Heuristic methods to consider rest allowance into assembly balancing problem

Proceedings,16th IFAC Symposium on Proceedings,16th IFAC Symposium on Information Control Problems in Manufacturing Proceedings,16th IFAC Symposium on Available online at www.sciencedirect.com Proceedings,16th IFAC Symposium on Information Control Problems in Manufacturing Proceedings,16th IFAC Symposium on Bergamo, Italy, June 11-13, 2018 Information Control Problems in Manufacturing Proceedings,16th IFAC Symposium on Information Control Problems in Manufacturing Bergamo, Italy, June 11-13, 2018 Information Control Problems in Manufacturing Bergamo, Italy, JuneProblems 11-13, 2018 Information Control in Manufacturing Bergamo, Italy, Italy, June 11-13, 11-13, 2018 Bergamo, Bergamo, Italy, June June 11-13, 2018 2018

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IFAC PapersOnLine 51-11 (2018) 669–674

Heuristic methods to consider rest allowance into assembly balancing problem Heuristic methods to consider rest allowance into assembly balancing problem Heuristic methods to consider allowance into assembly balancing problem Heuristic methods to to consider consider rest rest allowance into assembly assembly balancing balancing problem problem Heuristic methods to consider rest into assembly balancing problem Heuristic methods rest allowance allowance into

