Production-related Decision
Making in Large Corporations
Production-related Decision Making
in Large Corporations
(borrowed from Heizer and Render)
Product and Process Design,
Sourcing, Equipment Selection
and Capacity Planning
Major Topics
• Product and Process Design
• Documenting Product and Process Design
• Sourcing Decisions:
– A simple “Make or Buy” model
– Decision Trees: A scenario-based approach
• Equipment Selection and Capacity Planning
Product Selection and Development Stages
(borrowed from Heizer & Render)
Quality Function Deployment (DFD)
and the House of Quality
• QFD: The process of
– Determining what are the customer “requirements” /
“wants”, and
– Translating those desires into the target product design.
• House of quality: A graphic, yet systematic technique for
defining the relationship between customer desires and the
developed product (or service)
House of Quality Example
(borrowed from Heizer & Render)
The “House of Quality” Chain
(borrowed from Heizer & Render)
Concurrent Engineering: The current approach for
organizing the product and process development
• The traditional US approach (department-based):
Research & Development => Engineering => Manufacturing =>
Production
Clear-cut responsibilities but lack of communication and “forward
thinking”!
• The currently prevailing approach (cross-functional team-based):
Product development (or design for manufacturability, or value
engineering) teams: Include representatives from:
– Marketing
– Manufacturing
– Purchasing
– Quality assurance
– Field service
– (even from) vendors
Concurrent engineering: Less costly and more expedient product
development
The time factor: Time-based competition
• Some advantages of getting first a new product to the market:
– Setting the “standard” (higher market control)
– Larger market share
– Higher prices and profit margins
• Currently, product life cycles get shorter and product
technological sophistication increases => more money is
funneled to the product development and the relative risks
become higher.
• The pressures resulting from time-based competition have led to
higher levels of integrations through strategic partnerships, but
also through mergers and acquisitions.
Additional concerns in contemporary
product and process design
– promote robust design practices
Robustness: the insensitivity of the product performance to small variations in the
production or assembly process => ability to support product quality more reliably
and cost-effectively.
– Control the product complexity
– Improve the product maintainability / serviceability
– (further) standardize the employed components
Modularity: the structuring of the end product through easily segmented
components that can also be easily interchanged or replaced => ability to
support flexible production and product customization;increased product
serviceability.
– Improve job design and job safety
– Environmental friendliness: safe and environmentally sound products,
minimizing waste of raw materials and energy, complying with
environmental regulations, ability for reuse, being recognized as good
corporate citizen.
Documenting Product Designs
• Engineering Drawing: a drawing that shows the dimensions,
tolerances, materials and finishes of a component. (Fig. 5.9)
• Bill of Material (BOM): A listing of the components, their
description and the quantity of each required to make a unit of a
given product. (Fig. 5.10)
• Assembly drawing: An exploded view of the product, usually via a
three-dimensional or isometric drawing. (Fig. 5.12)
• Assembly chart: A graphic means of identifying how components
flow into subassemblies and ultimately into the final product. (Fig.
5.12)
• Route sheet: A listing of the operations necessary to produce the
component with the material specified in the bill of materials.
• Engineering change notice (ECN): a correction or modification of
an engineering drawing or BOM.
• Configuration Management: A system by which a product’s planned
and changing components are accurately identified and for which
control of accountability of change are maintained
Documenting Product Designs (cont.)
• Work order: An instruction to make a given quantity (known as
production lot or batch) of a particular item, usually to a given
schedule.
• Group technology: A product and component coding system that
specifies the type of processing and the involved parameters,
allowing thus the identification of processing similarities and the
systematic grouping/classification of similar products. Some
efficiencies associated with group technology are:
– Improved design (since the focus can be placed on a few
critical components
– Reduced raw material and purchases
– Improved layout, routing and machine loading
– Reduced tooling setup time, work-in-process and production
time
– Simplified production planning and control
Engineering Drawing Example
(borrowed from Heizer & Render)
Bill of Material (BOM) Example
(borrowed from Heizer & Render)
Assembly Drawing & Chart Examples
(borrowed from Heizer & Render)
Operation Process Chart Example
(borrowed from Francis et. al.)
