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 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) = 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. 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.

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

14. 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, (u_l_r)*Pt  (s_d)*(w_d)t*Wt+Ot
Prod. Capacity:
t, Pt+It-1+St = (Dt-Bt)+Bt-1+It
Material Balance:
t, Wt = Wt-1+Ht-Ft
Workforce Balance: (
Any additional policy constraints )
Var. sign restrictions:
t, Pt, Wt, Ot, Ht, Ft, St, It, Bt  0
Time unit: month / unit_labor_req. /shift_duration (in hours) /
(working_days) for month t

15. Disaggregation and Master Production Scheduling (MPS)

16. 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

17. 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:

18. Example: Implementing the Empirical Approach in Excel

19. 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})

20. Problem Decision Variables: Scheduled Releases

21. Testing the Schedule Feasibility

22. Fixing the Original Schedule

23. Infeasible Production Requirements

24. A feasible schedule with spoilage effects

25. 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

26. 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

27. Materials Requirements Planning (MRP)

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

29. Example: The (complete) MRP Explosion Calculus
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

30. 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

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

33. 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

34. 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.

35. Shop floor-level Production Control / Scheduling

36. 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.

37. Example
J_2
J_1
W_2
W_i
W_1
W_M
W_q
J_N

38. 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.

39. 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)

40. 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)

41. Performance Criteria

42. Example

43. 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

44. Schedule Performance Evaluation

45. 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.