Production-rel-Decision-Making (1).ppt

7/27/2019 Production-rel-Decision-Making (1).ppt

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Production-related Decision

Making in Large Corporations


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Production-related Decision Makingin Large Corporations

(borrowed from Heizer and Render)


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Product and Process Design,

Sourcing, Equipment Selection

and Capacity Planning


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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


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Product Selection and Development Stages

(borrowed from Heizer & Render)


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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)


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House of Quality Example(borrowed from Heizer & Render)


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The House of Quality Chain(borrowed from Heizer & Render)


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Concurrent Engineering: The current approach fororganizing the product and process development

The traditional US approach (department-based):

Research & Development => Engineering => Manufacturing =>Production

Clear-cut responsibilities but lack of communication and forwardthinking!

The currently prevailing approach (cross-functionalteam-based):Product development (or design for manufacturability, or valueengineering) teams: Include representatives from:

Marketing

Manufacturing

Purchasing Quality assurance

Field service

(even from) vendors

Concurrent engineering: Less costly and more expedient productdevelopment


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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 producttechnological sophistication increases => more money isfunneled 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, butalso through mergers and acquisitions.


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Additional concerns in contemporary

product and process design

promote robust design practices

Robustness: the insensitivity of the product performance to small variations in theproduction or assembly process => ability to support product quality more reliablyand 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 segmentedcomponents that can also be easily interchanged or replaced => ability tosupport 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 withenvironmental regulations, ability for reuse, being recognized as goodcorporate citizen.


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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, theirdescription and the quantity of each required to make a unit of agiven product. (Fig. 5.10)

Assembly drawing: An exploded view of the product, usually via athree-dimensional or isometric drawing. (Fig. 5.12)

Assembly chart: A graphic means of identifying how componentsflow 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 products plannedand changing components are accurately identified and for whichcontrol of accountability of change are maintained


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Documenting Product Designs (cont.)

Work order:An instruction to make a given quantity (known as

production lot orbatch) of a particular item, usually to a givenschedule.

Group technology: A product and component coding system thatspecifies the type of processing and the involved parameters,allowing thus the identification of processing similarities and thesystematic grouping/classification of similar products. Someefficiencies associated with group technology are:

Improved design (since the focus can be placed on a fewcritical components

Reduced raw material and purchases Improved layout, routing and machine loading

Reduced tooling setup time, work-in-process and productiontime

Simplified production planning and control


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Engineering Drawing Example

(borrowed from Heizer & Render)


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Bill of Material (BOM) Example(borrowed from Heizer & Render)


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Assembly Drawing & Chart Examples(borrowed from Heizer & Render)


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Operation Process Chart Example(borrowed from Francis et. al.)


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Route Sheet Example(borrowed from Francis et. al.)


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Make-or-buy decisions

Deciding whether to produce a product component in-house, 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 qualityand delivery times

Criticality of the considered component for theperformance/quality of the entire product

Potential for development of new core competencies ofstrategic significance to the company

Existing patents on this item

Costs of deploying and operating the necessaryinfrastructure

i l i d ff d l f


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A simple economic trade-off model forthe 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

X

Total cost as

a function of X

C

C+c2*X

c1*X

X0 = C / (c1-c2)

l d i ( bili i )


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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!

E l i Al i h h


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Evaluating Alternatives throughDecision Trees

Decision Trees: A mechanism for systematically pricing all options /alternatives under consideration, while taking into account variousuncertainties 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 thiseffort at the cost of $15,000 per engineer.

Alternatively, this task can be outsourced to an engineering serviceprovider (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, inwhich case, the ECC will experience a penalty of $15,000. The ESPoffers 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.


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Decision Trees: Example

1

2

3

0.8

0.2

0.8

0.2

60K-20K-2*15K=10K

10K

60K-40K=20K

60K-40K-15K=5K

17K

60K-45K=15K

60K-45K-7.5K=7.5K

13.5K

17K


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Technology selection

The selected technology must be able to support the qualitystandards set by the corporate / manufacturing strategy

This decision must take into consideration futureexpansion 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., environmentaland other legal concerns, operational safety etc.) that mightaffect the viability of certain choices

For the candidates satisfying the above concerns, the finalobjective is the minimization of the total (i.e., deployment

plus operational) cost


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Production Capacity

Design capacity:the theoretical maximum output of a system,typically stated as a rate, i.e.,product units / unit time.

