This Program is Presented This Program is Presented

as Oral Bulletin as Oral Bulletin

at XXV. National Conference at XXV. National Conference

on Operational Research/Industrial on Operational Research/Industrial Engineering Engineering

(OR/IE)(OR/IE)

( Koç University, July 4-6, 2005 )( Koç University, July 4-6, 2005 )

ARİF GÜRSOY, BELGİN VATANSEVERSCIENCE FAC., MATHS DEPART. COMP. SCIENCE,

MASTER STU.

PROF. DR. URFAT NURİYEVSCIENCE FAC., MATHS DEPART. COMP. SCIENCE,

ASSIST. PROF. MÜCELLA GÜNER

ENGINEERING FAC., TEXTILE ENGINEERING DEPART.

RESEARCH ASSIST. MURAT ERŞEN BERBERLERSCIENCE FAC., MATHS DEPART. COMP. SCIENCE

WITH LEAN MANUFACTURING COMPONENTSWITH LEAN MANUFACTURING COMPONENTS

PREPARING A MATHEMATICAL MODEL AND PREPARING A MATHEMATICAL MODEL AND A COMPUTER PROGRAM FOR LINE A COMPUTER PROGRAM FOR LINE

BALANCING PROBLEMBALANCING PROBLEM

THE AIM:THE AIM:

For line balancing in manufacturing,in order to

• Provide regular work flow,Provide regular work flow,

• Make idle times that may occur at workstations and Make idle times that may occur at workstations and cannot be removed , be at leastcannot be removed , be at least

determining the ideal production quantity.determining the ideal production quantity.

Line BalancingLine Balancing

Line balancing is the problem of assigning approximately the same Line balancing is the problem of assigning approximately the same amount of workload to each workstatition and reducing the idle time amount of workload to each workstatition and reducing the idle time to a minimal degree for smooth production.to a minimal degree for smooth production.

Lean ProductionLean Production

• Just-In-Time ProductionJust-In-Time Production

• Lean Manufacturing ComponentsLean Manufacturing Components– WorkerWorker– Cellular ProductionCellular Production– Synchronization Between Machines and WorkshopsSynchronization Between Machines and Workshops

PROCESS CHARTPROCESS CHART

Process chart is a diagram on which all Process chart is a diagram on which all tasks,control flow and material entry points in tasks,control flow and material entry points in process are indicated.process are indicated.

MANUFACTURING OPERATIONS OF TROUSERS-SKIRT MANUFACTURING OPERATIONS OF TROUSERS-SKIRT

PROCESS CHART FOR TROUSERS-SKIRTPROCESS CHART FOR TROUSERS-SKIRT

BIN and PACK NOTIONSBIN and PACK NOTIONS

Bin notion: Daily working time of a worker ( min. ) e.g. , 540 (+ overtime ) min.

Pack size notion: Required time for any production quantity

of any operation

For example;

1st pack’s size =Standart unit time of 1st operation * production

quantity

2nd pack’s size =Standart unit time of 2nd operation * production

quantity

Pack size of any operation changes according to production quantity; on the other hand,size difference between two packs at the same quantity

changes according to the standart unit times of operations which compose the packs.

GROUP CONCEPTGROUP CONCEPT

Group is the bin/bins that is filled by pack or packs.

If we consider a bin as a worker who has

daily working time + overtime;

a group consists of one or more workers.

If the group consists of two or more workers,required time for each operation is distributed equally to these

workers.

THE MATERIALTHE MATERIAL

Sewing department of garment company Sewing department of garment company

and trousers-skirt modal have chosen as material and trousers-skirt modal have chosen as material

of the problemof the problem..

THE METHODTHE METHOD• Line balancing is a planning problem and Line balancing is a planning problem and

most of the planning problems are in most of the planning problems are in NP-complete class.Bin Packing Problem NP-complete class.Bin Packing Problem (BPP) is also in NP-complete class.(BPP) is also in NP-complete class.

• BPPs are,in fact, the form of planning BPPs are,in fact, the form of planning problem obtained by reversing them.problem obtained by reversing them.

• BPP’s solution principles has considered for BPP’s solution principles has considered for the solution of line balancing problem.the solution of line balancing problem.

MATHEMATICAL MODAL OF THE MATHEMATICAL MODAL OF THE PROBLEMPROBLEM

and

( 1 )

operations’

required times ( std. unit time ); p is the production quantity and (T+t) is the maximum daily working time for a worker.

are

,

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( 2 )

• In this case,the goal is to minimize total In this case,the goal is to minimize total space in bins.space in bins.

• Operations have partial priority according to Operations have partial priority according to (1) ordering.(1) ordering.

• Another point is that capacities are flexible Another point is that capacities are flexible because of t variable.because of t variable.

• Let’s call BPP, defined like this, as Prior Let’s call BPP, defined like this, as Prior Group Bin Packing Problem (PGBPP).Group Bin Packing Problem (PGBPP).

( 3 )

( 4 )

( 5 )

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With these notations,mathematical modal for PGBPP becomes as follows;

( 15 )

In order to generate a synchronization between different

cells ; the most ideal value for all cells is chosen

from interval.

For this value, is determined, then it is written

in (5) and (10) formulas instead of . Thus,total idle time for determined assignment is assured.

Here ; is a variable, is the suggested plan,

is the flexibility constant and is the optimal solution.

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APPLICATION OF APPLICATION OF THE PROGRAMTHE PROGRAM