S. Finco*ˉ**, D. Battini*, X. Delorme**, A. Persona*, F. Sgarbossa* S. Finco*ˉ**, D. Battini*, X. Delorme**, S. D. Delorme**, A. A. Persona*, Persona*, F. F. Sgarbossa* Sgarbossa* S. Finco*ˉ**, Finco*ˉ**, D. D. Battini*, Battini*, X. X. S. X. Delorme**, Delorme**, A. A. Persona*, Persona*, F. F. Sgarbossa* Sgarbossa* S. Finco*ˉ**, Finco*ˉ**, D. Battini*, Battini*, X. Delorme**, A. Persona*, F. Sgarbossa* *Department of Management Engineering, University of Padova, Stradella San Nicola, 3 36100 Vicenza - Italy *Department of Management Engineering, University of Padova, Stradella San Nicola, 3 36100 Vicenza -- Italy *Department of Engineering, University of Stradella San Nicola, Vicenza Italy **Mines Saint-Étienne, LIMOS UMR CNRS 6158, 158 cours Fauriel, 42023 Saint-Étienne Cedex 2, France *Department of Management Management Engineering, University of Padova, Padova, Stradella SanSaint-Étienne Nicola, 3 3 36100 36100 Vicenza Italy *Department of Management Engineering, University of Padova, Stradella San Nicola, 3 36100 Vicenza --- Italy **Mines Saint-Étienne, LIMOS UMR CNRS 6158, 158 cours Fauriel, 42023 Cedex 2, France *Department of Management Engineering, University of Padova, Stradella San Nicola, 3 36100 Vicenza Italy **Mines Saint-Étienne, LIMOS UMR CNRS 6158, 158 cours Fauriel, 42023 Saint-Étienne Cedex 2, France **Mines Saint-Étienne, Saint-Étienne, LIMOS LIMOS UMR UMR CNRS CNRS 6158, 6158, 158 158 cours cours Fauriel, Fauriel, 42023 42023 Saint-Étienne Saint-Étienne Cedex Cedex 2, 2, France France **Mines **Mines Saint-Étienne, LIMOS UMR CNRS 6158, 158 cours Fauriel, 42023 Saint-Étienne Cedex 2, France Abstract: This study incorporates human energy expenditure and the related rest allowance into a SALBPAbstract: This study incorporates human factors energy expenditure and the into aa SALBPAbstract: This study incorporates energy expenditure and related rest allowance into SALBP2. During last impact of human the assembly linerelated designrest has allowance grown up and Abstract: Thisyears, studythe incorporates human factors energy on expenditure and the the related rest allowance into ergonomic SALBPAbstract: This study incorporates human energy expenditure and related rest allowance into aaaassembly SALBP2. During last years, the impact of the assembly line design has grown up and ergonomic Abstract: This studyskills, incorporates energy on expenditure and the the related rest allowance into SALBP2. During last years, the impact of human factors on the assembly line design has grown up and ergonomic restrictions, worker physical and psychological conditions have been considered in the 2. During last years, the impact of human factors on the assembly line design has grown up and ergonomic 2. During last years, the impact of human factors on the assembly line design has grown up and ergonomic restrictions, worker skills, physical and psychological conditions have been considered in the assembly 2. During last years, the the impact of human factors on theisconditions assembly line design has grown up and ergonomic restrictions, worker skills, physical and psychological have been considered in the assembly balancing. In this work, human energy expenditure applied. For this purpose, three heuristic methods restrictions, worker skills, physical and psychological conditions have been considered in the assembly restrictions, worker skills, physical and conditions have been considered in balancing. In this work, the human energy expenditure is applied. For this purpose, three heuristic methods restrictions, worker skills, physical and psychological psychological conditions have been considered in the the assembly assembly balancing. In this work, the human energy expenditure is applied. For this purpose, three heuristic methods are here proposed and compared in order to underline the effect of rest allowance in the balancing problem. balancing. In this work, the human energy expenditure is applied. For this purpose, three heuristic methods balancing. In this the human energy expenditure is For this purpose, three heuristic methods are here proposed and compared in order underline effect of rest allowance in the balancing balancing. Inexample this work, work, the human energy expenditure is applied. applied. For this purpose, three heuristicproblem. methods are here proposed and compared in order to underline the effect of rest allowance in the balancing problem. A numerical is used to show andto discuss the the differences between the three methods. are here proposed and compared in order to underline the effect of rest allowance in the balancing problem. are here proposed and compared in order to underline the effect of rest allowance in the balancing problem. A numerical example is used to show and discuss the differences between the three methods. are here proposed and is compared in order todiscuss underline the effect of between rest allowance in the balancing problem. A numerical example used to show and the differences the three methods. A example is used to show and discuss the differences between the three methods. © numerical 2018, IFAC (International of Automatic Hosting by Elsevier Ltd.Weights All rights reserved.Rest A numerical example is used to show discuss the differences between the methods. Keywords: SALBP-2, Heuristic Method, Ranked Positional Method, A numerical example isEnergy usedFederation toExpenditure, show and and discuss theControl) differences between the three three methods. Keywords: SALBP-2, Energy Expenditure, Heuristic Method, Ranked Positional Weights Method, Rest Keywords: SALBP-2, Energy Expenditure, Heuristic Method, Ranked Positional Weights Method, Allowance. Keywords: SALBP-2, Energy Expenditure, Heuristic Method, Ranked Positional Positional Weights Weights Method, Method, Rest Rest Keywords: SALBP-2, Energy Expenditure, Heuristic Method, Ranked Rest Allowance. Keywords: SALBP-2, Energy Expenditure, Heuristic Method, Ranked Positional Weights Method, Rest Allowance. Allowance. Allowance. Allowance. to-station assignment and assembly balancing. They included to-station assignment andinassembly assembly balancing. They included 1. INTRODUCTION AND BACKGROUND to-station They included also someassignment restrictionand term ofbalancing. operators’ ergonomic to-station assignment and assembly balancing. They included 1. INTRODUCTION AND BACKGROUND to-station assignment and assembly balancing. They included also some restriction in term of operators’ ergonomic 1. INTRODUCTION AND BACKGROUND to-station assignment andinassembly balancing. They included also some restriction term of operators’ ergonomic conditions. 1. INTRODUCTION AND BACKGROUND 1. INTRODUCTION AND BACKGROUND also some restriction in term of operators’ ergonomic Manual assembly lines are special flow-line production system also some restriction in term of operators’ ergonomic 1. INTRODUCTION AND BACKGROUND conditions. also some restriction in term of operators’ ergonomic conditions. Manual assembly lines are special flow-line production system conditions. In this work, we aim to analyse three different ways to Manual assembly are special production system (Scholl, 1999). lines They consistflow-line in several successive conditions. conditions. Manual assembly lines are special flow-line production system Manual assembly lines are special flow-line production system In this work, work, weexpenditure aim to to analyse analyse three differentmethod ways to to (Scholl, 1999). They consist in several several successive Manual assembly lines are special flow-line production system In this aim different ways integrate energywe withinthree a heuristic (Scholl, 1999). They consist in successive workstations in which manual assembly tasks are performed In this work, we aim to analyse three different ways to (Scholl, 1999). They consist in several successive In this work, we aim to analyse three different ways (Scholl, 1999). They consist in several successive integrate energy expenditure within a heuristic method to workstations in which manual assembly tasks are performed In this an work, weexpenditure aim analyse three differentmethod ways (Scholl, They inassembly several successive balance assembly line.toWe consider SALBP-2 as, in this energy within aaa heuristic to workstations in which manual assembly tasks are performed by skilled1999). operators. In aconsist manual line, human integrate integrate energy expenditure within heuristic method to workstations in which manual assembly tasks are performed integrate within aaaa heuristic method to workstations in assembly tasks are performed balance anenergy assembly line. We We to consider SALBP-2 as, energy in this this by skilled have operators. Inimpact manual assembly line, human integrate energy expenditure within heuristic method to workstations in which which manual assembly tasks are performed an assembly line. consider as, in way, there is the expenditure possibility evaluate the impact by skilled operators. In aaa manual line, human conditions a highmanual on theassembly final productivity. As balance balance an assembly line. We consider aa SALBP-2 SALBP-2 as, in this by skilled operators. In manual assembly line, human balance an assembly line. We consider SALBP-2 as, in this by skilled operators. In a manual assembly line, human way, there is the possibility to evaluate the impact energy conditions have a high impact on the final productivity. As balance an assembly line. We consider a SALBP-2 as, energy in this by skilled operators. In a manual assembly line,between human way, there is the possibility to evaluate the impact expenditure and the related rest allowance could have in the conditions have a high impact on the final productivity. As defined by Battini et al. (2011), there is a correlation way, there the possibility to evaluate the impact conditions have aa et high impact on the productivity. As way, there is is thethe possibility to allowance evaluate the impact energy conditions have high impact on the final productivity. As expenditure and the related rest allowance could haveenergy in the the defined by Battini Battini al.design (2011), there is final correlation between way, there is the possibility to evaluate impact energy conditions havesystem a et high impactand on the final productivity. As and related could have in final cycle time. In simple rest assembly linethe balancing 2 defined by al. (2011), there is aaaergonomics correlation between the assembly the level of expenditure expenditure and the related rest allowance could havetype in the the defined by Battini et al. (2011), there is correlation between expenditure and the related rest