Route Sheet Example
(borrowed from Francis et. al.)
“Make-or-buy” decisions
• Deciding whether to produce a product component “inhouse”, or purchase/procure it from an outside source.
• Issues to be considered while making this decision:
– Quality of the externally procured part
– Reliability of the supplier in terms of both item quality
and delivery times
– Criticality of the considered component for the
performance/quality of the entire product
– Potential for development of new core competencies of
strategic significance to the company
– Existing patents on this item
– Costs of deploying and operating the necessary
infrastructure
A simple economic trade-off model for
the “Make or Buy” problem
Model parameters:
• c1 ($/unit): cost per unit when item is outsourced (item price,
ordering and receiving costs)
• C ($): required capital investment in order to support internal
production
• c2 ($/unit): variable production cost for internal production (materials,
labor,variable overhead charges)
• Assume that c2 < c1
• X: total quantity of the item to be outsourced or produced internally
Total cost as
a function of X
c1*X
C+c2*X
C
X0 = C / (c1-c2)
X
Example: Introducing a new (stabilizing)
bracket for an existing product
• Machine capacity available
• Required “infrastructure” for in-house production
– new tooling: $12,500
– Hiring and training an additional worker: $1,000
• Internal variable production (raw material + labor) cost:
$1.12 / unit
• Vendor-quoted price: $1.55 / unit
• Forecasted demand: 10,000 units/year for next 2 years

X0 = (12,500+1,000)/(1.55-1.12) = 31,395 > 20,000

Buy!
Evaluating Alternatives through
Decision Trees
•
Decision Trees: A mechanism for systematically pricing all options /
alternatives under consideration, while taking into account various
uncertainties underlying the considered operational context.
•
Example
–
–
–
–
An engineering consulting company (ECC) has been offered the design
of a new product.The price offered by the customer is $60,000.
If the design is done in-house, some new software must be purchased at
the price of $20,000, and two new engineers must be trained for this
effort at the cost of $15,000 per engineer.
Alternatively, this task can be outsourced to an engineering service
provider (ESP) for the cost of $40,000. However, there is a 20% chance
that this ESP will fail to meet the due date requested by the customer, in
which case, the ECC will experience a penalty of $15,000. The ESP
offers also the possibility of sharing the above penalty at an extra cost of
$5,000 for the ECC.
Find the option that maximizes the expected profit for the ECC.
Decision Trees: Example
10K
60K-20K-2*15K=10K
1
17K
17K
0.8
60K-40K=20K
2
0.2
60K-40K-15K=5K
3
13.5K
0.8
0.2
60K-45K=15K
60K-45K-7.5K=7.5K
Technology selection
• The selected technology must be able to support the quality
standards set by the corporate / manufacturing strategy
• This decision must take into consideration future
expansion plans of the company in terms of
– production capacity (i.e., support volume flexibility)
– product portfolio (i.e., support product flexibility)
• It must also consider the overall technological trends in the
industry, as well as additional issues (e.g., environmental
and other legal concerns, operational safety etc.) that might
affect the viability of certain choices
• For the candidates satisfying the above concerns, the final
objective is the minimization of the total (i.e., deployment
plus operational) cost
Production Capacity
• Design capacity: the “theoretical” maximum output of a system,
typically stated as a rate, i.e., product units / unit time.
• Effective capacity: The percentage of the design capacity that
the system can actually achieve under the given operational
constraints, e.g., running product mix, quality requirements,
employee availability, scheduling methods, etc.
