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Manoeuvres in manual person-to-parts order picking systems: Is there a significant influence on travel time and metabolic rates?
Proceedings of the 20th World Congress The International Federation of Congress Automatic Control Proceedings of the 20th World Proceedings of the 20th9-14, World Toulouse, France, July 2017 Available online at www.sciencedirect.com The International Federation of Congress Automatic Control The International of Automatic Control Toulouse, France,Federation July 9-14, 2017 Toulouse, France, July 9-14, 2017
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IFAC PapersOnLine 50-1 (2017) 6894–6899 Manoeuvres in manual person-to-parts order picking systems: Manoeuvres in manual person-to-parts order systems: IsManoeuvres there a significant influence on travel time andpicking metabolic rates? in manual person-to-parts order picking systems: Is there a significant influence on travel time and metabolic rates? Is there a significant influence on travel time and metabolic rates? Ralf Elbert*, Jan Philipp Müller*
Ralf Elbert*, Jan Philipp Müller* Ralf Elbert*, Jan Philipp Müller* *Department of Management and Logistics, Technische Universität Darmstadt, Hochschulstraße 1, 64289 Darmstadt, *Department ande-mail: Logistics, Technische Universität Darmstadt, Hochschulstraße 1, 64289 Darmstadt, Germany (Tel:of+49Management 6151 16 24430; [email protected]). *Department of Management and Logistics, Technische Universität Darmstadt, Hochschulstraße 1, 64289 Darmstadt, Germany (Tel: +49 6151 16 24430; e-mail: [email protected]). Germany (Tel: +49 6151 16 24430; e-mail: [email protected]). Abstract: In current planning models for travel time calculation in manual person-to-parts order picking Abstract: for travel calculation in manual person-to-parts order picking systems itIn is current assumedplanning that the models order picker travelstime at constant velocity through the warehouse. Curves and Abstract: In current planning models for travel time calculation in manual person-to-parts order picking systems it is assumed thatnecessary the order for picker travelsthe at aisles constant through the warehouse. turn manoeuvres that are changing arevelocity neglected in operating strategiesCurves so far. and For systems it is assumed that the order picker travels at constant velocity through the warehouse. Curves and turn necessary for changing aislesa are neglected operatingwould strategies far. For ordermanoeuvres pickers thatthat useare a cart for transporting thethe items more realisticinapproach be tosoconsider turn manoeuvres that are necessary for changing the aisles are neglected in operating strategies so far. For order pickers thatforuse a cart for transporting a more realistic approach be to consider additional time those manoeuvres due tothea items reduced gait velocity as well aswould additional physical order pickers that use a cart for transporting the items a more realistic approach would be to consider additional time those manoeuvres forces. due to The a reduced velocity as well as additional exposure due to for higher pushing/pulling paper atgait hand investigates if those influencesphysical should additional time for those manoeuvres due to a reduced gait velocity as well as additional physical exposure to higherinpushing/pulling forces. and The in paper at handevaluation investigates influences should be furtherdue deliberated travel time calculation ergonomic by ifthethose means of a simulation exposure due to higher pushing/pulling forces. The paper at hand investigates if those influences should be further in travel time calculation andwarehouse in ergonomic evaluation the means of aassignment simulation study. Firstdeliberated results show that especially for small dimensions andby random storage be further deliberated in travel time calculation and in ergonomic evaluation by the means of a simulation study. results show that especially for small warehouse dimensions random storage assignment policiesFirst warehouse operators could prefer heuristic routing policies and (combined/composite/traversal) study. First results show that especially for small warehouse dimensions and random storage assignment policies prefer heuristic routing policies (combined/composite/traversal) instead ofwarehouse the optimaloperators (minimal could travel distance) policy when taking curves/turn manoeuvers into account. policies warehouse operators could prefer heuristic routing policies (combined/composite/traversal) instead of the optimal (minimal travel distance) policy when taking curves/turn manoeuvers into account. Keywords: Order Picking; Ergonomics; factors; Operating Simulation instead the optimal (minimal travel distance) policy when takingstrategy; curves/turn manoeuvers account. © 2017,of IFAC (International Federation ofHuman Automatic Control) Hosting by Elsevier Ltd. All rightsinto reserved. Keywords: Order Picking; Ergonomics; Human factors; Operating strategy; Simulation Keywords: Order Picking; Ergonomics; Human factors; Operating strategy; Simulation In consequence ergonomic aspects should be considered in 1. INTRODUCTION In ergonomic aspects should be considered in the consequence layout design of the warehouse, in storage equipment In consequence ergonomic aspects should be considered in 1. INTRODUCTION the layoutand design the warehouse, in storage equipment INTRODUCTION also of in operating strategies which mainly deal Efficient warehouse1.operations play a crucial role for the decisions the layout design of the warehouse, in storage equipment and also in operating strategies which batching mainly deal Efficient warehouse operations a crucial role with assigning products to storage locations, of competitiveness of a supply chainplay in terms of costs as for wellthe as decisions Efficient warehouse operations play a crucial role for the decisions and also in operating strategies which mainly deal competitiveness of a supply chain in terms of costs as well as with assigning products to storage locations, batching of orders and order picker routing through the warehouse (de in terms of short lead times (Bartholdi and Hackman, 2014). competitiveness of a supply chain in terms of costs as well as with assigning products to storage locations, batching of order picker theofwarehouse (de Koster and et al., 2007). Therouting primarythrough objective the operating in terms of shortorder lead picking, times (Bartholdi and of Hackman, In this context the retrieval products2014). from orders in terms of short lead times (Bartholdi and Hackman, 2014). orders and order picker routing through the warehouse (de Koster etinal., 2007). The primary objective of the operating picker-to-parts-systems is the reduction of travel In this context ordercustomer picking, orders, the retrieval products from strategy storage for specific is of of great importance In this context order picking, the retrieval of products from Koster et al., 2007). The primary objective of the operating in order picker-to-parts-systems is the reduction of travel time since pickers spent on average 55 % of their time storage for specific50–75% customerof orders, of great importance since it constitutes the totalis operating costs for a strategy storage for specific customer orders, is of great importance strategy in picker-to-parts-systems is the reduction of travel since to, orderfrom pickers on average % of their time traveling andspent between the 55 storage locations since it warehouse constitutes(Petersen 50–75% of total2004). operating costs for a time typical andthe Aase, Approximately since it constitutes 50–75% of the total operating costs for a time since order pickers spent on average 55 % of their time from andAdditionally between the storage locations (Tompkinsto, et al., 2010). this high proportion of typical (Petersen and Aase, 2004). Europe Approximately 80 % ofwarehouse all order picking systems in Western are still traveling to, from and between the storage locations typical warehouse (Petersen and Aase, 2004). Approximately traveling (Tompkins al.,emphasizes 2010). Additionally this highofproportion of time et also that the analysis the physical 80 % of all order picking systems in Western Europe areorder still travel operated manually in a picker-to-parts-manner, where (Tompkins et al., 2010). Additionally this high proportion of 80 % of all order picking systems in Western Europe are still travel time also emphasizes that the analysis of the physical operated manually in a picker-to-parts-manner, where order pickers travel along the storage aisles (de Koster et al., 2007). exposure during traveling is highly important for improving operated manually in a picker-to-parts-manner, where order travel time also emphasizes that the analysis of the physical pickers systems travel along theadvantages storage aisles (de Koster et al., 2007). traveling is conditions. highly important for improving the overallduring physical working Those have regarding flexibility and exposure pickers travel along the storage aisles (de Koster et al., 2007). exposure during traveling is highly important for improving Those systems advantages regarding flexibility and the overall physical working conditions. investment costshave compared to automated systems but make overall physicalmodels working conditions. Those systems have advantages regarding flexibility and the Existing planning assume a constant velocity of the investment costs compared to automated systems but in make order picking to the most labour-intensive operation the planning assume constant velocity the investment costs compared to automated systems but make Existing order picker for models the travel timea calculation. Underof this planning models assume a constant velocity of the order picking the most labour-intensive warehouse, tooto(Roodbergen and Vis, 2009). operation in the Existing order picker for the travel time calculation. Under this condition travel time is a linear function of travel distance order picking the most labour-intensive warehouse, tooto(Roodbergen and Vis, 2009). operation in the order picker for the travel time calculation. Under this travel time a linearthe function of traveltodistance warehouse, too (Roodbergen Vis, 2009). and it is sufficient to is minimize latter variable ensure Therefore recent research andstresses the relevance of condition condition travel time is a linear function of travel distance it is possible sufficient travel to minimize variable to ensure shortest times the (de latter Koster et al., 2007). Therefore recent researchin stresses of and considering human factors the designtheof relevance