allowance could have in defined by Battini et al. (2011), there is a correlation between final cycle time. In simple assembly line balancing type 2 the assembly system design and the ergonomics level of expenditure and the related rest allowance could have in the defined by Battini et al. (2011), there is a correlation between final cycle time. In simple assembly line balancing type 2 (SALBP-2) the number of station is given and the objective the assembly system design and the ergonomics level of workstations. In the last years, a lot of researches have focused final cycle cycle time. time. In simple simple assembly line and balancing type 2 2 the assembly Insystem system design and the ergonomics level of final In assembly line balancing type the assembly design and the ergonomics level of (SALBP-2) the number of station is given the objective workstations. the last years, a lot of researches have focused final cycle time. In simple assembly line balancing type the assembly system design and the ergonomics level of (SALBP-2) the number of station is given and the objective function is to minimize the cycle time. Generally, SALBP-2 workstations. In last aa lot of have on the optimisation theyears, operator conditions at the (SALBP-2) the number of station is given and the objective2 workstations. In the theof last years, lotergonomic of researches researches have focused focused (SALBP-2) the number of station is given and the objective workstations. In the last years, a lot of researches have focused function is to minimize the cycle time. Generally, SALBP-2 on the optimisation of the operator ergonomic conditions at the (SALBP-2) theminimize number the ofofstation is given and of thean objective workstations. In theand last years, a(2017) lotergonomic of researches haveprovided focused leads to the maximization the production rate existing is to cycle time. Generally, SALBP-2 on the optimisation of the operator conditions at the workstation. Otto Battaïa have recently function is to minimize the time. Generally, SALBP-2 on the optimisation of the operator ergonomic conditions at the function function is to minimize the cycle time. Generally, SALBP-2 on the optimisation of operator ergonomic conditions at leads to the the maximization ofcycle the production rate of an an existing workstation. Otto and Battaïa (2017) have recently recently provided function is line to minimize the cycle time. Generally, SALBP-2 on the optimisation of the the operator ergonomic conditions at the the leads to maximization of the production rate of existing assembly (Scholl and Voß, 1997). These types of workstation. Otto and Battaïa (2017) have provided an overview of the existing optimization approaches to leads to the maximization of the production rate of an existing workstation. Otto and Battaïa (2017) have recently provided leads to the maximization of the production rate of an existing workstation. Otto and Battaïa (2017) have recently provided assembly line (Scholl and Voß, 1997). These types of an overview of the existing optimization approaches to leads to the maximization of the production rate of antypes existing workstation. Otto and Battaïa (2017) have recently provided assembly line (Scholl and Voß, 1997). These of problems are generally analyzed when there are changes in the an overview of the existing optimization approaches to assembly line balancing that consider physical ergonomic assembly line (Scholl and Voß, 1997). These types of an overview of the existing optimization approaches to assembly line (Scholl and Voß, 1997). These types of an overview of the existing optimization approaches to problems are generally analyzed when there are changes in the assembly line balancing that consider physical ergonomic assembly line (Scholl anddemand Voß, 1997). These types of an overview of the research, existing optimization to problems are generally when there changes in the production process or inanalyzed the of someare products. assembly line balancing that consider physical risks. Following their it is possible to approaches noteergonomic that there problems are generally analyzed when there are changes in the assembly line balancing that consider physical ergonomic problems are generally analyzed when there are changes in the assembly line balancing that consider physical ergonomic production process or in the demand of some products. risks. Following their research, it is possible to note that there problems are generally analyzed whenof there are changes intime the assembly line balancing that it consider physical ergonomic production process or in the demand some products. risks. Following their research, is possible to note that there are a lot of researches on which ergonomic risks are evaluated Through this work, we want to define the minimum cycle process or in the of some products. risks. Following their research, it is possible to note that there production production process or inwant the demand demand of some products. risks. Following their research, it is possible to that are lot of researches on which which ergonomic risks are evaluated evaluated Through this work, or wethe to time defineand thesome minimum cycle time production process in the demand of products. risks. Following their research, itergonomic is OCRA, possiblerisks to note note that there are aaa lot of researches on are through NIOSH, RULA, REBA, EAWS but there little Through this work, we want to define the minimum cycle time taking into account task the operator energy are lot of researches on which ergonomic risks are evaluated Through this work, we want to define the minimum cycle time are a lot of researches on which ergonomic risks are evaluated through NIOSH, RULA, REBA, OCRA, EAWS but little Through this work, we want to define the minimum cycle time taking into account the task time and the operator energy are a lot of researches on which ergonomic risks are evaluated through NIOSH, REBA, OCRA, EAWS but little attention is given toRULA, the energy expenditure method (EnerExp) Through thisaccount work, to wethe want to time define the minimum time taking into task the operator energy expenditure linked each task. Weand compare threecycle methods through NIOSH, RULA, REBA, OCRA, EAWS but little taking into account the task time and the operator energy through NIOSH, RULA, REBA, OCRA, EAWS but little attention is given to the energy expenditure method (EnerExp) taking into account the task time and the operator energy expenditure linked to each task. We compare three methods through NIOSH, RULA, REBA, OCRA, EAWS but little attention is given to the energy expenditure method (EnerExp) (Garg et al. 1978). EnerExp estimates metabolic rates for taking into account the task time and the operator energy that consider rest allowance in different manner. In this way it expenditure linked to each task. We compare three methods attention isal.given given to the the energy expenditure expenditure method (EnerExp) (EnerExp) linked to each task. We compare three methods attention to energy method (Garg et is 1978). EnerExp estimates metabolic rates for expenditure expenditure linked to We three methods that consider rest understand allowance in different manner.expenditure, In this this way in it attention is given to the energy expenditure method (EnerExp) (Garg et al. 1978). EnerExp estimates rates for material manual handling tasks and it metabolic considers different expenditure linked to each each task. task. We compare compare three methods is possible better the impact energy that consider rest allowance in different manner. In way it (Garg et al. 1978). EnerExp estimates metabolic rates for that consider rest allowance in different manner. In this way it (Garg et al. EnerExp estimates rates for material manual handling tasks and load it metabolic considers different that consider rest allowance in different manner. In this way it is possible better understand the impact energy expenditure, in (Garg et manual al.as1978). 1978). EnerExp estimates metabolic rates fora is material handling tasks and it considers different parameters workers, task duration, weight to name that consider rest allowance in different manner. In this way it term of restbetter allowance, couldthe have into the assembly balancing possible understand impact energy expenditure, in material manual handling tasks and it considers different is possible better understand the impact energy expenditure, in material manual handling tasks and it considers different parameters as workers, task duration, load weight to name a is possible better understand the impact energy expenditure, in term of rest allowance, could have into the assembly balancing material manual handling tasks and itfirst considers different parameters as workers, task duration, load weight to name a few. To the best of our knowledge the research focused is possible better understand the impact energy expenditure, in problem. Inallowance, order to minimize only time balancing with rest could into the assembly parameters workers, duration, load weight to name a term term of of rest rest allowance, could have have intothe thecycle assembly balancing parameters as workers, task duration, load weight to name few. Tointegration theas best ofbetween our task knowledge the first research focused term could into the assembly problem. Inallowance, order to minimize minimize only the cycle time with rest parameters asbest workers, task duration, load weight to name aa problem. few. the of our knowledge the first research focused on theTo EnerExp and assembly balancing term of of rest rest allowance, could have have into thecycle assembly balancing allowance considerations, we transform thebalancing energy In order to only the time with rest few. To the best of our knowledge the first research focused problem. In order to minimize only the cycle time with rest few. To the best of our knowledge the first research focused on the integration between EnerExp and assembly balancing problem. In order to minimize only the cycle time with rest allowance considerations, we transform the energy few. Tointegration the knowledge the first research focused allowance problem wasbest madeofbetween byour Gunther et al. (1983). After thisbalancing research on the EnerExp and assembly problem. In in order to minimize only the cycle with rest expenditure a rest allowance as defined bytime Price (1990). considerations, we transform the energy on the integration between EnerExp and assembly balancing allowance considerations, we transform the energy on the integration between EnerExp and assembly balancing problem was made by Gunther et