• Plant utilization = actual prod. rate / design capacity
• Plant efficiency = actual prod. rate / (effective capacity x
design capacity)
• Notice that
actual prod. rate = (design capacity) x (utilization) =
(design capacity) x (effective capacity) x (efficiency)
Capacity Planning
• Capacity planning seeks to determine
– the number of units of the selected technology that needs to
be deployed in order to match the plant (effective) capacity
with the forecasted demand, and if necessary,
– a capacity expansion plan that will indicate the time-phased
deployment of additional modules / units, in order to support
a growing product demand, or more general expansion plans
of the company (e.g., undertaking the production of a new
product in the considered product family).
• Frequently, technology selection and capacity planning are
addressed simultaneously, since the required capacity affects the
economic viability of a certain technological option, while the
operational characteristics of a given technology define the
production rate per unit deployed and aspects like the possibility
of modular deployment.
Quantitative Approaches to Technology
Selection and Capacity Planning
• All these approaches try to select a technology (mix) and determine the capacity to
be deployed in a way that it maximizes the expected profit over the entire life-span
of the considered product (family).
• Expected profit is defined as expected revenues minus deployment and operational
costs.
• Typically, the above calculations are based on net present values (NPV’s) of the
expected costs and revenues, which take into consideration the cost of money:
NPV = (Expense or Revenue) / (1+i)N
where i is the applying interest rate and N the time period of the considered expense.
• Possible methods used include:
– Break-even analysis, similar to that applied to the “make or buy” problem, that
seeks to minimizes the total (fixed + variable) cost.
– Decision trees which allow the modeling of problem uncertainties like uncertain
market behavior, etc., and can determine a strategy as a reaction to these
unknown factors.
– Mathematical Programming formulations which allow the optimized selection of
technology mixes.
Selecting the Process Layout
Operation Process Chart Example
for discrete part manufacturing
(borrowed from Francis et. al.)
Major Layout Types
(borrowed from Francis et. al.)
Advantages and Limitations of the various
layout types (borrowed from Francis et. al.)
Advantages and Limitations of the various layout
types (cont. - borrowed from Francis et. al.)
Selecting an appropriate layout
(borrowed from Francis et. al.)
The product-process matrix
Production
volume
& mix
Process
type
Jumbled
flow (job
Shop)
Low volume,
low standardization
Commercial
printer
Disconnected
line flow
(batch)
High volume, high
standardization,
commodities
Void
Heavy
Equipment
Connected
line flow
(assembly
Line)
Continuous
flow
(chemical
plants)
Multiple products, Few major products,
low volume
high volume
Auto
assembly
Void
Sugar
refinery
Cell formation in group technology:
A clustering problem
Partition the entire set of parts to be produced on the plant-floor into
a set of part families, with parts in each family characterized by
similar processing requirements, and therefore, supported by the
same cell.
Part-Machine Indicator Matrix
P1
P2
P3
P4
P5
P6
P1
P3
P2
P4
P5
P6
M1
1
M2
M3
1
1
M4
1
M5
M4
1
1
1
1
1
1
M1
1
1
1
1
M6
1
1
M7
1
1
1
M6
1
M2
M3
M5
1
1
1
1
1
1
1
1
M7
1
1
Clustering Algorithms for Cellular Manufacturing
Row & Column Masking
P1
P2
P3
P4
P5
P6
P1
P3
P2
P4
P5
P6
M1
1
M2
M3
1
1
M4
1
M5
M4
1
1
1
1
1
1
M1
1
1
1
1
M6
1
1
M7
1
1
1
M6
1
M2
M3
M5
1
1
1
1
1
1
1
1
M7
1
1
Clustering Algorithms for Cellular Manufacturing:
Similarity Coefficients - Motivation
P1
P2
P3
P4
P5
P6
P1
P3
P2
P4
P5
P6
M1
1
1
M2
M3
1
1
M4
1
M5
1
M4
1
1
1
1
1
1
M1
1
1
1
1
M6
1
1
M7
1
1
1
M6
1
M2
M3
M5
1
1
1
1
1
1
1
1
M7
1
1
Clustering Algorithms for Cellular Manufacturing:
Similarity Coefficients - Definitions
• P(Mi) = set of parts supported by machine Mi
• |P(Mi)| = cardinality of P(Mi), i.e., the number of elements
of this set
• SC(Mi,Mj) = |P(Mi)P(Mj)| / |P(Mi)P(Mj)| =
|P(Mi)P(Mj)| / (|P(Mi)|+|P(Mj)|-|P(Mi)P(Mj)|)
• Notice that: 0  SC(Mi,Mj)  1.0, and the closer this value is
to 1.0 the greater the similarity among the part sets supported
by machines Mi and Mj.