order picking Therefore recent research stresses the relevance of and it is sufficient to minimize the latter variable to ensure shortest possible travel timesconsiderations (de Koster etinto al., account 2007). taking ergonomic considering human factors factors include in the design of order picking systems. Human physical, mental and However considering human factors in the design of order picking shortest possible travel times (de Koster et al., 2007). taking various factors can ergonomic influence theconsiderations velocity of theinto orderaccount picker. systems. Human factors includethatphysical, and However psychosocial working conditions influence mental the worker systems. Human factors include physical, mental and However taking ergonomic considerations into account factors can et influence thethey velocity ofgrouped the orderinto picker. According to Jung al. (2005) can be task psychosocial conditions influence the as worker health and theworking efficiency of orderthat picking systems well various psychosocial working conditions that influence the worker various factors can influence the velocity of the order picker. According Jungdirection et al. (2005) they can be grouped into task (e.g.toload, of motion, motion phases), design health and the2015). efficiency of orderis picking systems as work well factors (Grosse et al., An example the deviation from health and the efficiency of order picking systems as well According to Jung et al. (2005) they can be grouped into task load,cart direction of motion, motion phases), design of the (e.g. superstructure, wheels, handles), (Grosse et (so al., called 2015). maverick An example is the for deviation from work factors (e.g. schedules picking, example picking factors (e.g. load, direction of motion, motion phases), design (Grosse et al., 2015). An example is the deviation from work factors of thefactors cart (e.g. handles), schedules (so Glock called maverick picking, for example picking environment (e.g. superstructure, floors, slope, wheels, congestion) and wrong items, et al., 2016). Considering the physical schedules (so called maverick picking, for example picking factors of the cart (e.g. superstructure, wheels, handles), wrong items, Glock et al., 2016). Considering the physical environment factors (e.g. floors, slope, congestion) and operator factors (e.g. age, gender, anthropometry). Whereas working conditions ergonomics gain increasing attention. The wrong items, Glock et al., 2016). Considering the physical environment factors (e.g. floors, slope, congestion) and factors (e.g. age, anthropometry). design, environment and gender, operator factors are Whereas external working conditions ergonomics The operator manual material handling tasksgain in increasing warehousesattention. like lifting, working conditions ergonomics gain increasing attention. The operator factors (e.g. age, gender, anthropometry). Whereas environment and operator factors external constraints regarding operating strategies, task are factors have manual tasks likerisk lifting, carrying,material pushinghandling or pulling leadin towarehouses an increased for design, manual material handling tasks in warehouses like lifting, design, environment and operator factors are external task factors have almost beenregarding completelyoperating neglectedstrategies, in planning models so far. carrying, pushing or pulling lead to andisorders increased(Lavender risk for constraints order pickers to develop musculoskeletal carrying, pushing or pulling lead to an increased risk for constraints regarding operating strategies, task factors have order to develop musculoskeletal (Lavender et al., pickers 2012). 45.5 % of the workers in thedisorders EU-27 states report almost been completely neglected in planning models so far. completely in planning models so far. order pickers to develop musculoskeletal disorders (Lavender almost In orderbeen picking it couldneglected be beneficial to consider especially et al., 2012). % ofor the tiring workerspositions in the EU-27 states report working in 45.5 painful (Schneider and pickingand it could be beneficial to consider et al., 2012). 45.5 % of the workers in the EU-27 states report In theorder item weight the direction of motion in orderespecially to avoid working 2010). in painful or tiring positions and In order picking it could be beneficial to consider especially Irastorza, Ergonomic design of order (Schneider picking systems item weight and errors. the direction of approach motion infor order to avoid working in painful or tiring positions (Schneider and the systematic planning In a first considering Irastorza, 2010). Ergonomic design of order systems the item weight and the direction of motion in order to avoid cannot only improve physical conditions forpicking the workforce. systematic planning errors. first approach considering the item weight, Battini et In al.a (2015) showedfor that lot-sizing Irastorza, 2010). Ergonomic design of order picking systems cannot only improve conditions the workforce. Warehouse operatorsphysical can benefit fromfor higher worker systematic planning errors. In a first approach for considering the item weight, Battini et al. (2015) lot-sizing decisions for manual transportation (theshowed amountthat of items on a cannot only improve physical conditions the workforce. Warehouse operators can benefit fromfor higher availability and improved worker productivity asworker well the item weight, Battini et al. (2015) showed that lot-sizing decisions manual transportation (the in amount of items onarea cart per for tour) between two points a warehouse Warehouse operators can benefit from higher worker availability improved worker productivity as well decisions for manual transportation (the amount of items on a (Battini et al.,and 2011). per tour) between two points in a warehouse are availability improved worker productivity as well cart cart per tour) between two points in a warehouse are (Battini et al.,and 2011). (Battini et al., 2011).
Copyright © 2017, 2017 IFAC 7098Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © IFAC (International Federation of Automatic Control) Peer review©under of International Federation of Automatic Copyright 2017 responsibility IFAC 7098Control. Copyright © 2017 IFAC 7098 10.1016/j.ifacol.2017.08.1213
Proceedings of the 20th IFAC World Congress Toulouse, France, July 9-14, 2017 Ralf Elbert et al. / IFAC PapersOnLine 50-1 (2017) 6894–6899
dependent upon the cart load. Besides item weight the direction of motion can significantly influence the velocity of the order picker, too. During a tour through the warehouse one can define five different basic manoeuvres that the order picker can perform with the cart: pushing/pulling straight at constant velocity, accelerate from stop, decelerate for a stop, pushing/pulling a curve and turning around. For accelerating and decelerating a strictly monotonically increasing/decreasing velocity would be more realistic whereas for each a curve/turn manoeuvre an additional amount of time could be assumed. In various talks warehouse operators mentioned repeatedly that according to their impression especially curves and turn manoeuvres are not sufficiently considered in storage assignment and routing policies so far. Certain combinations lead to a higher number of curves and turn manoeuvres which is not reflected by an adequate additional time. An example is the combination of a return routing policy, where the order picker travels back in each aisle, and a classed-based ABC horizontal storage assignment policy, where the most frequently demanded items are stored across the aisles next to the depot (de Koster et al., 2007). Those policies could result in systematically higher travel times in practice because the order picker must turn around in each aisle. In contrast a traversal routing policy does not provide for turn manoeuvres when traveling between the pick locations (Bartholdi and Hackman, 2014). Considering specific manoeuvres cannot only improve the accuracy of travel time calculation. Regarding ergonomic evaluations they also affect the physical exposure and in this relation the metabolic rates of order pickers during their tours. The metabolic rate is the human energy expenditure per time unit (kcal/min) that is necessary for executing a predefined manual handling task (Garg et al., 1978). It provides an objective measurement for physical exposure and the resulting fatigue level. The metabolic rate is on the one hand determined by the travel distance but on the other hand push/pull forces between order picker and cart impact the metabolic rate as well. Those forces reach peak values in the starting phase when accelerating a cart (Jung et al., 2005) and can be significantly higher when pushing/pulling a turn compared to pushing/pulling straight (Jansen et al., 2002). The research gap addressed in the paper at hand is therefore to analyse the impact of curves and turn manoeuvres on travel time and on physical exposure. It is assumed that for travel time calculation the additional time for curves/turn manoeuvres and the warehouse dimensions (length of aisles, distance of aisles) determine the accuracy of the current calculation procedure based on constant velocity. Especially for small warehouse dimensions and high additional times for curves/turn manoeuvres (e.g. due to carts difficult to manoeuvre) the impact of travel length could be low compared to the time spent for pushing/pulling curves and turning around. In consequence warehouse operators might prefer different combinations of routing and storage assignment policies. Since prior research does not provide sufficiently valid information regarding additional time for curves/turn manoeuvres the aim here is to conduct a
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parameter study for answering the first research question (RQ): RQ 1:
For which parameter values regarding additional time for curves/ turn manoeuvres and warehouse dimensions (length of aisles, distance of aisles) warehouse operators should prefer different storage assignment and routing policies because they provide shorter travel times when curves and turn manoeuvres are considered in travel time calculation?
For ergonomic evaluation the metabolic rates are of special interest. They directly affect the rest allowance (Price 1990) and therefore worker productivity as well since the necessary break time increases for tours with high metabolic rates. Therefore the second RQ is as follows: RQ 2:
Which storage assignment and routing policies warehouse operators should prefer when taking the metabolic rates as an indicator for physical exposure into account?
