Production Planning

1
Production Planning Scheduling in Large
Corporations
2
Dealing with the Problem Complexity through
Decomposition
Corporate Strategy
Aggregate Planning
Aggregate Unit Demand
(Plan. Hor. 1 year, Time Unit 1 month)
Capacity and Aggregate Production Plans
Master Production Scheduling
End Item (SKU) Demand
(Plan. Hor. a few months, Time Unit 1 week)
SKU-level Production Plans
Materials Requirement Planning
Manufacturing and Procurement lead times
(Plan. Hor. a few months, Time Unit 1 week)
Component Production lots and due dates
Shop floor-level Production Control
Part process plans
(Plan. Hor. a day or a shift, Time Unit
real-time)
3
Aggregate Planning
4
Product Aggregation Schemes

• Items (or Stock Keeping Units - SKUs) 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)
4.856 hrs
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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

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Pure Aggregate Planning Strategies
1. Demand Chasing Vary the Workforce Level

• 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

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Pure Aggregate Planning Strategies
2. Varying Production Capacity with Constant
Workforce
PC
WC
OC
UC
SC
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

• I(t) Accumulated Inventory levels
• Costs involved
• PC, WC as before
• IC inventory holding costs e.g., interest lost,
  storage space, pilferage, obsolescence, etc.

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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

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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.

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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)
• gt The outcome of this type of planning is
  communicated to the overall aggregate planning
  procedure as (expected) changes in the demand
  forecast.

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Solution Approaches

• Graphical Approaches Spreadsheet-based
  simulation
• Analytical Approaches Mathematical (mainly
  linear programming) Programming formulations

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Analytical ApproachA Linear Programming
Formulation
min TC St ( PCtPtWCtWtOCtOtHCtHtFCtFt
SCtStICtItBCtBt )
s.t.

• t, (u_l_r)Pt ? (s_d)(w_d)tWtOt

Prod. Capacity

• t, PtIt-1St (Dt-Bt)Bt-1It

Material Balance

• t, Wt Wt-1Ht-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
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Disaggregation and Master Production
Scheduling(MPS)
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The (Master) Production Scheduling Problem
Capacity Consts.
Company Policies
Economic Considerations
Product Charact.
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
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MPS Example Company Operations
Fermentation Times
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Example Implementing the Empirical Approach in
Excel
19
Computing Inventory Positions and Net
Requirements
Net Requirement
NRi abs(min0, IPi)
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Problem Decision Variables Scheduled Releases
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Testing the Schedule Feasibility
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Fixing the Original Schedule
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Infeasible Production Requirements
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A feasible schedule with spoilage effects
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Computing Spoilage and Modified Inventory
Position
Spoilage
SPi max0, IPi-1-(SRi-1SRi-2SRi-sl1)
-(BNRi-1BNRi-2BNRi-sl1)
Inventory Position
IPi maxIPi-1,0 SRiBNRi -Di-SPi
(Material Balance Equation)
Di
(IPi-1)
i
SPi
SRiBNRi
IPi
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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
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Materials Requirements Planning(MRP)
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The MRP Explosion Calculus
Lot Sizing Policies
Lead Times
BOM
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Example The (complete) MRP Explosion Calculus
Item BOM
Alpha
B(1)
C(1)
C(2)
D(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
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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
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(No Transcript)
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Capacity Planning (Example)
Available labor hours
150
100
50
8
Periods
1
2
3
4
5
6
7
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Computing the item Scheduled Releases
Safety Stock Requirements
Lot Sizing Policy
Lead Time
Gross Reqs
Planned Order Releases
Parent Sched. Rel.
Planned Order Receipts
Net Reqs
Synthesizing item demand series
Projecting Inv. Positions and Net Reqs.
Lot Sizing
Time- Phasing
Item External Demand
Scheduled Receipts
Initial Inventory
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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.

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Shop floor-level Production Control / Scheduling
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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.

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Example
J_2
J_1
W_2
W_i
W_1
W_M
W_q
J_N
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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.

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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)

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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)

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Performance Criteria
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Example
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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
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Schedule Performance Evaluation
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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.