• By picking a desired threshold, one can cluster together all
machines that have a similarity coefficient greater than or
equal to this threshold.
A typical (logical) Organization of the
Production Activity in
Repetitive Manufacturing
Assembly Line 1: Product Family 1
S1,1
Raw
Material
& Comp.
Inventory
S1,i
S1,2
S1,n
Fabrication (or Backend Operations)
Dept. 1
S2,1
S2,2
Dept. 2
Dept. j
S2,i
Assembly Line 2: Product Family 2
Finished
Item
Inventory
Dept. k
S2,m
Synchronous Transfer Lines: Examples
(Pictures borrowed from Heragu)
Flow Patterns for Product-focused Layouts
(borrowed from Francis et. al.)
Discrete vs. Continuous Flow and
Repetitive Manufacturing Systems
(Figures borrowed from Heizer and Render)
Production Planning and
Scheduling
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)
Aggregate Planning
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.
Computing the Aggregate Unit
Production Requirements
Washing machine
Model Number
A5532
Required labor time
(hrs)
4.2
Item demand as % of
aggregate demand
32
K4242
4.9
21
L9898
5.1
17
3800
5.2
14
M2624
5.4
10
M3880
5.8
06
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
Aggregate Planning Problem
Aggr. Unit
Production Reqs
Corporate Strategy
Aggregate
Unit Demand
Aggregate
Unit Availability
(Current Inventory
Position)
Aggregate
Production Plan
Aggregate Planning
Aggregate Production Plan:
•Aggregate Production levels
•Aggregate Inventory levels
•Aggregate Backorder levels
Required
Production Capacity
Production Capacity Plan:
•Workforce level(s)
•Overtime level(s)
•Subcontracted Quantities
Pure Aggregate Planning Strategies
1. Demand Chasing: Vary the Workforce Level
PC WC HC FC
D(t)
P(t) = D(t)
W(t)
•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
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)
Pure Aggregate Planning Strategies
3. Accumulating (Seasonal) Inventories:
PC WC IC
D(t)
P(t)
I(t)
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.
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
Typical Aggregate Planning Strategy
A “mixture” of the previously discussed pure options:
PC WC HC FC OC UC SC IC BC
P
W
H
F
O
U
S
I
B
D
Io
Wo
+
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.
Solution Approaches
• Graphical Approaches: Spreadsheet-based simulation
• Analytical Approaches: Mathematical (mainly linear
programming) Programming formulations
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
Cost structure:
Inv. holding cost: $80/unit x month
Hiring cost: $500/worker
Firing cost: $1000/worker
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
A prototype problem (cont.)
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
Net predicted demand:
Jan: 780
Feb: 640
Mar: 900
Apr: 1200
May: 2000
Jun: 2000
An LP formulation for the prototype problem
Problem Parameters
Dt = Forecasted demand for period t
dt = working days at period t
c = daily worker capacity
W0=Initial workforce level
I0 = Current on-hand inventory
CH = Hiring cost per worker
CF = Firing cost per worker
CI = Inventory holding cost per unit per period
Problem Decision Variables
Ht = Workers hired at period t
Ft = Workers fired at period t
Wt = Workforce level at period t
Pt = Level of production at period t
It = Inventory at the end of period t
An LP formulation for the prototype problem
6
6
6
t 1
t 1
t 1
min( C H  H t  C F  Ft  C I  I t )
s.t.