al. (1983). After this research allowance considerations, we transform the energy expenditure in a rest allowance as defined by Price (1990). on the integration between EnerExp and assembly balancing problem was made by Gunther et al. (1983). After this research EnerExp has been considered by Battini et al. (2016) whom allowance considerations, we transform the energy Following what was defined by Price (1990), each operator has expenditure in a rest allowance as defined by Price (1990). problem was made by Gunther et et al.Battini (1983).etAfter After this research research expenditure in aawas rest allowance as defined by Price (1990). problem was made by Gunther (1983). this EnerExp has been considered byal. al. (2016) whom expenditure in rest allowance as defined by Price (1990). Following what defined by Price Price (1990), each operator has problem was made by Gunther et al.Battini (1983). After this research EnerExp has been considered by et al. (2016) whom proposed two different models. The first one is a multiexpenditure in a rest allowance as defined by Price (1990). an acceptable work level which could be considered equal to Following what was defined by (1990), each operator has EnerExp has been considered by Battini Battini et al. al. (2016) whom Following what was defined by Price (1990), each operator has EnerExp has been considered by et (2016) whom proposed two different models. The first one is a multiFollowing what was defined by Price (1990), each operator has an acceptable work level which could be considered equal to EnerExp has been considered by Battini et al. (2016) whom proposed two different models. The first one is a multiobjective model that minimizes EnerExp and the cycle time of Following what was defined by Price (1990), each operator has 4.3 kCal/min. In order to define the work level of each task or an acceptable work level which could be considered equal to proposed model two different different models. The first first onecycle is aa time multiacceptable work level which could be considered equal to proposed two models. The one is multiobjective that minimizes minimizes EnerExp and the of an an acceptable work level which could be considered equal to 4.3 kCal/min. In order to define the work level of each task or proposed two different models. The first onecycle is a time multiobjective model that EnerExp and the of the assembly line. The second one transforms energy an acceptable work level which the could be level considered to a4.3 set of tasks we use theto energy/time ratio as defined inequal Battini 4.3 kCal/min. In order define work of each task or objective model that minimizes EnerExp and the cycle time of kCal/min. In order to define the work level of each task or objective model that minimizes EnerExp and the cycle time of the assembly line. The second one transforms energy 4.3 kCal/min. In order to define the work level of each task or aetset set of tasks we use the energy/time ratio as defined in Battini objective model that time minimizes EnerExp and the cyclein time of a4.3 the assembly line. The second one transforms energy expenditure in a rest provided by Rohmert (1973) order kCal/min. In order to define the work level of each task or al. (2016). With this index we can understand, for the task of tasks we use the energy/time ratio as defined in Battini the assembly line. The second one transforms energy set of tasks we we usethis the index energy/time ratio as defined defined inthe Battini the assembly The second transforms energy expenditure in aa line. rest time time provided byone Rohmert (1973) in order aaaetset tasks use the energy/time as in Battini al.of (2016). With we can canratio understand, for task theobtain assembly line. Theprovided second one transforms energy to a single-objective model. Recently, a new in mixedexpenditure in by Rohmert (1973) order set of tasks we usethis the energy/time ratio as defined inthe Battini under consideration, if index the operator exceeds the for acceptable et al. (2016). With we understand, task expenditure in aa rest rest time provided by Rohmert (1973) in order et al. (2016). With this index we can understand, for the task expenditure in rest time provided by Rohmert (1973) in order to obtain a single-objective model. Recently, a new mixedet al. (2016). With this index we can understand, for the task under consideration, if the operator exceeds the acceptable expenditure in ahas restbeen timedeveloped provided by Rohmert (1973) in order to obtain a single-objective model. Recently, a new mixedinteger model by Battini et al. (2017) to et al. (2016). With this index we can understand, for the task work level or not. If this happens, it is necessary to evaluate under consideration, if the operator exceeds the acceptable to obtain aa single-objective model. Recently, aa al. new mixedunder consideration, if the operator exceeds the acceptable to obtain single-objective model. Recently, new mixedinteger model has been developed by Battini et (2017) to under consideration, if the operator exceeds the acceptable work level or not. If this happens, it is necessary to evaluate to obtain a single-objective model. Recently, a al. new mixedinteger model has been developed by Battini et (2017) to evaluate the ergonomic impact, in term of energy expenditure, under consideration, if the operator exceeds the acceptable the recovery time and in this way the total time of the task work level or not. If this happens, it is necessary to evaluate integer model has been impact, developed by Battini et al. (2017) to work level or not. If this it is necessary to evaluate integer model has developed by et (2017) to evaluate the ergonomic ergonomic in term term ofassembly energy expenditure, work level or not. If happens, it is necessary evaluate the recovery time and in happens, this the wayimpact the total time ofallowance the task task integer model has been been developed by Battini et al. al. (2017)and to the evaluate the impact, in of energy expenditure, in synchronised operations of theBattini line work levelWe ortime not. and Ifto this this happens, itthe is total necessary to evaluate increases. want evaluate of the restto recovery in this way time of the evaluate the ergonomic impact, in term of energy expenditure, the recovery time and in this way the total time of the task evaluate the ergonomic impact, in term of energy expenditure, in synchronised operations of the assembly line and the recovery time and in this way the total time of the increases. We want to evaluate the impact of the rest allowance evaluate the ergonomic impact, in term of energy expenditure, in synchronised operations the and supermarket area. Through theirof study it isassembly possible toline note that the recovery and inwe thisconsider wayimpact thethe total time ofallowance the task task on the cycle time when energy expenditure increases. We want to evaluate the of the rest in synchronised operations of the assembly line and increases. We want to evaluate the impact of the rest allowance in synchronised operations of the assembly line and supermarket area. Through Through their study it is isassembly possible to toline note that increases. We want to evaluate the impact the rest allowance on the to cycle time when we consider the of energy expenditure in synchronised operations of the and supermarket area. their study it possible note that integrated planning may reduce the ergonomic risks at increases. We want to evaluate the impact of the rest allowance linked a single task or a set of tasks. In fact, there is the on the cycle time when we consider the energy expenditure supermarketplanning area. Through Through their studythe it is isergonomic possible to to note that the cycle time when consider the energy expenditure supermarket area. their study it possible that integrated may number reduce risks at on on the cycle time when we consider the energy expenditure linked to a that single task orwe a aset set of tasks. tasks. In fact, thereenergy is the the supermarket area. their studythe it isergonomic possible note that workplaces and Through the of requiredto note workers integrated planning may reduce risks at on the to cycle time whenwith we consider the and energy expenditure possibility a task high time a small linked a single task or a of In fact, there is integrated planning may reduce the ergonomic risks at linked to aa that single task or aa aset of tasks. In fact, there is the integrated planning may reduce ergonomic risks at workplaces and the number of (2016) required workers linked to single task or set of tasks. In fact, there is the possibility a task with high time and a small energy integrated planning may reduce the the ergonomic risks at possibility workplaces and the number of required workers simultaneously. Akyol and Baykasoğlu minimized the linked to a single task or a set of tasks. In fact, there is the expenditure, thataadoes not require a rest allowance can balance that task with aa high time and aa small energy workplaces and the number of required workers possibility that task with high time and small energy workplaces and the number of required workers simultaneously. Akyol and Baykasoğlu (2016) minimized the possibility that a task with a high time and a small energy expenditure, that does not require a rest allowance can balance workplaces and the number of (2016) required workers simultaneously. Akyol and Baykasoğlu minimized the cycle time of the line considering simultaneously the workerpossibility that a task with a high time and a small energy aexpenditure, task that has a lower time but aaahigher energy expenditure, expenditure, that does require rest can simultaneously. and Baykasoğlu (2016) minimized the that does not not require rest allowance allowance can balance balance simultaneously. Akyol and (2016) the cycle time of of the theAkyol line considering considering simultaneously the workerworkerthat does require rest can aexpenditure, task that that has has lower time but aaaahigher higher energy expenditure, expenditure, simultaneously. Akyol and Baykasoğlu Baykasoğlu (2016) minimized minimized the aexpenditure, cycle time line simultaneously the that does not not require rest allowance allowance can balance balance task aaa lower time but energy cycle time of the line considering simultaneously the workera task that has lower time but a higher energy expenditure, cycle time of the line considering simultaneously the workera task that has a lower time but a higher energy expenditure, cycle time of the line considering simultaneously the worker- a task that has a lower time but a higher energy expenditure,