In this aspect the ratio of hand forces when pushing/pulling a turn and when pushing/pulling straight is a decisive parameter since it determines the contribution of curves/turning around to the overall physical exposure of the tours. In lack of reliable values metabolic rates will analysed under variation of this parameter as well. 2. SIMULATION STUDY For the parameter study we analyse a picker-to-parts-system in a warehouse with rectangular layout with a single picker operation by the means of an agent-based simulation study. Rectangular layouts are frequent in real-world warehouses (Bartholdi and Hackman, 2014). Agent-based simulation is well suited to investigate complex, weakly structured systems and enables the researcher to conduct systematic parameter studies (Bonabeau 2002). During a tour the order picker visits every position on the pick list to retrieve the requested items until the order has been completed and he can return to the depot. The order of the items on the pick list is determined by the routing policy. A picking cart is used for transport. For this systems the total amount of time for a tour 𝑖𝑖 (𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡,𝑖𝑖 ) can be calculated as the sum of travel time of tour 𝑖𝑖 (𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡,𝑖𝑖 ) and time for searching and picking the items (𝑡𝑡𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝,𝑖𝑖 ). For the latter a constant time for each item is assumed. The travel time can be derived as follows: 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡,𝑖𝑖 = 𝑡𝑡𝑠𝑠,𝑖𝑖 + 𝑛𝑛𝑐𝑐,𝑖𝑖 ∙ ∆𝑡𝑡𝑐𝑐 + 𝑛𝑛𝑡𝑡,𝑖𝑖 ∙ ∆𝑡𝑡𝑡𝑡
(1)
whereby 𝑡𝑡𝑠𝑠,𝑖𝑖 is the travel time for pushing/pulling straight in tour 𝑖𝑖, ∆𝑡𝑡𝑐𝑐 , ∆𝑡𝑡𝑡𝑡 is a constant additional amount of time for each curve/turn manoeuvre resp. and 𝑛𝑛𝑐𝑐,𝑖𝑖 , 𝑛𝑛𝑡𝑡,𝑖𝑖 are the number of curves/turn manoeuvres in tour 𝑖𝑖 resp. A curve includes the phase of deceleration before the actual turn and the phase of acceleration afterwards for reaching a constant velocity 𝑣𝑣 again. Therefore ∆𝑡𝑡𝑐𝑐 is the additional amount of time for the curve length compared to a situation where the curve would be travelled with a constant velocity 𝑣𝑣. For turn manoeuvres it is assumed that the order picker does not cover any distance during this manoeuvre. The modelling approach with
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Proceedings of the 20th IFAC World Congress 6896 Ralf Elbert et al. / IFAC PapersOnLine 50-1 (2017) 6894–6899 Toulouse, France, July 9-14, 2017
constant additional amounts of time represents a simplified consideration of curves/turn manoeuvres for this first analysis of the topic. Various further influences on the velocity of the order picker like item weight, construction and manoeuvrability of the cart or anthropometry of the order picker are neglected and deemed to be subject of future research. Under consideration of the constant velocity 𝑣𝑣 of the order picker the value for 𝑡𝑡𝑠𝑠,𝑖𝑖 can be calculated based on the travel distance 𝑠𝑠𝑖𝑖 of tour 𝑖𝑖 which is the sum of the distance between depot and storage location of the first item to pick 𝑠𝑠𝑑𝑑,1,𝑖𝑖 , the sum of the distances between the consecutive items 𝑗𝑗 to pick in the tour 𝑠𝑠𝑗𝑗,𝑗𝑗+1,𝑖𝑖 and the distance between the last item to pick and the depot 𝑠𝑠𝐽𝐽,𝑑𝑑,𝑖𝑖 : 𝑡𝑡𝑠𝑠,𝑖𝑖 =
𝑠𝑠𝑖𝑖 𝑣𝑣
combination of routing policy and storage assignment policy together with warehouse dimension (63 in total) we simulate 1000 tours. Regarding storage assignment the three policies random storage, ABC vertical and ABC horizontal storage are analysed. Regarding order picker routing six heuristic policies that are frequently used in practice (return, traversal, midpoint, largest gap, composite, combined policy) and the optimal routing policy are considered. The optimal policy determines a tour with minimal travel distance by solving a special form of a Travelling Salesman Problem (for a detailed description of storage assignment and routing policies please refer to de Koster et al. 2007). For reasons of simplicity it is assumed that additional time for turn manoeuvres is twice as high as additional time for curves. Order lists are created using a random number generator.
𝐽𝐽
=
𝑠𝑠𝑑𝑑,1,𝑖𝑖 +∑𝑗𝑗=1 𝑠𝑠𝑗𝑗,𝑗𝑗+1,𝑖𝑖 +𝑠𝑠𝐽𝐽,𝑑𝑑,𝑖𝑖 𝑣𝑣
Table 1. Parameter values for the simulation study
(2)
Velocity of order picker 𝑣𝑣 Constant pick time for each item Number of items per tour 𝐽𝐽 Item weight Warehouse layout Warehouse capacity
Regarding the ergonomic evaluation for calculating the metabolic rate of traveling 𝐸𝐸̇𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡,𝑖𝑖 (kcal/min) of a tour 𝑖𝑖 the respective net metabolic cost ∆𝐸𝐸𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡,𝑖𝑖 (kcal) must be determined first. The net metabolic costs describe the absolute value of human energy expenditure (additionally to the basal metabolic rate) for traveling during a tour. The metabolic rate for traveling can then be calculated by dividing 𝐸𝐸𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡,𝑖𝑖 by the travel time 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡,𝑖𝑖 and adding the basal metabolic rate. The net metabolic costs for traveling can be calculated as follows, whereby the equation for pushing/pulling at bench height according to Garg et al. (1978) is used:
Warehouse dimensions
Routing policies
∆𝐸𝐸𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡,𝑖𝑖 = 𝑒𝑒𝑠𝑠 (𝑤𝑤, 𝑔𝑔, 𝐹𝐹) ∙ 𝑠𝑠𝑖𝑖 + 𝑒𝑒𝑐𝑐 (𝑤𝑤, 𝑔𝑔, 𝑠𝑠𝑐𝑐 , 𝑓𝑓 ∙ 𝐹𝐹) ∙ 𝑛𝑛𝑐𝑐,𝑖𝑖 + +𝑒𝑒𝑡𝑡 (𝑤𝑤, 𝑔𝑔, 𝑠𝑠𝑤𝑤 , 𝑓𝑓 ∙ 𝐹𝐹) ∙ 𝑛𝑛𝑡𝑡,𝑖𝑖 (3)
Storage assignment Item classes for ABC storage assignment policies (share of picking frequency, share of number of items) Body weight of order picker 𝑤𝑤 Gender of order picker Constant force for pushing/pulling straight 𝐹𝐹 curve distance 𝑠𝑠𝑐𝑐 turn manoeuvre distance 𝑠𝑠𝑡𝑡 Factor for additional force in curves/turn manoeuvres Additional time for curve ∆𝑡𝑡𝑐𝑐 Additional time for turn manoeuvre ∆𝑡𝑡𝑤𝑤
The first part accounts for pushing/pulling straight, the second part for curves and the last part for turn manoeuvres. 𝑒𝑒𝑠𝑠/𝑐𝑐/𝑡𝑡 are constant parameters dependent on body weight, gender of the operator 𝑔𝑔, pushing/pulling force 𝐹𝐹, curve distance 𝑠𝑠𝑐𝑐 , and turn manoeuvre distance 𝑠𝑠𝑤𝑤 . Furthermore we assume a factor 𝑓𝑓 that account for the additional necessary pushing/puling forces for curves/turn manoeuvres (for reasons of simplicity we use an equal factor for curves and turn manoeuvres). The metabolic cost for pushing/pulling straight increases linearly in travel distance 𝑠𝑠𝑖𝑖 . The metabolic cost for curves/turn manoeuvres increase linearly in their numbers and factor 𝑓𝑓. The overall impact of curves and turn manoeuvres on travel time and on energy expenditure can be captured by considering the rest allowance 𝑅𝑅𝐴𝐴𝑖𝑖 for a tour 𝑖𝑖. According to Price (1990) 𝑅𝑅𝐴𝐴𝑖𝑖 is a function of the overall metabolic rate 𝐸𝐸̇𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡,𝑖𝑖 (kcal/min) of a tour. Besides 𝐸𝐸̇𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡,𝑖𝑖 this value additionally includes the metabolic rate for picking 𝐸𝐸̇𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝,𝑖𝑖 which is assumed to be constant for each tour and calculated according to Garg et al. (1978). The total time for a tour including the rest allowance then becomes: 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡,𝑖𝑖,𝑅𝑅𝑅𝑅 = 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡,𝑖𝑖 (1 + 𝑅𝑅𝐴𝐴𝑖𝑖 )
(4)
The parameter values for the simulation study are summarized in Table 1. Warehouse dimensions are scaled to “small”, “medium”, or “large”, resp. For each possible
0.75 m/s 20 s 20 0.2 kg Rectangular, 10 aisles 1000 items Small, medium, lager (aisle length 25m, 50m, 100m; aisle distance 3m, 6m, 12m) return, traversal, midpoint, largest gap, composite, combined, and optimal policy (see de Koster et al., 2007) Random, ABC vertical, ABC horizontal (see de Koster et al., 2007) A-items (80%, 20%) B-items (15%, 30%) C-items (5%, 50%) 𝑤𝑤 = 75 kg male 𝐹𝐹 = 3.5 kg 𝑠𝑠𝑐𝑐 = 3 m 𝑠𝑠𝑡𝑡 = 1.5 m variable, 𝑓𝑓 ≥ 1 variable, ∆𝑡𝑡𝑐𝑐 ≥ 0 ∆𝑡𝑡𝑤𝑤 = 2 ∙ ∆𝑡𝑡𝑐𝑐
3. RESULTS 3.1 Evaluation of travel time ̅ Based on the simulation results the mean travel times 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 of the tours for all three warehouse dimensions in relation to storage assignment and routing policies are calculated. For the parameter study additional time for curves/turn manoeuvres is varied. Fig. 1 shows the mean travel times for small warehouse dimensions (for random storage and ABC vertical storage). Zero additional time represents travel time calculations completely neglecting curves and turn manoeuvres and only taking the travel distance into account
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as usual in existing planning models. The mean travel time is linearly increasing in additional time for curves/turn manoeuvres. The gradient is determined by the mean number of curves/turn manoeuvres in a tour (see eq. 1). Warehouse dimension small and random storage assignment
Mean travel time 𝒕𝒕̅ 𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕 [s]
800 700
500 400 300 2
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Additional time for curve ∆𝒕𝒕𝒄𝒄 [s] return largestGap optimal
traversal composite
manoeuvres underlies this result. The optimal policy reaches minimal travel distances at the expense of a higher number of curves and turn manoeuvres compared to several heuristic policies (see Table 2). For random storage the number of curves of the optimal policy is 10.03 % higher than for the composite policy. For the ABC vertical storage it is 5.38 % higher compared to the return policy and for ABC horizontal storage assignment it is 1.75 % higher compared to the return or traversal policy, resp. For random and ABC horizontal storage the number of curves for all routing policies is significantly higher than for the ABC vertical storage (e.g. for the optimal policy 86.03%, and 73.60 %, resp.). This is due to a reduced number of aisles the order picker must visit when practicing ABC vertical storage, because the frequently demanded items are stored in a few number of aisles. Furthermore this leads to a significantly lower number of turn manoeuvres, too (for the optimal policy 55.65 % lower compared to random storage and 65.10 % lower compared to ABC horizontal storage).