Effective capacity: Thepercentage of the design capacity thatthe system can actually achieve under the given operationalconstraints, 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 thatactual prod. rate = (design capacity) x (utilization) =

(design capacity) x (effective capacity) x (efficiency)


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Capacity Planning

Capacity planning seeks to determine the number of units of the selected technology that needs tobe deployed in order to match the plant (effective) capacitywith the forecasted demand, and if necessary,

a capacity expansion plan that will indicate the time-phased

deployment of additional modules / units, in order to supporta growing product demand, or more general expansion plansof the company (e.g., undertaking the production of a new

product in the considered product family).

Frequently, technology selection and capacity planning areaddressed simultaneously, since the required capacity affects theeconomic viability of a certain technological option, while theoperational characteristics of a given technology define the

production rate per unit deployed and aspects like the possibility

of modular deployment.

Q tit ti A h t T h l


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Quantitative Approaches to TechnologySelection and Capacity Planning

All these approaches try to select a technology (mix) and determine the capacity tobe deployed in a way that it maximizes the expected profit over the entire life-spanof the considered product (family).

Expected profit is defined as expected revenues minus deployment and operationalcosts.

Typically, the above calculations are based on net present values (NPVs) 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 andN 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 theseunknown factors.

Mathematical Programming formulations which allow the optimized selection of

technology mixes.


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Selecting the Process Layout

O ti P Ch t E l


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Operation Process Chart Examplefor discrete part manufacturing(borrowed from Francis et. al.)

M j L t T


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Major Layout Types(borrowed from Francis et. al.)

Ad t d Li it ti f th i


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Advantages and Limitations of the variouslayout types (borrowed from Francis et. al.)

Ad t d Li it ti f th i l t


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Advantages and Limitations of the various layouttypes (cont. - borrowed from Francis et. al.)

Selecting an appropriate layout


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Selecting an appropriate layout(borrowed from Francis et. al.)

Th d t t i


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The product-process matrix

Jumbled

flow (job

Shop)

Disconnected

line flow

(batch)

Connected

line flow

(assemblyLine)

Continuous

flow

(chemical

plants)

Process

type

Production

volume

& mix

Low volume,

low standardi-

zation

Multiple products,

low volumeFew major products,

high volume

High volume, high

standardization,

commodities

Commercial

printer

HeavyEquipment

Auto

assembly

Sugar

refinery

Void

Void

Cell formation in group technology:


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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 bysimilar processing requirements, and therefore, supported by the

same cell.

M1 M2 M3 M4 M5 M6 M7

P1 1 1 1

P2 1 1 1

P3 1 1

P4 1 1

P5 1 1

P6 1 1 1

M1 M4 M6 M2 M3 M5 M7P1 1 1 1

P3 1 1

P2 1 1 1

P4 1 1

P5 1 1

P6 1 1 1

Part-Machine Indicator Matrix


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Clustering Algorithms for Cellular Manufacturing

Row & Column Masking

M1 M2 M3 M4 M5 M6 M7

P1 1 1 1

P2 1 1 1

P3 1 1

P4 1 1

P5 1 1P6 1 1 1

M1 M4 M6 M2 M3 M5 M7

P1 1 1 1

P3 1 1

P2 1 1 1

P4 1 1

P5 1 1

P6 1 1 1


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Clustering Algorithms for Cellular Manufacturing:

Similarity Coefficients - Motivation

M1 M2 M3 M4 M5 M6 M7

P1 1 1 1

P2 1 1 1

P3 1 1

P4 1 1

P5 1 1P6 1 1 1

M1 M4 M6 M2 M3 M5 M7

P1 1 1 1

P3 1 1

P2 1 1 1

P4 1 1

P5 1 1

P6 1 1 1

1

1


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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


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A typical (logical) Organization of theProduction Activity in

Repetitive Manufacturing

Raw

Material

& Comp.