Wt  Wt 1  H t  Ft , t  1,...,6
Pt  (dt  c) Wt , t  1,...,6
It  It 1  Pt  Dt , t  1,...,6
I 6  600
Wt , H t , Ft , Pt , I t  0, t  1,...,6
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
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.
Prod. Capacity:
t, (u_l_r)*Pt  (s_d)*(w_d)t*Wt+Ot
Material Balance: t, Pt+It-1+St = (Dt-Bt)+Bt-1+It
Workforce Balance: t, Wt = Wt-1+Ht-Ft
( Any additional policy constraints )
Var. sign restrictions: t, P , W , O , H , F , S , I , B  0
t
t
t
t
t
t
t
t
Time unit: month / unit_labor_req. /shift_duration (in hours) /
(working_days) for month t
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.
Disaggregation and
Master Production Scheduling
(MPS)
The (Master) Production Scheduling Problem
Capacity Company Product Economic
Consts. Policies Charact. Considerations
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
MPS
Planning
Horizon
Time
unit
Capacity
Planning
MPS Example: Company Operations
Grain cracking
(1 milling
machine)
Fermentation
(3 40-barrel
ferm. tanks)
Mashing
(1 mashing tun)
Boiling
(1 brew kettle)
Bottling
(1 bottling
station)
Filtering
(1 filter tank)
Fermentation Times:
Brew
Pale Ale
Stout
Ferm. Time
2 weeks
3 weeks
Winter Ale
2 weeks
Summer Brew
2 weeks
Octoberfest
8-10 weeks
Example: Implementing the Empirical
Approach in Excel
# Fermentors:
1
Microbrewery Performance
Week
# Fermentors Req'd
Feasible Loading?
Min # Fermentors Req'd
Fermentor Utilization
Total Spoilage
Pale Ale
Week
Demand
Scheduled Receipts
Fermentors Released
Inventory Spoilage
Inventory Position
Net Requirements
Batched Net Receipts
Scheduled Releases
Fermentors Seized
Total Fermentors Occupied
Stout
Week
Demand
Scheduled Receipts
Fermentors Released
Inventory Spoilage
Inventory Position
Net Requirements
Batched Net Receipts
Scheduled Releases
Fermentors Seized
Total Fermentors Occupied
0
Unit Cap:
200
1
0
2
0
3
0
2
0%
0
2
0%
0
2
0%
0
Fermentation Time:
0
1
45
200
1
100
255
Fermentation Time:
0
1
35
150
2
2
115
3
Shelf Life:
20
4
0
5
0
6
0
7
0
8
0
9
0
10
0
2
0%
0
2
0%
0
2
0%
0
2
0%
0
2
0%
0
2
0%
0
2
0%
0
4
5
6
7
8
9
10
50
40
40
40
40
40
40
40
40
205
165
125
85
45
5
-35
35
-40
40
-40
40
3
2
3
4
5
6
7
8
9
10
40
30
30
40
40
40
40
50
50
75
45
15
-25
25
-40
40
-40
40
-40
40
-50
50
-50
50
Computing Inventory Positions and
Net Requirements
Inventory Position:
IPi = max{IPi-1,0}+ SRi+BNRi -Di
(Material Balance Equation)
(IPi-1)+
SRi+BNRi
i
Di
IPi
Net Requirement:
NRi = abs(min{0, IPi})
Problem Decision Variables:
Scheduled Releases
# Fermentors:
1
Microbrewery Performance
Week
# Fermentors Req'd
Feasible Loading?