600
0
midpoint combined
Table 2. Mean travel time for ∆𝒕𝒕𝒄𝒄 = 𝟎𝟎, mean number of curves, and mean number of turn manoeuvres in relation to routing and storage assignment policy routing policy
Warehouse dimension small and ABC vertical storage assignment
Mean travel time 𝒕𝒕̅𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕 [s]
450
return traversal midpoint largest gap composite combined optimal
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Additional time for curve ∆𝒕𝒕𝒄𝒄 [s] return largestGap optimal
traversal composite
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midpoint combined
Fig. 1. Mean travel time for small warehouse dimensions in relation to storage assignment and routing policy, varying additional time for curves/turn manoeuvres For zero additional time of course the optimal routing policy ensures the shortest travel time whereby the combined and composite policies are the best performing heuristic solutions. For each combination of storage assignment and routing policy there is a lower bound from which the optimal routing policy does not provide the shortest travel times anymore (∆𝑡𝑡𝑐𝑐 = 3.90 s for random storage, ∆𝑡𝑡𝑐𝑐 = 5.83 s for ABC vertical storage, and ∆𝑡𝑡𝑐𝑐 = 9.78 s for ABC horizontal storage, not shown in fig.1). For random and ABC vertical storage the combined policy, for ABC horizontal storage the traversal policy results in lower travel times than the optimal policy. The optimal policy only considers the travel distance. Up from a certain value of ∆𝑡𝑡𝑐𝑐 the influence of curves and turn manoeuvres on travel time is so high that a minimal travel distance does not ensure minimal travel times as well. A comparison of mean number of curves and turn
return traversal midpoint largest gap composite combined optimal return traversal midpoint largest gap composite combined optimal
Mean travel Mean number Mean number time for of curves of turn ∆𝒕𝒕𝒄𝒄 = 𝟎𝟎 [s] 𝒏𝒏𝒄𝒄 ̅̅̅ manoeuvres ̅̅̅ 𝒏𝒏𝒕𝒕 storage assignment: random 459.51 17.64 8.82 373.34 17.64 0.50 356.06 23.87 10.51 340.18 21.64 8.85 345.82 17.55 2.52 331.06 17.64 3.16 300.83 19.31 6.20 storage assignment: ABC vertical 268.38 9.85 4.92 213.27 10.01 0.49 232.29 13.34 5.72 219.92 12.44 4.47 201.09 9.98 1.24 193.20 9.98 1.53 176.63 10.38 2.75 storage assignment: ABC horizontal 230.61 17.71 8.85 361.36 17.71 0.51 267.59 19.08 8.43 266.47 18.87 7.43 225.12 17.80 7.83 224.46 17.77 7.84 214.12 18.02 7.88
In summary the ABC vertical storage is the most preferable policy regarding travel times since it combines short travel distances (for the optimal policy 41.28 % lower compared to random storage and 17.51 % lower compared to ABC horizontal storage) and low additional time for curves/turn manoeuvres. The traversal routing policy provides the lowest possible number of turn manoeuvres throughout all storage assignment policies. In this case the order picker must only turn in 50 % of the tours after the last pick when being
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For medium and large warehouse dimensions in general the same findings can be derived. However the lower bounds from which other routing policies result in shorter travel times increase proportionally in warehouse dimensions since curves/turn manoeuvres contribute a constant amount to the overall travel time. Only for medium warehouse dimension and random storage assignment this lower bound lies in a range that is assumed to be realistic for real-world warehouse operations (∆t c = 7.80 s).
expenditure) that is determined by the number of curves/turn manoeuvres routing policies that focus on minimal travel distances (like the optimal policy) can increase metabolic rates (as energy expenditure per time unit) by a further effect: The comparable less physical demanding parts of pushing/pulling straight are shorter so that curves and turn manoeuvres must be completed in shorter time intervals. In total this relationship can cause a higher overall exposure. Warehouse dimension small and random storage assignment 9
̅̅̅̅̅̅̅̅ ̇ 𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕,𝒊𝒊 [kcal/min] Mean metabolic rate 𝑬𝑬
directed backwards to the depot. In consequence the traversal policy leads to the shortest travel times for high additional time for curves/turn manoeuvres, not only for ABC horizontal storage assignment (see above), but also for the two other storage assignment policies (lower bound for random storage ∆𝑡𝑡𝑐𝑐 = 7.91 s, and for ABC vertical storage ∆𝑡𝑡𝑐𝑐 = 9.74 s).
Regarding RQ 1 especially for small warehouse dimensions curves and turn manoeuvres can significantly influence decisions regarding the operating strategy. The ABC vertical storage assignment policy provides the shortest travel times regardless of additional time for curves/turning manoeuvres. However the traversal or combined routing policy can save travel times compared to the optimal policy above certain lower bounds for additional time for curves/turning manoeuvres. 3.2 Evaluation of metabolic rate and rest allowance For the ergonomic evaluation the mean overall metabolic rate ̅̅̅̅̅̅̅̅ ̇ 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡,𝑖𝑖 are analysed in relation to warehouse for the tours 𝐸𝐸 dimensions, routing and storage assignment policy and factor for additional pushing/pulling forces in curves/turn manoeuvres. Fig. 2 shows the results for small warehouse dimensions and random storage for assuming ∆t c = 2 s (∆t c affects the travel time 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡,𝑖𝑖 and therefore the metabolic rate as energy expenditure per time unit) A factor 𝑓𝑓 = 1 represents calculating metabolic rates without special consideration of additional physical efforts in curves/turn manoeuvres. Analogous to the travel time evaluation there is a lower bound for the factor 𝑓𝑓 from which the optimal routing policy does not provide the lowest metabolic rates anymore because the impact of curves/turn manoeuvres outweighs the energy expenditure caused by travel distance (for small warehouse dimensions 𝑓𝑓 = 2.64 for random storage, 𝑓𝑓 = 5.12 for ABC vertical storage and 𝑓𝑓 = 6.03 for ABC horizontal storage). For medium and large warehouse dimensions the values are accordingly higher (medium: 𝑓𝑓 = 3.65, 𝑓𝑓 = 7.25, and 𝑓𝑓 = 7.24, resp.; large: 𝑓𝑓 = 4.38, 𝑓𝑓 = 8.95, and 𝑓𝑓 = 8.00, resp.) In view of those values it is assumed that especially for small warehouse dimensions and for warehouses using random storage assignment curves and turn manoeuvres could influence the choice of routing policy in terms of ergonomic aspects. When taking manoeuvres into account a minimization of travel distance does not necessarily results in minimal physical exposure for traveling. Besides the impact of manoeuvres on metabolic costs (absolute energy
8.5 8 7.5 7 6.5 6 5.5 5 1
3
5
7
9
Factor for additional force in curves/turn manoeuvres 𝒇𝒇 return largest gap optimal
traversal composite
midpoint combined
Fig. 2. Mean metabolic rate for small warehouse dimensions in relation to storage assignment and routing policy, varying factor for additional force in curves/turn manoeuvres ̅ according to eq. 4 The mean total time for the tours 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡,𝑅𝑅𝑅𝑅 depends on additional time for curves/turn manoeuvres as well as on factor for additional force. There is no empirical evidence on how additional time and additional force are interrelated. On the one hand it could be possible that for example in case of a cart difficult to handle the order picker exerts larger forces and is able to travel curves in comparable short times. On the other hand lower forces at the expense of higher additional times are possible, too. Therefore in fig. 3 the additional time for curve from which a heuristic routing policy provides shorter total tour times including rest allowance is shown as function of factor for additional force in curves/turn manoeuvres. The graphs show the results for small warehouse dimensions in relation to storage assignment policy. For all values of ∆𝑡𝑡𝑐𝑐 below the graphs the corresponding heuristic routing policy (combined or traversal, see above) leads to shorter total times than the optimal routing policy (represented by the arrows). There is again a lower bound for 𝑓𝑓 from which on this is the case (𝑓𝑓 = 4.34 for random storage, 𝑓𝑓 = 8.49 for ABC vertical storage and 𝑓𝑓 = 20.92 for ABC horizontal storage). From those values the graphs are rapidly rising so that even for small values of ∆𝑡𝑡𝑐𝑐 the heuristics outperform the optimal policy. However this effect only occurs for small warehouse dimensions and random or ABC vertical storage in a range of additional force which is assumed to be realisitic for realworld warehouses.
