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This Program is Presented as Oral Bulletin at XXV. National Conference on Operational Research/Industrial Engineering (OR/IE) ( Koç University, July 4-6, 2005 )

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ARİF GÜRSOY, BELGİN VATANSEVER SCIENCE FAC., MATHS DEPART. COMP. SCIENCE, MASTER STU. PROF. DR. URFAT NURİYEV SCIENCE FAC., MATHS DEPART. COMP. SCIENCE, ASSIST. PROF. MÜCELLA GÜNER ENGINEERING FAC., TEXTILE ENGINEERING DEPART. RESEARCH ASSIST. MURAT ERŞEN BERBERLER SCIENCE FAC., MATHS DEPART. COMP. SCIENCE WITH LEAN MANUFACTURING COMPONENTS PREPARING A MATHEMATICAL MODEL AND A COMPUTER PROGRAM FOR LINE BALANCING PROBLEM

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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 cannot be removed, be at leastMake idle times that may occur at workstations and cannot be removed, be at least determining the ideal production quantity.

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Line Balancing Line balancing is the problem of assigning approximately the same amount of workload to each workstatition and reducing the idle time to a minimal degree for smooth production. Line balancing is the problem of assigning approximately the same amount of workload to each workstatition and reducing the idle time to a minimal degree for smooth production. Lean Production Just-In-Time ProductionJust-In-Time Production Lean Manufacturing ComponentsLean Manufacturing Components – Worker – Cellular Production – Synchronization Between Machines and Workshops

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

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MANUFACTURING OPERATIONS OF TROUSERS-SKIRT

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PROCESS CHART FOR TROUSERS-SKIRT

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BIN 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.

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GROUP 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.

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THE MATERIAL Sewing department of garment company and trousers-skirt modal have chosen as material of the problem.

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THE METHOD Line balancing is a planning problem and most of the planning problems are in NP-complete class.Bin Packing Problem (BPP) is also in NP-complete class.Line balancing is a planning problem and most of the planning problems are in NP-complete class.Bin Packing Problem (BPP) is also in NP-complete class. BPPs are,in fact, the form of planning problem obtained by reversing them.BPPs are,in fact, the form of planning problem obtained by reversing them. BPP’s solution principles has considered for the solution of line balancing problem.BPP’s solution principles has considered for the solution of line balancing problem.

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MATHEMATICAL MODAL OF THE PROBLEM 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, ( 2 )

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In this case,the goal is to minimize total space in bins.In this case,the goal is to minimize total space in bins. Operations have partial priority according to (1) ordering.Operations have partial priority according to (1) ordering. Another point is that capacities are flexible because of t variable.Another point is that capacities are flexible because of t variable. Let’s call BPP, defined like this, as Prior Group Bin Packing Problem (PGBPP).Let’s call BPP, defined like this, as Prior Group Bin Packing Problem (PGBPP).

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( 3 ) ( 4 ) ( 5 )

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( 6 ) ( 7 ) ( 8 ) ( 9 )

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( 10 ) ( 11 ) ( 12 ) ( 13 ) ( 14 ) With these notations,mathematical modal for PGBPP becomes as follows; ( 15 )

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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 THE PROGRAM

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