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S. Finco et al. / IFAC PapersOnLine 51-11 (2018) 669–674

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that requires rest allowance. In this way, we consider energy expenditure only if it is necessary and we avoid having a higher cycle time when it is not necessary. The first method, that is also the simplest one, consider ergonomic condition after the balancing phase while others two evaluate in a different way rest allowance during the task allocation phase. The remainder of this paper is composed of following sections. Section 2 presents the initial framework and the three-different method. The new heuristic method is described in paragraph 2.3. In section 3, the case study and final results are explained. Finally, in section 4, the conclusion and future researches are presented.

Rest

Allowance (Price, 1990) 0if ET(j)  4.3  (2) RA( j )   ET ( j )  4.3  4.3  1.86 otherwise  The Rest Allowance represents the percentage of recovery, in term of time, for an operator after performing a task and it is a way to consider the energy expenditure in the task time. Considering the RA, the final task time becomes: (3) t '( j )  t ( j )*(1  RA( j ))  j  1,.., n This value could be equal or larger than the initial task time t(j). For each task it is now possible to define these others two data: (4) • tp ' j  t '( j )  t '(h)

2. METHODS DESCRIPTION



In this section, three heuristic procedures for SALBP-2 are provided and compared. They are all based on the ranked positional weights method (RPW) concept and task energy expenditure, in term of rest allowance, is considered in different ways. The first method considers the task time without rest allowance to assign tasks to a workstation and in a second phase the total time of each workstation is calculated considering the total energy expenditure linked to the workstation. In the second method each task time is incremented by its rest allowance and then RPW procedure is applied. The third method evaluates the rest allowance and eventually the new total time of each station whenever a new task is assigned to the station under study, in this case rest allowance is associated to a set of tasks and not only to a single task.

•

hPj '

which is defined as the total time of all tasks that precede task j; tf ' j  t '( j )  t '(h) (5)



hF j '

which is defined as the total time of all tasks that follow task j. If the Rest Allowance is not considered into the task time formulas (4) and (5) become: tp j  t ( j )  t ( h) (6) • •

tf j

  t ( j)  

hPj '

hF j '

t ( h)

(7)

2.1 First method

As defined in Klein and Scholl (1996) solving SALBP-2 includes two main steps which have to be executed simultaneously. The first step is to determine the minimum cycle time and the second one is to assign the task to the station considering the cycle time defined in the first step. This procedure could be represented as an iterative procedure. For this reason, it is necessary to define a lower bound for the cycle time and start with this value the resolution of the balancing problem. In the sequel, a task-oriented procedure (Hackman et al., 1989) is proposed and tasks are ranked according to a descending positional weight. The aim is to minimize the cycle time considering both time and human energy expenditure of each task.