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Warehouse dimension small Additional time for curve ∆𝒕𝒕𝒄𝒄 [s]
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Fig. 3. Additional time for curve from which a heuristic routing policy provides shorter total tour times including rest allowance as function of factor for additional force in curves/turn manoeuvres Regarding RQ 2 it can be summarized that especially for small warehouse dimensions or warehouses using random storage assignment routing policies that reduce or minimize travel distance (like the optimal policy) does not guarntee minimal metabolic rates as well. Curves and turn manoeuvres should also be considered in evaluating the physical exposure for order pickers. 4. CONCLUSION In summary especially for small warehouse dimensions and random storage considering curves/turn manoeuvers in travel time calculation as well as in calculation of metabolic rates can influence decisions regarding the operating strategy. Since random storage is frequently used in real-world warehouses due to lower space requirements (de Koster et al., 2007) the results could be of high relevance for warehouse operators. The simplified assumption of constant additional times for curve/turn manoeuvres and of a constant factor for additional force together with a lack of empirical data for those parameters are limitations of this study. Therefore further research should systematically investigate which values for additional time and forces in curves/turn manoeuvres in relation to other influencing factors (resulting from task, design of the cart, environment, and operator) occur in practice. In a next step routing policies could be adapted for considering both travel distance and manoeuvres to realize further improvements regarding travel time and metabolic rates. REFERENCES Bartholdi, J.J., and Hackman, S.T. (2014). Warehouse and Distribution Science, Available at: www.warehousescience.com. Battini, D., Glock, C.H., Grosse, E.H., Persona, A., and Sgarbossa, F. (2015). Ergo-lot-sizing: Considering ergonomics in lot-sizing decisions. IFAC Proceedings Volumes (IFAC-PapersOnline), 48(3), pp.326–331. Battini, D., Faccio, M., Persona, A., and Sgarbossa, F.
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(2011). New methodological framework to improve productivity and ergonomics in assembly system design. International Journal of Industrial Ergonomics, 41(1), pp.30–42. Bonabeau, E. (2002). Agent-based Methods and techniques for simulating human systems. Proceedings of the National Academy of Sciences of the USA, 99(10), pp.7280–7287. Garg, A., Chaffin, D.B., and Herrin, G.D. (1978). Prediction of metabolic rates for manual materials handling jobs. American Industrial Hygiene Association journal, 39(8), pp.661–674. Glock, C.H., Grosse, E.H., Elbert, R., and Franzke, T. (2016). Maverick picking: the impact of modifications in work schedules on manual order picking processes. International Journal of Production Research. Available at: http://www.tandfonline.com/doi/abs/ 10.1080/00207543.2016.1252862?journalCode=tprs20 Grosse, E.H., Glock, C.H., Jaber, M.Y., and Neumann, W.P. (2015). Incorporating human factors in order picking planning models: framework and research opportunities. International Journal of Production Research, 11(2), pp.4979–4996. Jansen, J.P., Hoozemans, M.J.M., van der Beek, A.J., and Frings-Dresen, M. (2002). Evaluation of ergonomic adjustments of catering carts to reduce external pushing forces. Applied Ergonomics, 33(2), pp.117–127. Jung, M.C., Haight, J.M., and Freivalds, A. (2005). Pushing and pulling carts and two-wheeled hand trucks. International Journal of Industrial Ergonomics, 35(1), pp.79–89. de Koster, R., Le-duc, T., and Roodbergen, K.J. (2007). Design and control of warehouse order picking : a literature review. European Journal of Operational Research, 182(2), pp.481–501. Lavender, S.A., Marras, W.S., Ferguson, S.A., Splittstoesser, R.E., and Yang, G. (2012). Developing Physical Exposure-based Back Injury Risk Models Applicable to Manual Handling Jobs in Distribution Centers. Journal of Occupational and Environmental Hygiene, 9(7), pp.450–459. Petersen, C.G., and Aase, G. (2004). A comparison of picking, storage, and routing policies in manual order picking. International Journal of Production Economics, 92(1), pp.11–19. Price, A.D.F. (1990). Calculating relaxation allowances for construction operatives — Part 1: Metabolic cost. Applied Ergonomics, 21(4), pp.311–317. Roodbergen, K.J., and Vis, I.F.A. (2009). A survey of literature on automated storage and retrieval systems. European Journal of Operational Research, 194(2), pp.343–362. Schneider, E., and Irastorza, X. (2010). Work-related musculoskeletal disorders in the EU — Facts and figures, Available at: https://osha.europa.eu/en/toolsandpublications/publications/reports/TERO09009ENC. Tompkins, J.A., White, J.A., Bozer, Y.A., and Tanchoco, J.M.A. (2010) . Facilities Planning. John Wiley & Sons, New York.
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IFAC PapersOnLine 50-1 (2017) 6894–6899 Manoeuvres in manual person-to-parts order picking systems: Manoeuvres in manual person-to-parts order systems: IsManoeuvres there a significant influence on travel time andpicking metabolic rates? in manual person-to-parts order picking systems: Is there a significant influence on travel time and metabolic rates? Is there a significant influence on travel time and metabolic rates? Ralf Elbert*, Jan Philipp Müller*
Ralf Elbert*, Jan Philipp Müller* Ralf Elbert*, Jan Philipp Müller* *Department of Management and Logistics, Technische Universität Darmstadt, Hochschulstraße 1, 64289 Darmstadt, *Department ande-mail: Logistics, Technische Universität Darmstadt, Hochschulstraße 1, 64289 Darmstadt, Germany (Tel:of+49Management 6151 16 24430; [email protected]). *Department of Management and Logistics, Technische Universität Darmstadt, Hochschulstraße 1, 64289 Darmstadt, Germany (Tel: +49 6151 16 24430; e-mail: [email protected]). Germany (Tel: +49 6151 16 24430; e-mail: [email protected]). Abstract: In current planning models for travel time calculation in manual person-to-parts order picking Abstract: for travel calculation in manual person-to-parts order picking systems itIn is current assumedplanning that the models order picker travelstime at constant velocity through the warehouse. Curves and Abstract: In current planning models for travel time calculation in manual person-to-parts order picking systems it is assumed thatnecessary the order for picker travelsthe at aisles constant through the warehouse. turn manoeuvres that are changing arevelocity neglected in operating strategiesCurves so far. and For systems it is assumed that the order picker travels at constant velocity through the warehouse. Curves and turn necessary for changing aislesa are neglected operatingwould strategies far. For ordermanoeuvres pickers thatthat useare a cart for transporting thethe items more realisticinapproach be tosoconsider turn manoeuvres that are necessary for changing the aisles are neglected in operating strategies so far. For order pickers thatforuse a cart for transporting a more realistic approach be to consider additional time those manoeuvres due tothea items reduced gait velocity as well aswould additional physical order pickers that use a cart for transporting the items a more realistic approach would be to consider additional time those manoeuvres forces. due to The a reduced velocity as well as additional exposure due to for higher pushing/pulling paper atgait hand investigates if those influencesphysical should additional time for those manoeuvres due to a reduced gait velocity as well as additional physical exposure to higherinpushing/pulling forces. and The in paper at handevaluation investigates influences should be furtherdue deliberated travel time calculation ergonomic by ifthethose means of a simulation exposure due to higher pushing/pulling forces. The paper at hand investigates if those influences should be further in travel time calculation andwarehouse in ergonomic evaluation the means of aassignment simulation study. Firstdeliberated results show that especially for small dimensions andby random storage be further deliberated in travel time calculation and in ergonomic evaluation by the means of a simulation study. results show that especially for small warehouse dimensions random storage assignment policiesFirst warehouse operators could prefer heuristic routing policies and (combined/composite/traversal) study. First results show that especially for small warehouse dimensions and random storage assignment policies prefer heuristic routing policies (combined/composite/traversal) instead ofwarehouse the optimaloperators (minimal could travel distance) policy when taking curves/turn manoeuvers into account. policies warehouse operators could prefer heuristic routing policies (combined/composite/traversal) instead of the optimal (minimal travel distance) policy when taking curves/turn manoeuvers into account. Keywords: Order Picking; Ergonomics; factors; Operating Simulation instead the optimal (minimal travel distance) policy when takingstrategy; curves/turn manoeuvers account. © 2017,of IFAC (International Federation ofHuman Automatic Control) Hosting by Elsevier Ltd. All rightsinto reserved. Keywords: Order Picking; Ergonomics; Human factors; Operating strategy; Simulation Keywords: Order Picking; Ergonomics; Human factors; Operating strategy; Simulation In consequence ergonomic aspects should be considered in 1. INTRODUCTION In ergonomic aspects should be considered in the consequence layout design of the warehouse, in storage equipment In consequence ergonomic aspects should be considered in 1. INTRODUCTION the layoutand design the warehouse, in storage equipment INTRODUCTION also of in operating strategies which mainly deal Efficient warehouse1.operations play a crucial role for the decisions the layout design of the warehouse, in storage equipment and also in operating strategies which batching mainly deal Efficient warehouse operations a crucial role with assigning products to storage locations, of competitiveness of a supply chainplay in terms of costs as for wellthe as decisions Efficient warehouse operations play a crucial role for the decisions and also in operating strategies which mainly deal competitiveness of a supply chain in terms of costs as well as with assigning products to storage locations, batching of orders and order picker routing through the warehouse (de in terms of short lead times (Bartholdi and Hackman, 2014). competitiveness of a supply chain in terms of costs as well as with assigning products to storage locations, batching of order picker theofwarehouse (de Koster and et al., 2007). Therouting primarythrough objective the operating in terms of shortorder lead picking, times (Bartholdi and of Hackman, In this context the retrieval products2014). from orders in terms of short lead times (Bartholdi and Hackman, 2014). orders and order picker routing through the warehouse (de Koster etinal., 2007). The primary objective of the operating picker-to-parts-systems is the reduction of travel In this context ordercustomer picking, orders, the retrieval products from strategy storage for specific is of of great importance In this context order picking, the retrieval of products from Koster et al., 2007). The primary objective of the operating in order picker-to-parts-systems is the reduction of travel time since pickers spent on average 55 % of their time storage for specific50–75% customerof orders, of great importance since it constitutes the totalis operating costs for a strategy storage for specific customer orders, is of great importance strategy in picker-to-parts-systems is the reduction of travel since to, orderfrom pickers on average % of their time traveling andspent between the 55 storage locations since it warehouse constitutes(Petersen 50–75% of total2004). operating costs for a time typical andthe Aase, Approximately since it constitutes 50–75% of the total operating costs for a time since order pickers spent on average 55 % of their time from andAdditionally between the storage locations (Tompkinsto, et al., 2010). this high proportion of typical (Petersen and Aase, 2004). Europe Approximately 80 % ofwarehouse all order picking systems in Western are still traveling to, from and between the storage locations typical warehouse (Petersen and Aase, 2004). Approximately traveling (Tompkins al.,emphasizes 2010). Additionally this highofproportion of time et also that the analysis the physical 80 % of all order picking systems in Western