Inventory

Finished

Item

Inventory

S1,2S1,1 S1,n

S2,1 S2,2 S2,m

Assembly Line 1: Product Family 1

Assembly Line 2: Product Family 2

Fabrication (or Backend Operations)

Dept. 1 Dept. 2 Dept. k

S1,i

S2,i

Dept. j


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Synchronous Transfer Lines: Examples

(Pictures borrowed from Heragu)


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Flow Patterns for Product-focused Layouts(borrowed from Francis et. al.)

Discrete vs Continuous Flow and


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Discrete vs. Continuous Flow andRepetitive Manufacturing Systems

(Figures borrowed from Heizer and Render)


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Production Planning and

Scheduling

Dealing with the Problem Complexity


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Dealing with the Problem Complexitythrough 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 Procurementlead 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)

(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)


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Aggregate Planning


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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.

C ti th A t U it


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Computing the Aggregate UnitProduction Requirements

Washing machineModel Number

Required labor time(hrs)

Item demand as % ofaggregate demand

A5532 4.2 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


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Aggregate Planning Problem

Aggregate Planning

Aggregate

Unit Demand

Aggregate

Unit Availability

(Current Inventory

Position)

Aggregate

Production Plan

Required

Production Capacity

Aggr. UnitProduction 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


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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, trainingFC: Firing costs: e.g., compensation, social cost


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2.Varying Production Capacity with Constant Workforce:

D(t) P(t)

O(t)

PC WC OC UC

U(t)

S(t)

SC

W = constantS(t): Subcontracted quantities

O(t): Overtime levels

U(t): Undertime levelsCosts 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)


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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.

l i i


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4.Backlogging:

D(t) P(t)

B(t)

PC WC BC

W(t), O(t), U(t), S(t) = constant

B(t):Accumulated Backlog levelsCosts involved:

PC, WC:as before

BC:backlog (handling) costs: e.g., expediting costs, penalties, lost sales

(eventually), customer dissatisfaction

i l A l i S


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Typical Aggregate Planning Strategy

A mixture of the previously discussed pure options:

D

PC WC HC FC OC UC SC IC BC

PWHFOUS

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 stocksetc.

Io

Wo


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Solution Approaches

Graphical Approaches: Spreadsheet-based simulation Analytical Approaches: Mathematical (mainly linear

programming) Programming formulations


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A prototype problem

Forecasted demand:

Jan: 1280

Feb: 640

Mar: 900

Apr: 1200

May:2000Jun: 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: 26May: 22

Jun: 15

Cost structure:

Inv. holding cost: $80/unit x month

Hiring cost: $500/worker

Firing cost: $1000/worker


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A prototype problem (cont.)

Net predicted demand:

Jan: 780

Feb: 640

Mar: 900

Apr: 1200

May: 2000Jun: 2000

Forecasted demand:

Jan: 1280

Feb: 640

Mar: 900

Apr: 1200

May:2000Jun: 1400

On-hand Inventory:

500

Required on-hand

Inventory at end

of June:

600

A LP f l ti f th t t bl


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An LP formulation for the prototype problemProblem 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 workerCF = Firing cost per worker

CI = Inventory holding cost per unit per period

Problem Decision Variables

Ht = Workers hired at period tFt = 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

A LP f l ti f th t t bl


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An LP formulation for the prototype problem

)min(

6

1

6

1

6

1 ttI

t

tF

t

tH ICFCHC

s.t.

6,...,1,1 tFHWW tttt

6,...,1,)( tWcdPttt

6,...,1,1

tDPIItttt

6006 I6,...,1,0,,,, tIPFHW

ttttt

O ti l Pl f th id d l


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Optimal Plan for the considered example

Fire 27 workers in JanuaryHire 465 workers in May

Produce at full (labor) capacity every month

Resulting total cost:

$379320.900

Analytical Approach:


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y pp

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,(u_l_r)*Pt (s_d)*(w_d)t*Wt+Ot

t, Pt, Wt, Ot, Ht, Ft, St, It, Bt 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

Demand (vs. Capacity) Options or


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( p y) pProactive Approaches to

Aggregate Planning

Influencing demand variation so that it aligns to availableproduction capacity: advertising

promotional plans

pricing(e.g., airline and hotel weekend discounts, telecommunication

companies weekend rates)

Counter -seasonal product (and service) mixing: Developa 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 communicatedto the overall aggregate planning procedure as (expected)changes in the demand forecast.