In this first model, we consider only the task time during the balancing phase while energy expenditure is considered in the last instance. As energy expenditure is not considered we consider (6) and (7) to determinate total time of all tasks that precede (resp. follow) task j.

We have a list of n tasks and m stations. For each task, the following data are noted: • task time [s], t(j); • human energy expenditure [kCal/s], e(j); Pj (resp. Fj ) : set of tasks which directly precede •

Step 1: Calculate (Scholl, 1999): E j (c) : earliest station of task j for cycle time c; -

•

In order to start the heuristic model, we define the Lower Bound as: n (8) LB1   max(max(t ( j );( t ( j )) / m))  j 1  



Initially, cycle time, c, is equal to LB1 and the following steps are executed:

-

L j (c) : latest station of task j for cycle time c;

-

SI j (c)   E j (c); L j (c)  : station interval of task j for

cycle time c; Step 2: List the tasks in increasing order of the E j (c) and

(follow) task j in the precedence graph; P ' j (resp. F ' j ) : set of all tasks which precede

descending order of tf j ;

(follow) task j in the precedence graph; Through these two sets of data it is possible to define, for each task, the following data: • Energy-Time Ratio (Battini et al, 2015), e( j ) (1) ET ( j )  *60 t ( j)

Step 3: Consider the set of available tasks for each workstation i=1,…,m. Initialize tsum (i)  0 which is the initial station time of the station i;

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Step 4: Assign to station i all tasks belonging to   { j  1,.., n | E j (c)=L j (c)} ;

The cycle time is incremented by 1 and the procedure is repeated until all tasks are assigned to a station avoiding cycle time violations.

Step 5: • Define tsum (i) 

2.3 Third method

•



j

t ( j)

Define Ii (c)  c  tsum (i)

(12)

This is a new heuristic approach to consider human energy expenditure and the related rest allowance directly into assembly line balancing problem. With this approach, initially, the cycle time is equal to LB1 defined in (17) and the following steps are executed:

(13)

Step 6: Assign the others available tasks to station i in decreasing order of their tf j value and repeat step 5 for each task assigned.

Step 1: Calculate:

Note that a new station is opened if Ii (c) becomes less or equal to 0 while the cycle time is increased by 1 and the algorithm is again executed in the following cases: Ii (c)  0 and there are some tasks which must be assigned to station i; Some tasks are not assigned to a station. The algorithm stops when every task is assigned to a station and for each station, Ii (c) is equal or greater than 0.

-

-

-

After this first phase for each station it is possible to define the ET value defined as follow: e ( j) j i (14) ET (i )  * 60 ti ( j )

 

  E ' j (c)  (t '( j )  t '( h)) / c  : (19)  h P j'   earliest station of task j for cycle time c;   L ' j (c)  m  1  (t '( j )  t '( h)) / c  (20)  h F j'   latest station of task j for cycle time c; SI ' j (c)   E ' j (c); L ' j (c)  : station interval of task j for cycle time c;





Step 2: List the tasks in increasing order of the E ' j (c) and descending order of tf ' j ; Step 3: Consider the set of available tasks for each workstation i=1,…,m. Initialize tsum (i)  0 and esum (i)  0 which are respectively the station time of the station i and the total energy expenditure of the station i;

j

In this way, RA(i) is calculated and the total time of station i becomes: tsum (i )if ET(i)  4.3 t ''sum (i )   (15) tsum (i ) *(1  RA(i )) otherwise

Step 4: First the tasks that have E ' j (c)  L ' j (c) are assigned to the station i;

In this model, a first cycle time is defined but it could not be the final cycle time. Indeed, if the energy/time ratio in a station is greater than 4.3 rest allowance is calculated and for this reason the total time of a station increases. In this way, the final cycle time becomes: (16) CT  max(c;max(t ''sum (i)))

Step 5: • Define tsum (i) 

 t ( j) (i)   e( j )

(21)

j

•

Define esum

•

Calculate ET(i) considering tsum (i ) and esum (i) ;

2.2 Second method

•

With this method, the energy expenditure is included directly in each task time through the rest allowance define in (2). In this way, each task time is equal to t '( j ) as defined in (3).

Calculate RA(i) and t ''sum (i)  tsum (i)*(1  RA(i))

•

Define the remaining available time of the station i as (24) Ii (c)  c  t ''sum (i)

the

new (23)

Step 6: Assigned the others available tasks to station i in decreasing order of their tf ' j value and repeat step 5 for each

The lower bound is defined as follow: n (17) LB2   max(max(t '( j );( t '( j )) / m    j 1 The initial cycle time, c, is equal to LB2 the define in (17). To assign a task to a station the same procedure used in Section 2.1 is used but in this case, there are some changes. The first one is linked to Step 1, as the calculation of the earliest and latest station considers t '( j ) . The second one is linked to step 5 as: (18) t 'sum (i)  t '( j )





(22)

j

task assigned. If there are some tasks not assign to a station the cycle time is increased by 1 and the algorithm stops when all tasks are associated with a station without exceeding cycle time. Through this model, there is a balancing between the energy expenditure of the tasks already assigned to a station and the available tasks. In step 5 tsum (i ) and esum (i) are calculated to evaluate ET step by step every time a task is assigned to a

j

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station. In this way, it is possible considering RA only in the case on which the ET value associated with the station is greater to 4.3. Following this method, the cycle time should be less or at least equal to the one obtained considering the two more-simple algorithms proposed in section 2.1 and 2.2.