Europe areorder still travel operated manually in a picker-to-parts-manner, where (Tompkins et al., 2010). Additionally this high proportion of 80 % of all order picking systems in Western Europe are still travel time also emphasizes that the analysis of the physical operated manually in a picker-to-parts-manner, where order pickers travel along the storage aisles (de Koster et al., 2007). exposure during traveling is highly important for improving operated manually in a picker-to-parts-manner, where order travel time also emphasizes that the analysis of the physical pickers systems travel along theadvantages storage aisles (de Koster et al., 2007). traveling is conditions. highly important for improving the overallduring physical working Those have regarding flexibility and exposure pickers travel along the storage aisles (de Koster et al., 2007). exposure during traveling is highly important for improving Those systems advantages regarding flexibility and the overall physical working conditions. investment costshave compared to automated systems but make overall physicalmodels working conditions. Those systems have advantages regarding flexibility and the Existing planning assume a constant velocity of the investment costs compared to automated systems but in make order picking to the most labour-intensive operation the planning assume constant velocity the investment costs compared to automated systems but make Existing order picker for models the travel timea calculation. Underof this planning models assume a constant velocity of the order picking the most labour-intensive warehouse, tooto(Roodbergen and Vis, 2009). operation in the Existing order picker for the travel time calculation. Under this condition travel time is a linear function of travel distance order picking the most labour-intensive warehouse, tooto(Roodbergen and Vis, 2009). operation in the order picker for the travel time calculation. Under this travel time a linearthe function of traveltodistance warehouse, too (Roodbergen Vis, 2009). and it is sufficient to is minimize latter variable ensure Therefore recent research andstresses the relevance of condition condition travel time is a linear function of travel distance it is possible sufficient travel to minimize variable to ensure shortest times the (de latter Koster et al., 2007). Therefore recent researchin stresses of and considering human factors the designtheof relevance order picking Therefore recent research stresses the relevance of and it is sufficient to minimize the latter variable to ensure shortest possible travel timesconsiderations (de Koster etinto al., account 2007). taking ergonomic considering human factors factors include in the design of order picking systems. Human physical, mental and However considering human factors in the design of order picking shortest possible travel times (de Koster et al., 2007). taking various factors can ergonomic influence theconsiderations velocity of theinto orderaccount picker. systems. Human factors includethatphysical, and However psychosocial working conditions influence mental the worker systems. Human factors include physical, mental and However taking ergonomic considerations into account factors can et influence thethey velocity ofgrouped the orderinto picker. According to Jung al. (2005) can be task psychosocial conditions influence the as worker health and theworking efficiency of orderthat picking systems well various psychosocial working conditions that influence the worker various factors can influence the velocity of the order picker. According Jungdirection et al. (2005) they can be grouped into task (e.g.toload, of motion, motion phases), design health and the2015). efficiency of orderis picking systems as work well factors (Grosse et al., An example the deviation from health and the efficiency of order picking systems as well According to Jung et al. (2005) they can be grouped into task load,cart direction of motion, motion phases), design of the (e.g. superstructure, wheels, handles), (Grosse et (so al., called 2015). maverick An example is the for deviation from work factors (e.g. schedules picking, example picking factors (e.g. load, direction of motion, motion phases), design (Grosse et al., 2015). An example is the deviation from work factors of thefactors cart (e.g. handles), schedules (so Glock called maverick picking, for example picking environment (e.g. superstructure, floors, slope, wheels, congestion) and wrong items, et al., 2016). Considering the physical schedules (so called maverick picking, for example picking factors of the cart (e.g. superstructure, wheels, handles), wrong items, Glock et al., 2016). Considering the physical environment factors (e.g. floors, slope, congestion) and operator factors (e.g. age, gender, anthropometry). Whereas working conditions ergonomics gain increasing attention. The wrong items, Glock et al., 2016). Considering the physical environment factors (e.g. floors, slope, congestion) and factors (e.g. age, anthropometry). design, environment and gender, operator factors are Whereas external working conditions ergonomics The operator manual material handling tasksgain in increasing warehousesattention. like lifting, working conditions ergonomics gain increasing attention. The operator factors (e.g. age, gender, anthropometry). Whereas environment and operator factors external constraints regarding operating strategies, task are factors have manual tasks likerisk lifting, carrying,material pushinghandling or pulling leadin towarehouses an increased for design, manual material handling tasks in warehouses like lifting, design, environment and operator factors are external task factors have almost beenregarding completelyoperating neglectedstrategies, in planning models so far. carrying, pushing or pulling lead to andisorders increased(Lavender risk for constraints order pickers to develop musculoskeletal carrying, pushing or pulling lead to an increased risk for constraints regarding operating strategies, task factors have order to develop musculoskeletal (Lavender et al., pickers 2012). 45.5 % of the workers in thedisorders EU-27 states report almost been completely neglected in planning models so far. completely in planning models so far. order pickers to develop musculoskeletal disorders (Lavender almost In orderbeen picking it couldneglected be beneficial to consider especially et al., 2012). % ofor the tiring workerspositions in the EU-27 states report working in 45.5 painful (Schneider and pickingand it could be beneficial to consider et al., 2012). 45.5 % of the workers in the EU-27 states report In theorder item weight the direction of motion in orderespecially to avoid working 2010). in painful or tiring positions and In order picking it could be beneficial to consider especially Irastorza, Ergonomic design of order (Schneider picking systems item weight and errors. the direction of approach motion infor order to avoid working in painful or tiring positions (Schneider and the systematic planning In a first considering Irastorza, 2010). Ergonomic design of order systems the item weight and the direction of motion in order to avoid cannot only improve physical conditions forpicking the workforce. systematic planning errors. first approach considering the item weight, Battini et In al.a (2015) showedfor that lot-sizing Irastorza, 2010). Ergonomic design of order picking systems cannot only improve conditions the workforce. Warehouse operatorsphysical can benefit fromfor higher worker systematic planning errors. In a first approach for considering the item weight, Battini et al. (2015) lot-sizing decisions for manual transportation (theshowed amountthat of items on a cannot only improve physical conditions the workforce. Warehouse operators can benefit fromfor higher availability and improved worker productivity asworker well the item weight, Battini et al. (2015) showed that lot-sizing decisions manual transportation (the in amount of items onarea cart per for tour) between two points a warehouse Warehouse operators can benefit from higher worker availability improved worker productivity as well decisions for manual transportation (the amount of items on a (Battini et al.,and 2011). per tour) between two points in a warehouse are availability improved worker productivity as well cart cart per tour) between two points in a warehouse are (Battini et al.,and 2011). (Battini et al., 2011).
Copyright © 2017, 2017 IFAC 7098Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © IFAC (International Federation of Automatic Control) Peer review©under of International Federation of Automatic Copyright 2017 responsibility IFAC 7098Control. Copyright © 2017 IFAC 7098 10.1016/j.ifacol.2017.08.1213
Proceedings of the 20th IFAC World Congress Toulouse, France, July 9-14, 2017 Ralf Elbert et al. / IFAC PapersOnLine 50-1 (2017) 6894–6899
dependent upon the cart load. Besides item weight the direction of motion can significantly influence the velocity of the order picker, too. During a tour through the warehouse one can define five different basic manoeuvres that the order picker can perform with the cart: pushing/pulling straight at constant velocity, accelerate from stop, decelerate for a stop, pushing/pulling a curve and turning around. For accelerating and decelerating a strictly monotonically increasing/decreasing velocity would be more realistic whereas for each a curve/turn manoeuvre an additional amount of time could be assumed. In various talks warehouse operators mentioned repeatedly that according to their impression especially curves and turn manoeuvres are not sufficiently considered in storage assignment and routing policies so far. Certain combinations lead to a higher number of curves and turn manoeuvres which is not reflected by an adequate additional time. An example is the combination of a return routing policy, where the order picker travels back in each aisle, and a classed-based ABC horizontal storage assignment policy, where the most frequently demanded items are stored across the aisles next to the depot (de Koster et al., 2007). Those policies could result in systematically higher travel times in practice because the order picker must turn around in each aisle. In contrast a traversal routing policy does not provide for turn manoeuvres when traveling between the pick locations (Bartholdi and Hackman, 2014). Considering specific manoeuvres cannot only improve the accuracy of travel time calculation. Regarding ergonomic evaluations they also affect the physical exposure and in this relation the metabolic rates of order pickers during their tours. The metabolic rate is the human energy expenditure per time unit (kcal/min) that is necessary for executing a predefined manual handling task (Garg et al., 1978). It provides an objective measurement for physical exposure and the resulting fatigue level. The metabolic rate is on the one hand determined by the travel distance but on the other hand push/pull forces between order picker and cart impact the metabolic rate as well. Those forces reach peak values in the starting phase when accelerating a cart (Jung et al., 2005) and can be significantly higher when pushing/pulling a turn compared to pushing/pulling straight (Jansen et al., 2002). The research gap addressed in the paper at hand is therefore to analyse the impact of curves and turn manoeuvres on travel time and on physical exposure. It is assumed that for travel time calculation the additional time for curves/turn manoeuvres and the warehouse dimensions (length of aisles, distance of aisles) determine the accuracy of the current calculation procedure based on constant velocity. Especially for small warehouse dimensions and high additional times for curves/turn manoeuvres (e.g. due to carts difficult to manoeuvre) the impact of travel length could be low compared to the time spent for pushing/pulling curves and turning around. In consequence warehouse operators might prefer different combinations of routing and storage assignment policies. Since prior research does not provide sufficiently valid information regarding additional time for curves/turn manoeuvres the aim here is to conduct a
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parameter study for answering the first research question (RQ): RQ 1:
For which parameter values regarding additional time for curves/ turn manoeuvres and warehouse dimensions (length of aisles, distance of aisles) warehouse operators should prefer different storage assignment and routing policies because they provide shorter travel times when curves and turn manoeuvres are considered in travel time calculation?
