availability:
Compute Future
Inventory Positions
Net
Requirements
Future inventories
Lot Sizing
Scheduled
Releases
Resource (Fermentor)
Occupancy
Product i
Revise
Prod. Reqs
Feasibility
Testing
Schedule
Infeasibilities
Master Production Schedule

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: 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 ( ) 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 Fermentation Times: 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
IPi = max{IPi-1,0}+ SRi+BNRi -Di
(Material Balance Equation) i Di
IPi
(IPi-1)+
SRi+BNRi
Net Requirement:
NRi = abs(min{0, IPi})

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
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
SPi = max{0, IPi-1-(SRi-1+SRi-2+…+SRi-sl+1)
-(BNRi-1+BNRi-2+…+BNRi-sl+1)}
Inventory Position:
IPi = max{IPi-1,0}+ SRi+BNRi -Di-SPi
(Material Balance Equation)
(IPi-1)+ Di i
SPi
SRi+BNRi
IPi

50. Materials Requirements Planning (MRP)

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

52. Example: The (complete) MRP Explosion Calculus (J. Heizer and B
Example: The (complete) MRP Explosion Calculus (J. Heizer and B. Render “Operations Management”, 6th Ed. Prentice Hall)
Item BOM:
Alpha
B(1)
C(1)
D(2)
C(2)
E(1)
F(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
External Demand
Level 0
Capacity
Planning
Initial
Inventories
Level 1
Level 2
Scheduled
Receipts
Level N
Planned
Order Releases
Gross Requirements

55. Capacity Planning (Example)
Available
labor
hours
150
100 50 1 2 3 8 4 5 6 7
Periods

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

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
J_2
J_1
W_2
W_i
W_1
W_M
W_q
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
Machine 1 2 3 4 5 5 10 15 20
Time
Job 1
Job 2
Job 3
Job 4
Job 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.