4

In this section, a numerical example is presented. We consider the precedence graph and the task time presented in Battini et al. 2015. There are 17 tasks to perform in 4 stations. As explained before the aim of this paper is to propose a heuristic method for SALPB-2. For the energy expenditure value of each task, we consider the set of data shown in Fig. 1. The Energy-Time ratio, in this case, is equal to 4.45. In order to better understand the impact of ET on final results in section 3.4. is reported the cycle time obtained applying the three methods for different value of ET. A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

TIME [s]

24

46

13

7

25

15

5

38

11

80

85

25

60

65

45

25

16

4.45

0.37

0.52

2.82

1.78

0.96

1.85

0.82

1.85

3.41

4.82

3.34

1.85

1.19

ENERGY [kCal] 1.11

5.93 6.3

Table 3. Final cycle time with human energy expenditure considerations Station 1 2 3 4

Fig. 1. Input data 3.1 Data and results with the application of the first method

Table 1. Task times, total time of previous and following tasks

tp j

tf j

24 70 83 31 49 64 29 62 73 264 349 209 434 439 544 569 585

585 460 414 408 441 416 406 450 412 376 296 236 146 151 86 41 16

Assigned tasks A, B, H, E, F C, I, D, G, J, L K, N

esum

ET

RA

t ''sum

148

12.01

4.87

0.23

182.55

141

10.45

4.45

0.06

149.60

150

11.12

4.45

0.06

159.15

146

9.79

4.02

0

146

Table 4. Task time with rest allowance considerations

Table 2. Final assembly line balancing with RPW method Station 1 2 3

tsum

Through this method, we consider directly t’(j) as defined in (3) in the phase related to assigning a task to a station. Considering Table 4. the ET(j) value is calculated for each task and if it is greater than 4.3 the related Rest Allowance is defined. In this way, a new final time t'(j) is obtained as defined in (3). With the new task times, the initial cycle time is defined and also the t Pj and t F j for j=1,…,n.

t(j) (Table 1). In this case, the initial cycle time is equal to 147 seconds but only with c=150 seconds all tasks are assigned to a station in a correct way. Using the RPW method the final solution is presented in Table 2.

t(j) 24 46 13 7 25 15 5 38 11 80 85 25 60 65 45 25 16

Assigned tasks A, B, H, E, F C, I, D, G, J, L K, M N, O, P, Q

3.2 Data and results with the application of the second method

This procedure considers energy expenditure only in the last phase. In this model, t Pj , t F j and c are calculated considering

TASK A B C D E F G H I J K L M N O P Q

146

We consider the energy expenditure after the balancing. In fact, for each station, we define the total energy associated with a station and we calculated the new time of each station considering the rest allowance. Doing this, the final cycle time is greater or at least equal to the initial cycle time 150 seconds. In Table 3, the total time, total energy, rest allowance and new station time are proposed. In this case, the final cycle time is equal to 182.55 seconds.

3. NUMERICAL EXAMPLES AND DISCUSSION

TASK

M, O, P, Q

Task

t(j)

ET

RA

t’(j)

tp ' j

A B C D E F G H I J K L M N O P Q

24 46 13 7 25 15 5 38 11 80 85 25 60 65 45 25 16

2.78 5.80 1.71 4.45 6.76 7.12 11.57 2.93 4.45 4.45 4.45 4.45 3.41 4.45 4.45 4.45 4.45

0.00 0.62 0.00 0.06 1.01 1.15 2.98 0.00 0.06 0.06 0.06 0.06 0.00 0.06 0.06 0.06 0.06

24.00 74.33 13.00 7.43 50.23 32.32 19.89 38.00 11.67 84.88 90.18 26.52 60.00 68.96 47.74 26.52 16.98

24.00 98.33 111.33 31.43 74.23 106.55 43.89 62.00 73.67 355.75 445.93 297.39 532.45 541.42 649.16 675.69 692.66

tf ' j 692.66 509.12 434.79 429.22 504.34 454.12 441.68 471.46 433.46 395.27 310.39 246.73 151.24 160.21 91.24 43.50 16.98

The initial cycle time is equal to 174 seconds but it is not a sufficient time and some restrictions are violated, in particular, some tasks are not assigned to a station includes in the range

tsum 148 141 150

SI j (c) . 679

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It is necessary to increase it by one until 187 seconds which represents the minimum cycle time. With this cycle time, the solution is that one illustrated in Table 5. Table 5. Assembly line balancing applying the 2nd method Station 1 2 3 4

Assigned tasks A, B, E, H F, G, C, I, D, J L, K, N M, O, P, Q

t 'sum 186.56 169.19 185.67 151.24

Fig. 2. Earliest and latest station for each task with a cycle time equal to 180 s.

t ''sum 150.23 155.4 185.67 151.24

Table 6. Final solution with the third method proposed Station

3.3 Data and results with the application of the third model

1 nd

With this algorithm, the first steps are the same of the 2 algorithm. Initially, the cycle time is equal to 174 seconds, but some constraints are violated so it is necessary to increase the cycle time until 180 s to assign all tasks to a station. This cycle time represents also the minimum cycle time for this case with 4 stations. Fig. 2. reports E ' j (c) and L ' j (c) with c=180 seconds. Note

2 3 4

tsum

esum

ET

RA

t ''sum

133

10.23

4.61

0.13

150.23

131

10.38

4.75

0.19

155.4

170

11.57

4.08

0

170

151

11.20

4.45

0.06

160.21

3.4 Final results and discussion In Table 7, we list the final cycle time for each method defined above. With an ET=4.45 the best solution is given with the third method. The main difference with the other two methods is related to the definition of the rest allowance associated with a station. In the first method, rest allowance is calculated after the balancing phase for each station, while in the second one rest allowance is calculated for each task separately. In the third method rest allowance is evaluated each time a task is assigned to a station as a task could require a less energy expenditure than another one and in this way, it would be an automatic reduction of rest allowance into the station.

that task A must be assigned to station 1 as E '1 (180)  L '1 (180) ; the same procedure will be applied for task J that must be assigned to station 2 and tasks N, O, P, Q must be assigned to station 4. The other tasks are listed following an increasing order of E ' j (180) and a decreasing order of t 'F j at the same time. We explain step by step the procedure to assign tasks to a station only to the first station. For station 2, 3 and 4 the final results and the tasks assigned are reported in Table 6. The available tasks for station 1 are: A, B, E, H, F, G, C, I, D, they are listed following the order defined above. Task A is assigned directly to station 1 and tsum (1)  24 while esum (1)  1.10 . The next step evaluates the RA of the tasks assigned to the station. For this task, RA=0 as ET is less than 4.3. In this way ''(1) tsum  24 and Ii (c)  180  24 .