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Disaggregation and

Master Production Scheduling

(MPS)


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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

CapacityConsts.

CompanyPolicies

EconomicConsiderations

ProductCharact.

Planning

Horizon

Time

unit

Capacity

Planning


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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:

Brew Ferm. Time

Pale Ale 2 weeks

Stout 3 weeks

Winter Ale 2 weeks

Summer Brew 2 weeks

Octoberfest 8-10 weeks

Example: Implementing the Empirical


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Example: Implementing the Empirical

Approach in Excel

# Fermentors: 1 Unit Cap: 200 Shelf Life: 20

Microbrewery Performance

Week 0 1 2 3 4 5 6 7 8 9 10

# Fermentors Req'd 0 0 0 0 0 0 0 0 0 0

Feasible Loading?

Min # Fermentors Req'd 2 2 2 2 2 2 2 2 2 2

Fermentor Utilization 0% 0% 0% 0% 0% 0% 0% 0% 0% 0%

Total Spoilage 0 0 0 0 0 0 0 0 0 0

Pale Ale Fermentation Time: 2

Week 0 1 2 3 4 5 6 7 8 9 10Demand 45 50 40 40 40 40 40 40 40 40

Scheduled Receipts 200

Fermentors Released 1

Inventory Spoilage

Inventory Position 100 255 205 165 125 85 45 5 -35 -40 -40

Net Requirements 35 40 40

Batched Net Receipts

Scheduled Releases

Fermentors Seized

Total Fermentors Occupied

Stout Fermentation Time: 3Week 0 1 2 3 4 5 6 7 8 9 10

Demand 35 40 30 30 40 40 40 40 50 50

Scheduled Receipts

Fermentors Released

Inventory Spoilage

Inventory Position 150 115 75 45 15 -25 -40 -40 -40 -50 -50

Net Requirements 25 40 40 40 50 50


Scheduled Releases

Fermentors Seized



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Computing Inventory Positions and

Net Requirements

Net Requirement:

NRi = abs(min{0, IPi})

Inventory Position:

IPi = max{IPi-1,0}+ SRi+BNRi -Di

(Material Balance Equation)

iDi

IPi

(IPi-1)+

SRi+BNRi

Problem Decision Variables:


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Scheduled Releases



Week 0 1 2 3 4 5 6 7 8 9 10

# Fermentors Req'd 0 0 0 0 0 1 1 0 0 0

Feasible Loading?



Total Spoilage 0 0 0 0 0 0 0 0 0 0


Week 0 1 2 3 4 5 6 7 8 9 10

Demand 45 50 40 40 40 40 40 40 40 40Scheduled Receipts 200


Inventory Spoilage

Inventory Position 100 255 205 165 125 85 45 5 165 125 85

Net Requirements

Batched Net Receipts 200

Scheduled Releases 200

Fermentors Seized 1

Total Fermentors Occupied 1 1


Demand 35 40 30 30 40 40 40 40 50 50

Scheduled Receipts

Fermentors Released

Inventory Spoilage

Inventory Position 150 115 75 45 15 -25 -40 -40 -40 -50 -50

Net Requirements 25 40 40 40 50 50


Scheduled Releases

Fermentors Seized



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Testing the Schedule Feasibility



Week 0 1 2 3 4 5 6 7 8 9 10

# Fermentors Req'd 0 1 1 1 0 1 2 1 1 0

Feasible Loading? NO



Total Spoilage 0 0 0 0 0 0 0 0 0 0


Week 0 1 2 3 4 5 6 7 8 9 10

Demand 45 50 40 40 40 40 40 40 40 40



Inventory Spoilage


Net Requirements



Fermentors Seized 1


Stout Fermentation Time: 3

Week 0 1 2 3 4 5 6 7 8 9 10

Demand 35 40 30 30 40 40 40 40 50 50

Scheduled Receipts

Fermentors Released

Inventory Spoilage


Net Requirements

Batched Net Receipts 200 200

Scheduled Releases 200 200

Fermentors Seized 1 1

Total Fermentors Occupied 1 1 1 1 1 1

Fixing the Original Schedule


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Fixing the Original Schedule



Week 0 1 2 3 4 5 6 7 8 9 10

# Fermentors Req'd 0 1 1 1 1 1 1 1 1 0

Feasible Loading?