Min # Fermentors Req'd
Fermentor Utilization
Total Spoilage
Pale Ale
Week
Demand
Scheduled Receipts
Fermentors Released
Inventory Spoilage
Inventory Position
Net Requirements
Batched Net Receipts
Scheduled Releases
Fermentors Seized
Total Fermentors Occupied
Stout
Week
Demand
Scheduled Receipts
Fermentors Released
Inventory Spoilage
Inventory Position
Net Requirements
Batched Net Receipts
Scheduled Releases
Fermentors Seized
Total Fermentors Occupied
0
Unit Cap:
200
1
0
2
0
3
0
2
0%
0
2
0%
0
2
0%
0
Fermentation Time:
0
1
45
200
1
100
2
2
255
3
Shelf Life:
20
4
0
5
0
6
1
7
1
8
0
9
0
10
0
2
0%
0
2
0%
0
2
100%
0
2
100%
0
2
0%
0
2
0%
0
2
0%
0
6
7
8
4
5
9
10
50
40
40
40
40
40
40
40
40
205
165
125
85
45
5
165
125
85
200
200
1
1
Fermentation Time:
0
1
35
150
115
3
2
3
4
5
6
1
7
8
9
10
40
30
30
40
40
40
40
50
50
75
45
15
-25
25
-40
40
-40
40
-40
40
-50
50
-50
50
Testing the Schedule Feasibility
# Fermentors:
1
Microbrewery Performance
Week
# Fermentors Req'd
Feasible Loading?
Min # Fermentors Req'd
Fermentor Utilization
Total Spoilage
Pale Ale
Week
Demand
Scheduled Receipts
Fermentors Released
Inventory Spoilage
Inventory Position
Net Requirements
Batched Net Receipts
Scheduled Releases
Fermentors Seized
Total Fermentors Occupied
Stout
Week
Demand
Scheduled Receipts
Fermentors Released
Inventory Spoilage
Inventory Position
Net Requirements
Batched Net Receipts
Scheduled Releases
Fermentors Seized
Total Fermentors Occupied
0
Unit Cap:
200
1
0
2
1
3
1
2
0%
0
2
100%
0
2
2
Fermentation Time:
0
1
45
200
1
100
255
Shelf Life:
20
4
1
5
0
6
1
2
100%
0
2
100%
0
2
0%
0
3
4
5
8
1
9
1
10
0
2
100%
0
7
2
NO
2
200%
0
2
100%
0
2
100%
0
2
0%
0
6
7
8
9
10
50
40
40
40
40
40
40
40
40
205
165
125
85
45
5
165
125
85
200
200
1
1
Fermentation Time:
0
1
35
150
115
3
2
3
4
5
6
1
7
8
9
10
40
30
30
40
40
40
40
50
50
75
45
15
175
135
95
55
5
155
200
200
1
1
1
1
200
200
1
1
1
1
Fixing the Original Schedule
# Fermentors:
1
Microbrewery Performance
Week
# Fermentors Req'd
Feasible Loading?
Min # Fermentors Req'd
Fermentor Utilization
Total Spoilage
Pale Ale
Week
Demand
Scheduled Receipts
Fermentors Released
Inventory Spoilage
Inventory Position
Net Requirements
Batched Net Receipts
Scheduled Releases
Fermentors Seized
Total Fermentors Occupied
Stout
Week
Demand
Scheduled Receipts
Fermentors Released
Inventory Spoilage
Inventory Position
Net Requirements
Batched Net Receipts
Scheduled Releases
Fermentors Seized
Total Fermentors Occupied
0
Unit Cap:
200
1
0
2
1
3
1
2
0%
0
2
100%
0
2
2
Fermentation Time:
0
1
45
200
1
100
255
Shelf Life:
20
4
1
5
1
6
1
7
1
8
1
9
1
10
0
2
100%
0
2
100%
0
2
100%
0
2
100%
0
2
100%
0
2
100%
0
2
100%
0
2
0%
0
3
4
5
6
7
8
9
10
50
40
40
40
40
40
40
40
40
205
165
125
85
45
205
165
125
85
200
200
1
1
Fermentation Time:
0
1
35
150
115
3
2
3
4
5
1
6
7
8
9
10
40
30
30
40
40
40
40
50
50
75
45
15
175
135
95
55
5
155
200
200
1
1
1
1
200
200
1
1
1
1
Infeasible Production Requirements
# Fermentors:
1
Microbrewery Performance
Week
# Fermentors Req'd
Feasible Loading?