For ergonomic evaluation the metabolic rates are of special interest. They directly affect the rest allowance (Price 1990) and therefore worker productivity as well since the necessary break time increases for tours with high metabolic rates. Therefore the second RQ is as follows: RQ 2:
Which storage assignment and routing policies warehouse operators should prefer when taking the metabolic rates as an indicator for physical exposure into account?
In this aspect the ratio of hand forces when pushing/pulling a turn and when pushing/pulling straight is a decisive parameter since it determines the contribution of curves/turning around to the overall physical exposure of the tours. In lack of reliable values metabolic rates will analysed under variation of this parameter as well. 2. SIMULATION STUDY For the parameter study we analyse a picker-to-parts-system in a warehouse with rectangular layout with a single picker operation by the means of an agent-based simulation study. Rectangular layouts are frequent in real-world warehouses (Bartholdi and Hackman, 2014). Agent-based simulation is well suited to investigate complex, weakly structured systems and enables the researcher to conduct systematic parameter studies (Bonabeau 2002). During a tour the order picker visits every position on the pick list to retrieve the requested items until the order has been completed and he can return to the depot. The order of the items on the pick list is determined by the routing policy. A picking cart is used for transport. For this systems the total amount of time for a tour 𝑖𝑖 (𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡,𝑖𝑖 ) can be calculated as the sum of travel time of tour 𝑖𝑖 (𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡,𝑖𝑖 ) and time for searching and picking the items (𝑡𝑡𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝,𝑖𝑖 ). For the latter a constant time for each item is assumed. The travel time can be derived as follows: 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡,𝑖𝑖 = 𝑡𝑡𝑠𝑠,𝑖𝑖 + 𝑛𝑛𝑐𝑐,𝑖𝑖 ∙ ∆𝑡𝑡𝑐𝑐 + 𝑛𝑛𝑡𝑡,𝑖𝑖 ∙ ∆𝑡𝑡𝑡𝑡
(1)
whereby 𝑡𝑡𝑠𝑠,𝑖𝑖 is the travel time for pushing/pulling straight in tour 𝑖𝑖, ∆𝑡𝑡𝑐𝑐 , ∆𝑡𝑡𝑡𝑡 is a constant additional amount of time for each curve/turn manoeuvre resp. and 𝑛𝑛𝑐𝑐,𝑖𝑖 , 𝑛𝑛𝑡𝑡,𝑖𝑖 are the number of curves/turn manoeuvres in tour 𝑖𝑖 resp. A curve includes the phase of deceleration before the actual turn and the phase of acceleration afterwards for reaching a constant velocity 𝑣𝑣 again. Therefore ∆𝑡𝑡𝑐𝑐 is the additional amount of time for the curve length compared to a situation where the curve would be travelled with a constant velocity 𝑣𝑣. For turn manoeuvres it is assumed that the order picker does not cover any distance during this manoeuvre. The modelling approach with
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constant additional amounts of time represents a simplified consideration of curves/turn manoeuvres for this first analysis of the topic. Various further influences on the velocity of the order picker like item weight, construction and manoeuvrability of the cart or anthropometry of the order picker are neglected and deemed to be subject of future research. Under consideration of the constant velocity 𝑣𝑣 of the order picker the value for 𝑡𝑡𝑠𝑠,𝑖𝑖 can be calculated based on the travel distance 𝑠𝑠𝑖𝑖 of tour 𝑖𝑖 which is the sum of the distance between depot and storage location of the first item to pick 𝑠𝑠𝑑𝑑,1,𝑖𝑖 , the sum of the distances between the consecutive items 𝑗𝑗 to pick in the tour 𝑠𝑠𝑗𝑗,𝑗𝑗+1,𝑖𝑖 and the distance between the last item to pick and the depot 𝑠𝑠𝐽𝐽,𝑑𝑑,𝑖𝑖 : 𝑡𝑡𝑠𝑠,𝑖𝑖 =
𝑠𝑠𝑖𝑖 𝑣𝑣
combination of routing policy and storage assignment policy together with warehouse dimension (63 in total) we simulate 1000 tours. Regarding storage assignment the three policies random storage, ABC vertical and ABC horizontal storage are analysed. Regarding order picker routing six heuristic policies that are frequently used in practice (return, traversal, midpoint, largest gap, composite, combined policy) and the optimal routing policy are considered. The optimal policy determines a tour with minimal travel distance by solving a special form of a Travelling Salesman Problem (for a detailed description of storage assignment and routing policies please refer to de Koster et al. 2007). For reasons of simplicity it is assumed that additional time for turn manoeuvres is twice as high as additional time for curves. Order lists are created using a random number generator.
𝐽𝐽
=
𝑠𝑠𝑑𝑑,1,𝑖𝑖 +∑𝑗𝑗=1 𝑠𝑠𝑗𝑗,𝑗𝑗+1,𝑖𝑖 +𝑠𝑠𝐽𝐽,𝑑𝑑,𝑖𝑖 𝑣𝑣
Table 1. Parameter values for the simulation study
(2)
Velocity of order picker 𝑣𝑣 Constant pick time for each item Number of items per tour 𝐽𝐽 Item weight Warehouse layout Warehouse capacity
Regarding the ergonomic evaluation for calculating the metabolic rate of traveling 𝐸𝐸̇𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡,𝑖𝑖 (kcal/min) of a tour 𝑖𝑖 the respective net metabolic cost ∆𝐸𝐸𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡,𝑖𝑖 (kcal) must be determined first. The net metabolic costs describe the absolute value of human energy expenditure (additionally to the basal metabolic rate) for traveling during a tour. The metabolic rate for traveling can then be calculated by dividing 𝐸𝐸𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡,𝑖𝑖 by the travel time 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡,𝑖𝑖 and adding the basal metabolic rate. The net metabolic costs for traveling can be calculated as follows, whereby the equation for pushing/pulling at bench height according to Garg et al. (1978) is used:
Warehouse dimensions
Routing policies
∆𝐸𝐸𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡,𝑖𝑖 = 𝑒𝑒𝑠𝑠 (𝑤𝑤, 𝑔𝑔, 𝐹𝐹) ∙ 𝑠𝑠𝑖𝑖 + 𝑒𝑒𝑐𝑐 (𝑤𝑤, 𝑔𝑔, 𝑠𝑠𝑐𝑐 , 𝑓𝑓 ∙ 𝐹𝐹) ∙ 𝑛𝑛𝑐𝑐,𝑖𝑖 + +𝑒𝑒𝑡𝑡 (𝑤𝑤, 𝑔𝑔, 𝑠𝑠𝑤𝑤 , 𝑓𝑓 ∙ 𝐹𝐹) ∙ 𝑛𝑛𝑡𝑡,𝑖𝑖 (3)
Storage assignment Item classes for ABC storage assignment policies (share of picking frequency, share of number of items) Body weight of order picker 𝑤𝑤 Gender of order picker Constant force for pushing/pulling straight 𝐹𝐹 curve distance 𝑠𝑠𝑐𝑐 turn manoeuvre distance 𝑠𝑠𝑡𝑡 Factor for additional force in curves/turn manoeuvres Additional time for curve ∆𝑡𝑡𝑐𝑐 Additional time for turn manoeuvre ∆𝑡𝑡𝑤𝑤
The first part accounts for pushing/pulling straight, the second part for curves and the last part for turn manoeuvres. 𝑒𝑒𝑠𝑠/𝑐𝑐/𝑡𝑡 are constant parameters dependent on body weight, gender of the operator 𝑔𝑔, pushing/pulling force 𝐹𝐹, curve distance 𝑠𝑠𝑐𝑐 , and turn manoeuvre distance 𝑠𝑠𝑤𝑤 . Furthermore we assume a factor 𝑓𝑓 that account for the additional necessary pushing/puling forces for curves/turn manoeuvres (for reasons of simplicity we use an equal factor for curves and turn manoeuvres). The metabolic cost for pushing/pulling straight increases linearly in travel distance 𝑠𝑠𝑖𝑖 . The metabolic cost for curves/turn manoeuvres increase linearly in their numbers and factor 𝑓𝑓. The overall impact of curves and turn manoeuvres on travel time and on energy expenditure can be captured by considering the rest allowance 𝑅𝑅𝐴𝐴𝑖𝑖 for a tour 𝑖𝑖. According to Price (1990) 𝑅𝑅𝐴𝐴𝑖𝑖 is a function of the overall metabolic rate 𝐸𝐸̇𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡,𝑖𝑖 (kcal/min) of a tour. Besides 𝐸𝐸̇𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡,𝑖𝑖 this value additionally includes the metabolic rate for picking 𝐸𝐸̇𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝,𝑖𝑖 which is assumed to be constant for each tour and calculated according to Garg et al. (1978). The total time for a tour including the rest allowance then becomes: 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡,𝑖𝑖,𝑅𝑅𝑅𝑅 = 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡,𝑖𝑖 (1 + 𝑅𝑅𝐴𝐴𝑖𝑖 )
(4)
The parameter values for the simulation study are summarized in Table 1. Warehouse dimensions are scaled to “small”, “medium”, or “large”, resp. For each possible
0.75 m/s 20 s 20 0.2 kg Rectangular, 10 aisles 1000 items Small, medium, lager (aisle length 25m, 50m, 100m; aisle distance 3m, 6m, 12m) return, traversal, midpoint, largest gap, composite, combined, and optimal policy (see de Koster et al., 2007) Random, ABC vertical, ABC horizontal (see de Koster et al., 2007) A-items (80%, 20%) B-items (15%, 30%) C-items (5%, 50%) 𝑤𝑤 = 75 kg male 𝐹𝐹 = 3.5 kg 𝑠𝑠𝑐𝑐 = 3 m 𝑠𝑠𝑡𝑡 = 1.5 m variable, 𝑓𝑓 ≥ 1 variable, ∆𝑡𝑡𝑐𝑐 ≥ 0 ∆𝑡𝑡𝑤𝑤 = 2 ∙ ∆𝑡𝑡𝑐𝑐