Table 7. Final comparison Methodology 1° method 2° method 3° method

Minimum cycle time [s] 182.55 185.67 170

As the last method is also the more difficult to apply it is necessary to understand if it gives always the best solution if compared with the other two methods. The third method requires a major computational time as for each task assigned is necessary evaluate the new rest allowance of the station.

As Ii (c) is greater than 0 we can assign another task to this station and we choose that one has a greater value of t F j , in this case, task B. With task B, tsum (1)  24  46 while esum (1)  1.10  4.39 . In this case, ET becomes equal to 4.77 and as it is greater than 4.3 it is necessary to increase the total time of the station by the rest allowance. For this instance, ''(1) RA=0.19 and tsum  83.38 .

In order to evaluate if the third method always gives the best solution, we have defined different energy expenditure value to obtain different ET value. We have created 18 scenarios in term of energy expenditure while the task time is always the same as the correlation between time and energy. To do this the initial set of energy expenditure has been incremented by a constant value included between [1.1; 2.5] with a step of 0.1. In this way we obtain different ET ratio and different solutions. As it is possible to note in Fig. 3. with different ET value the method that gives the best solution changes. In fact, for ET value lower than 4 the best solution is given by the first method, while for ET value greater than 4 the best solution is given by the third or the second method. In addition, for ET value greater than 5.2 the second and the third method give the same solution.

Following the same procedure tasks, E and H are assigned to station 1. After assigning task H the idle time of station 1 is 29.77. As task F is equal to 15 it is assignable to station 1, so tsum (1)  24  46  25  38  15

esum (1)  1.10  4.39  2.81  1.85  1.78 ,

Assigne d tasks A, B, E, H F, G, C, I, D, J L, K, M N, O, P, Q

ET(1)=4.86,

RA(1)=0.23 and t ''sum (1)  182.55 . In this case, t 'sum (1) is greater than c=180 so the last task must not assign to station 1 and it is necessary to open a new station. In Table 6 final results are reported.

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Battini, D., Delorme, X., Dolgui, A., & Sgarbossa, F. (2015). Assembly line balancing with ergonomics paradigms: two alternative methods. IFAC-PapersOnLine, 48(3), 586591. Battini, D., Delorme, X., Dolgui, A., Persona, A., & Sgarbossa, F. (2016). Ergonomics in assembly line balancing based on energy expenditure: a multi-objective model. International Journal of Production Research, 54(3), 824-845. Battini, D., Faccio, M., Persona, A., & Sgarbossa, F. (2011). New methodological framework to improve productivity and ergonomics in assembly system design. International Journal of industrial ergonomics, 41(1), 30-42. Garg, A., Chaffin, D. B., & Herrin, G. D. (1978). Prediction of metabolic rates for manual materials handling jobs. The American Industrial Hygiene Association Journal, 39(8), 661-674. Hackman, S. T., Magazine, M. J., & Wee, T. S. (1989). Fast, effective algorithms for simple assembly line balancing problems. Operations Research, 37(6), 916-924. Jaturanonda, C., Nanthavanij, S., & Das, S. K. (2013). Heuristic procedure for the assembly line balancing problem with postural load smoothness. International Journal of Occupational Safety and Ergonomics, 19(4), 531-541. Klein, R., & Scholl, A. (1996). Maximizing the production rate in simple assembly line balancing—a branch and bound procedure. European Journal of Operational Research, 91(2), 367-385. Otto, A., & Battaïa, O. (2017). Reducing physical ergonomic risks at assembly lines by line balancing and job rotation: A survey. Computers & Industrial Engineering. Otto, A., & Scholl, A. (2011). Incorporating ergonomic risks into assembly line balancing. European Journal of Operational Research, 212(2), 277-286. Price, A. D. (1990). Calculating relaxation allowances for construction operatives—Part 1: Metabolic cost. Applied ergonomics, 21(4), 311-317. Rohmert, W. (1973). Problems in determining rest allowances: part 1: use of modern methods to evaluate stress and strain in static muscular work. Applied ergonomics, 4(2), 91-95. Scholl, A., & Scholl, A. (1999). Balancing and sequencing of assembly lines. Heidelberg: Physica-Verlag. Scholl, A., & Voß, S. (1997). Simple assembly line balancing—Heuristic approaches. Journal of Heuristics, 2(3), 217-244.4.

Fig. 3. Comparison between the best solution obtained applying the three methods for different energy/time ratio values. 4. CONCLUSION Even if lot of research exist on the assembly line balancing, the integration between the necessary time to execute a manual operation and the related human energy expenditure still needs further investigation. In this paper, the authors define a new method to consider task time and the rest allowance (Price, 1990) if the energy expenditure of workers exceeds the recommended limit. The novelty of this approach is linked to the definition of the total time required to perform a set of tasks into a station. This new model has been compared with two more simple models to show the main differences in term of cycle time. The SALBP-2 is considered for this analysis and a numerical case study has been analyzed to better understand the goodness of the new method proposed. Through this work, it is possible to understand that the rest allowance (Price, 1990) for each station depends on task assignment and the related time and energy expenditure. At the same time, the energy/time ratio of all tasks can influence the conclusive results. Future researches will focus on the correlation between task time and task energy expenditure to evaluate the impact on the final results. An exact model could be developed in order to compare its solution, in term of cycle time, with that one of the heuristic approaches. Furthermore, further dataset will be analyzed to evaluate the robustness of the methods proposed and the impact of energy expenditure, in term of rest allowance, in the final cycle time. REFERENCES Akyol, S. D., & Baykasoğlu, A. (2016). ErgoALWABP: A multiple-rule based constructive randomized search algorithm for solving assembly line worker assignment and balancing problem under ergonomic risk factors. Journal of Intelligent Manufacturing, 1-12. Battini, D., Calzavara, M., Otto, A., & Sgarbossa, F. (2017). Preventing ergonomic risks with integrated planning on assembly line balancing and parts feeding. International Journal of Production Research, 1-21.

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