Min # Fermentors Req'd
Fermentor Utilization
Total Spoilage
Pale Ale
Week
Demand
Scheduled Receipts
Fermentors Released
Inventory Spoilage
Inventory Position
Net Requirements
Batched Net Receipts
Scheduled Releases
Fermentors Seized
Total Fermentors Occupied
Stout
Week
Demand
Scheduled Receipts
Fermentors Released
Inventory Spoilage
Inventory Position
Net Requirements
Batched Net Receipts
Scheduled Releases
Fermentors Seized
Total Fermentors Occupied
0
Unit Cap:
200
1
1
2
1
3
1
2
100%
0
2
100%
0
2
2
Fermentation Time:
0
1
45
100
55
Shelf Life:
20
4
1
5
0
6
0
7
0
8
0
9
0
10
0
2
100%
0
2
100%
0
2
0%
0
2
0%
0
2
0%
0
2
0%
0
2
0%
0
2
0%
0
3
4
5
6
7
8
9
10
50
200
1
40
40
40
40
40
40
40
40
205
165
125
85
45
5
-35
35
-40
40
-40
40
1
Fermentation Time:
0
1
35
150
115
3
2
3
4
5
6
7
8
9
10
40
40
40
40
40
40
40
50
50
75
35
-5
5
160
120
80
40
-10
10
-50
50
200
200
1
1
1
1
A feasible schedule with spoilage effects
# Fermentors:
1
Microbrewery Performance
Week
# Fermentors Req'd
Feasible Loading?
Min # Fermentors Req'd
Fermentor Utilization
Total Spoilage
Pale Ale
Week
Demand
Scheduled Receipts
Fermentors Released
Inventory Spoilage
Inventory Position
Net Requirements
Batched Net Receipts
Scheduled Releases
Fermentors Seized
Total Fermentors Occupied
Stout
Week
Demand
Scheduled Receipts
Fermentors Released
Inventory Spoilage
Inventory Position
Net Requirements
Batched Net Receipts
Scheduled Releases
Fermentors Seized
Total Fermentors Occupied
0
Unit Cap:
200
1
1
2
1
3
1
2
100%
0
2
100%
0
2
2
Fermentation Time:
0
1
45
200
1
100
255
Shelf Life:
6
4
1
5
1
6
0
7
1
8
1
9
1
10
0
2
100%
0
2
100%
0
2
100%
0
2
0%
0
2
100%
45
2
100%
0
2
100%
0
2
0%
5
3
4
5
6
7
8
9
10
50
40
40
40
40
40
40
40
40
205
165
125
85
245
45
160
120
80
40
200
200
1
1
Fermentation Time:
0
1
35
150
115
3
2
3
4
1
5
6
7
8
9
10
40
30
30
40
40
40
40
50
50
75
45
215
175
135
95
55
5
5
150
200
200
1
1
1
1
200
200
1
1
1
1
Computing Spoilage and
Modified Inventory Position
Spoilage:
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)+
SRi+BNRi
i
Di
SPi
IPi
The Driving Logic behind the Empirical Approach
Demand
Availability:
•Initial Inventory Position
•Scheduled Receipts due to
initiated production or
subcontracting
Compute Future
Inventory Positions
Net
Requirements
Future inventories
Lot Sizing
Scheduled
Releases
Resource (Fermentor)
Occupancy
Feasibility
Testing
Product i
Schedule
Infeasibilities
Master Production Schedule
Revise
Prod. Reqs
Materials Requirements Planning
(MRP)
The “MRP Explosion” Calculus
BOM
Lead
Times
Planned
Order Releases
MPS
Current
Availabilities
Lot Sizing
Policies
MRP
Priority
Planning
Example: The (complete) MRP Explosion
Calculus
Item BOM:
Alpha
B(1)
D(2)
C(1)
C(2)
E(1)
E(1)
F(1)
F(1)
Item
Alpha
B
C
D
E
F
Gross Reqs for Alpha
Period
Gross Reqs.