Total Spoilage 0 0 0 0 0 0 0 0 0 0


Week 0 1 2 3 4 5 6 7 8 9 10

Demand 45 50 40 40 40 40 40 40 40 40



Inventory Spoilage


Net Requirements



Fermentors Seized 1



Week 0 1 2 3 4 5 6 7 8 9 10

Demand 35 40 30 30 40 40 40 40 50 50

Scheduled Receipts

Fermentors Released

Inventory Spoilage


Net Requirements





Infeasible Production Requirements


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Infeasible Production Requirements



Week 0 1 2 3 4 5 6 7 8 9 10# Fermentors Req'd 1 1 1 1 0 0 0 0 0 0

Feasible Loading?



Total Spoilage 0 0 0 0 0 0 0 0 0 0


Week 0 1 2 3 4 5 6 7 8 9 10

Demand 45 50 40 40 40 40 40 40 40 40



Inventory Spoilage

Inventory Position 100 55 205 165 125 85 45 5 -35 -40 -40



Scheduled Releases

Fermentors Seized

Total Fermentors Occupied 1


Week 0 1 2 3 4 5 6 7 8 9 10

Demand 35 40 40 40 40 40 40 40 50 50

Scheduled Receipts

Fermentors Released

Inventory Spoilage

Inventory Position 150 115 75 35 -5 160 120 80 40 -10 -50




Fermentors Seized 1

Total Fermentors Occupied 1 1 1

A feasible schedule with spoilage effects


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A feasible schedule with spoilage effects



Week 0 1 2 3 4 5 6 7 8 9 10

# Fermentors Req'd 1 1 1 1 1 0 1 1 1 0

Feasible Loading?



Total Spoilage 0 0 0 0 0 0 45 0 0 5


Week 0 1 2 3 4 5 6 7 8 9 10

Demand 45 50 40 40 40 40 40 40 40 40Scheduled Receipts 200


Inventory Spoilage 45


Net Requirements



Fermentors Seized 1



Demand 35 40 30 30 40 40 40 40 50 50

Scheduled Receipts

Fermentors Released

Inventory Spoilage 5


Net Requirements





Computing Spoilage and


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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)

i

Di

IPi

(IPi-1)+

SRi+BNRiSPi

The Driving Logic behind the Empirical Approach


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Demand Availability:Initial Inventory Position

Scheduled Receipts due toinitiated production or

subcontracting

Future inventoriesNetRequirements

Lot Sizing

ScheduledReleases

Resource (Fermentor)Occupancy Product i

FeasibilityTesting

Master Production Schedule

Schedule

Infeasibilities

ReviseProd. Reqs

Compute FutureInventory Positions


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Materials Requirements Planning

(MRP)


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The MRP Explosion Calculus

BOM

MRP

MPS

Current

Availabilities

Planned

Order Releases

Priority

Planning

LeadTimes

Lot Sizing

Policies

Example: The (complete) MRP Explosion


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p ( p ) pCalculus

Item BOM:

Alpha

C(2)D(2)

B(1) C(1)

E(1)

E(1)

F(1)

F(1)

Item Lead Time Current Inv. Pos.

Alpha 1 10

B 2 20

C 3 0

D 1 100

E 1 10

F 1 50

Gross Reqs for Alpha

Period 6 7 8 9 10 11 12 13

Gross Reqs. 50 50 100

Item Levels:

Level 0: Alpha Level 1: B Level 2: C, D Level 3: E, F



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Level 0

Level 1

Level 2

Level N

Initial

Inventories

ScheduledReceipts

External Demand

Capacity

Planning

Planned

Order ReleasesGross Requirements

Computing the item Scheduled Releases


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Computing the item Scheduled Releases

Item C

Period 1 2 3 4 5 6 7 8 9 10 11 12

Gross Requirements 12 10 90 75


Inventory Position: 20 20 40 40 40 40 28 18 18 -72 0 -75 0

Net Requirements 72 75

Planned Sched. Receipts 72 75

Planned Sched. Releases 72 75

Synthesizing

item demand

series

ProjectingInv. Positions

and

Net Reqs.