Item Levels:
Level 0: Alpha Level 1: B Level 2: C, D Level 3: E, F
Lead Time
1
2
3
1
1
1
6
7
8
9
50
Current Inv. Pos.
10
20
0
100
10
50
10
11 12
50
13
100
(borrowed from Heizer and Render)
The “MRP Explosion” Calculus
External Demand
Level 0
Initial
Inventories
Level 1
Capacity
Planning
Level 2
Scheduled
Receipts
Level N
Gross Requirements
Planned
Order Releases
Computing the item Scheduled Releases
Item C
Period
Gross Requirements
Scheduled Receipts
Inventory Position: 20
Net Requirements
Planned Sched. Receipts
Planned Sched. Releases
1
2
3
20
20
40
40
4
40
5
6
12
7
10
40
28
18
72
Safety Stock
Requirements
Parent
Sched. Rel.
Item External
Demand
Synthesizing
item demand
series
Gross
Reqs
Projecting Net
Inv. Positions Reqs
and
Net Reqs.
Scheduled
Receipts
Initial
Inventory
8
9
90
18
-72
72
72
10
11
75
0
-75
75
75
12
0
75
Lot Sizing
Policy
Lot Sizing
Lead Time
Planned
Order
Receipts
TimePhasing
Planned
Order
Releases
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.
Capacity Planning (Example)
Available
labor
hours
150
100
50
1
2
3
4
5
6
7
8
Periods
Pegging and Bottom-up Replanning
(borrowed from Heizer and Render)
Shop floor-level
Production Control / Scheduling
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.
Example
J_2
J_1
W_1
W_2
W_q
J_N
W_i
W_M
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.
Example
Jon number Due Date Oper. #1 Oper. #2 Oper. #3 Oper. #4 Oper. #5
1
17
(1,2)
(2,4)
(4,3)
(5,3)
2
18
(1,4)
(3,2)
(2,6)
(4,2)
(5,3)
3
19
(2,1)
(5,4)
(1,3)
(3,4)
(2,2)
4
17
(2,4)
(4,2)
(1,2)
(3,5)
5
20
(4,5)
(5,3)
(1,7)
A feasible schedule and its Gantt Chart
Machine
1
2
3
4
5
5
Job 1
Job 2
10
Job 3
15
Job 4
20 Time
Job 5
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)
Performance Criteria
Job Attribute
Lateness
Tardiness
Flow time
Tardy index
Completion
min total
S_j L_j
S_j T_j
S_j F_j
NT
S_j C_j
min weighted total
S_j w_j*L_j
S_j w_j*T_j
S_j w_j*F_j
min max
max_j L_j
max_j T_j
max_j F_j
min weighted max
max_j w_j*L_j
max_j w_j*T_j
max_j w_j*F_j
S_j w_j*C_j
max_j C_j
max_j w_j*C_j
Schedule Performance Evaluation
Job
1
2
3
4
5
Total
average
max
d_j
17
18
19
17
20
C_j
15
20
17
18
18
F_j
15
20
17
18
18
L_j
-2
2
-2
1
-2
T_j
0
2
0
1
0
TI_j
0
1
0
1
0
88
17.6
20
88
17.6
20
-3
-0.6
2
3
0.6
2
2
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)
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
Assembly Line Balancing
Synchronous Transfer Lines: Examples
(Pictures borrowed from Heragu)
Balancing Synchronous Transfer Lines
• Given:
– a set of m tasks, each requiring a certain (nominal) processing
time t_i, and
– a set of precedence constraints regarding the execution of these
m tasks,
• assign these tasks to a sequence of k workstations, in a way that
– the total amount of work assigned to each workstation does not
exceed a pre-defined cycle time c, (constraint I)
– the precedence constraints are observed, (constraint II)
– while the number of the employed workstations k is
minimized. (objective)
• Remark: The problem is hard to solve optimally, and
quite often it is addressed through heuristics.
Heuristics for Assembly Line Balancing
Developed in class – c.f. your class notes!