Lot SizingTime-

Phasing

ParentSched. Rel.

Item ExternalDemand

GrossReqs

ScheduledReceipts

InitialInventory

Safety StockRequirements

NetReqs

Lot SizingPolicy

PlannedOrderReceipts

Lead Time

PlanneOrderRelease

Some Lot Sizing Heuristics


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Economic Order Quantity (EOQ): Compute a lot size using theEOQ formula with the demand rate D set equal to the average ofthe 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 netrequirements for the subsequent T periods.

Silver-Meal (SM): Every time you start a new lot, keep addingthe net requirements of the subsequent periods, as long as theaverage (setup plus holding) cost per period decreases.

Least Unit Cost (LUC): Every time you start a new lot, keepadding 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 holdingcost matches the lot set up cost as much as possible.

C i Pl i (E l )


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Capacity Planning (Example)

Available

labor

hours

Periods1 2 3 4 5 6 7 8

50

100

150

Pegging and Bottom-up Replanning


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gg g p p g


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Shop floor-level

Production Control / Scheduling

G l P bl D fi iti


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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 forthe 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

W_q

W_2 W_i

W_M

W_1J_1

J_2

J_N

A modeling abstraction


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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 ajob 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 thematerial required for starting the job processing will beavailable.

E l


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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


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eas b e sc edu e a d ts Ga tt C a t

1

2

3

4

5

5 10 15 20

Machine

TimeJob 1 Job 2 Job 3 Job 4 Job 5

Performance-related job and schedule


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attributes

job completion time: C_j schedule makespan: max_j C_j

job lateness: L_j = C_j - d_j (notice that, by definition, joblateness can be either positive or negative - in which casethat 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 thejob 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, themore important the job)

P f C it i


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Performance Criteria

Job Attribute min total min weighted total min max min weighted max

Lateness S_j L_j S_j w_j*L_j max_j L_j max_j w_j*L_j

Tardiness S_j T_j S_j w_j*T_j max_j T_j max_j w_j*T_jFlow time S_j F_j S_j w_j*F_j max_j F_j max_j w_j*F_j

Tardy index NT

Completion S_j C_j S_j w_j*C_j max_j C_j max_j w_j*C_j

Schedule Performance Evaluation


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Schedule Performance Evaluation

Job d_j C_j F_j L_j T_j TI_j

1 17 15 15 -2 0 0

2 18 20 20 2 2 1

3 19 17 17 -2 0 0

4 17 18 18 1 1 1

5 20 18 18 -2 0 0

Total 88 88 -3 3 2

average 17.6 17.6 -0.6 0.6max 20 20 2 2

Problem variations


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Based on job routing:

job shop: each job has an arbitrary route

flow shop: all jobs have the same route, but different operationalprocessing times

re-entrant flow shop: some machine(s) is visited more than once by thesame 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 interruptedupon the arrival of a new job

non-preemptive: each machine must complete its currently running jobbefore switching to another one.

Based on the considered performance objective(s)

Solution Approaches


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pp

Analytical (Mixed Integer Programming) formulations:

Notoriously difficult to solve even for relatively smallconfigurations

Heuristics:

In thescheduling literature, the applied heuristics areknown as dispatching rules, and they determine the

sequencing of the various jobs waiting upon the differentmachines, 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


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Assembly Line Balancing

Synchronous Transfer Lines: Examples


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(Pictures borrowed from Heragu)

Balancing Synchronous Transfer Lines


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g y

Given:

a set ofmtasks, each requiring a certain (nominal) processingtime t_i, and

a set ofprecedence constraints regarding the execution of thesem tasks,

assign these tasks to a sequence ofk workstations, in a way that

the total amount of work assigned to each workstation does notexceed a pre-defined cycle time c, (constraint I)

theprecedence 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


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Heuristics for Assembly Line Balancing

Developed in classc.f. your class notes!

Production-rel-Decision-Making (1).ppt

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