3. RESULTS 3.1 Evaluation of travel time ̅ Based on the simulation results the mean travel times 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 of the tours for all three warehouse dimensions in relation to storage assignment and routing policies are calculated. For the parameter study additional time for curves/turn manoeuvres is varied. Fig. 1 shows the mean travel times for small warehouse dimensions (for random storage and ABC vertical storage). Zero additional time represents travel time calculations completely neglecting curves and turn manoeuvres and only taking the travel distance into account
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as usual in existing planning models. The mean travel time is linearly increasing in additional time for curves/turn manoeuvres. The gradient is determined by the mean number of curves/turn manoeuvres in a tour (see eq. 1). Warehouse dimension small and random storage assignment
Mean travel time 𝒕𝒕̅ 𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕 [s]
800 700
500 400 300 2
4
6
8
10
Additional time for curve ∆𝒕𝒕𝒄𝒄 [s] return largestGap optimal
traversal composite
manoeuvres underlies this result. The optimal policy reaches minimal travel distances at the expense of a higher number of curves and turn manoeuvres compared to several heuristic policies (see Table 2). For random storage the number of curves of the optimal policy is 10.03 % higher than for the composite policy. For the ABC vertical storage it is 5.38 % higher compared to the return policy and for ABC horizontal storage assignment it is 1.75 % higher compared to the return or traversal policy, resp. For random and ABC horizontal storage the number of curves for all routing policies is significantly higher than for the ABC vertical storage (e.g. for the optimal policy 86.03%, and 73.60 %, resp.). This is due to a reduced number of aisles the order picker must visit when practicing ABC vertical storage, because the frequently demanded items are stored in a few number of aisles. Furthermore this leads to a significantly lower number of turn manoeuvres, too (for the optimal policy 55.65 % lower compared to random storage and 65.10 % lower compared to ABC horizontal storage).
600
0
midpoint combined
Table 2. Mean travel time for ∆𝒕𝒕𝒄𝒄 = 𝟎𝟎, mean number of curves, and mean number of turn manoeuvres in relation to routing and storage assignment policy routing policy
Warehouse dimension small and ABC vertical storage assignment
Mean travel time 𝒕𝒕̅𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕 [s]
450
return traversal midpoint largest gap composite combined optimal
400 350 300 250 200 150 0
2
4
6
8
10
Additional time for curve ∆𝒕𝒕𝒄𝒄 [s] return largestGap optimal
traversal composite
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midpoint combined
Fig. 1. Mean travel time for small warehouse dimensions in relation to storage assignment and routing policy, varying additional time for curves/turn manoeuvres For zero additional time of course the optimal routing policy ensures the shortest travel time whereby the combined and composite policies are the best performing heuristic solutions. For each combination of storage assignment and routing policy there is a lower bound from which the optimal routing policy does not provide the shortest travel times anymore (∆𝑡𝑡𝑐𝑐 = 3.90 s for random storage, ∆𝑡𝑡𝑐𝑐 = 5.83 s for ABC vertical storage, and ∆𝑡𝑡𝑐𝑐 = 9.78 s for ABC horizontal storage, not shown in fig.1). For random and ABC vertical storage the combined policy, for ABC horizontal storage the traversal policy results in lower travel times than the optimal policy. The optimal policy only considers the travel distance. Up from a certain value of ∆𝑡𝑡𝑐𝑐 the influence of curves and turn manoeuvres on travel time is so high that a minimal travel distance does not ensure minimal travel times as well. A comparison of mean number of curves and turn
return traversal midpoint largest gap composite combined optimal return traversal midpoint largest gap composite combined optimal
Mean travel Mean number Mean number time for of curves of turn ∆𝒕𝒕𝒄𝒄 = 𝟎𝟎 [s] 𝒏𝒏𝒄𝒄 ̅̅̅ manoeuvres ̅̅̅ 𝒏𝒏𝒕𝒕 storage assignment: random 459.51 17.64 8.82 373.34 17.64 0.50 356.06 23.87 10.51 340.18 21.64 8.85 345.82 17.55 2.52 331.06 17.64 3.16 300.83 19.31 6.20 storage assignment: ABC vertical 268.38 9.85 4.92 213.27 10.01 0.49 232.29 13.34 5.72 219.92 12.44 4.47 201.09 9.98 1.24 193.20 9.98 1.53 176.63 10.38 2.75 storage assignment: ABC horizontal 230.61 17.71 8.85 361.36 17.71 0.51 267.59 19.08 8.43 266.47 18.87 7.43 225.12 17.80 7.83 224.46 17.77 7.84 214.12 18.02 7.88
In summary the ABC vertical storage is the most preferable policy regarding travel times since it combines short travel distances (for the optimal policy 41.28 % lower compared to random storage and 17.51 % lower compared to ABC horizontal storage) and low additional time for curves/turn manoeuvres. The traversal routing policy provides the lowest possible number of turn manoeuvres throughout all storage assignment policies. In this case the order picker must only turn in 50 % of the tours after the last pick when being
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For medium and large warehouse dimensions in general the same findings can be derived. However the lower bounds from which other routing policies result in shorter travel times increase proportionally in warehouse dimensions since curves/turn manoeuvres contribute a constant amount to the overall travel time. Only for medium warehouse dimension and random storage assignment this lower bound lies in a range that is assumed to be realistic for real-world warehouse operations (∆t c = 7.80 s).
expenditure) that is determined by the number of curves/turn manoeuvres routing policies that focus on minimal travel distances (like the optimal policy) can increase metabolic rates (as energy expenditure per time unit) by a further effect: The comparable less physical demanding parts of pushing/pulling straight are shorter so that curves and turn manoeuvres must be completed in shorter time intervals. In total this relationship can cause a higher overall exposure. Warehouse dimension small and random storage assignment 9
̅̅̅̅̅̅̅̅ ̇ 𝒕𝒕𝒕𝒕𝒕𝒕𝒕𝒕,𝒊𝒊 [kcal/min] Mean metabolic rate 𝑬𝑬
directed backwards to the depot. In consequence the traversal policy leads to the shortest travel times for high additional time for curves/turn manoeuvres, not only for ABC horizontal storage assignment (see above), but also for the two other storage assignment policies (lower bound for random storage ∆𝑡𝑡𝑐𝑐 = 7.91 s, and for ABC vertical storage ∆𝑡𝑡𝑐𝑐 = 9.74 s).
Regarding RQ 1 especially for small warehouse dimensions curves and turn manoeuvres can significantly influence decisions regarding the operating strategy. The ABC vertical storage assignment policy provides the shortest travel times regardless of additional time for curves/turning manoeuvres. However the traversal or combined routing policy can save travel times compared to the optimal policy above certain lower bounds for additional time for curves/turning manoeuvres. 3.2 Evaluation of metabolic rate and rest allowance For the ergonomic evaluation the mean overall metabolic rate ̅̅̅̅̅̅̅̅ ̇ 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡,𝑖𝑖 are analysed in relation to warehouse for the tours 𝐸𝐸 dimensions, routing and storage assignment policy and factor for additional pushing/pulling forces in curves/turn manoeuvres. Fig. 2 shows the results for small warehouse dimensions and random storage for assuming ∆t c = 2 s (∆t c affects the travel time 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡,𝑖𝑖 and therefore the metabolic rate as energy expenditure per time unit) A factor 𝑓𝑓 = 1 represents calculating metabolic rates without special consideration of additional physical efforts in curves/turn manoeuvres. Analogous to the travel time evaluation there is a lower bound for the factor 𝑓𝑓 from which the optimal routing policy does not provide the lowest metabolic rates anymore because the impact of curves/turn manoeuvres outweighs the energy expenditure caused by travel distance (for small warehouse dimensions 𝑓𝑓 = 2.64 for random storage, 𝑓𝑓 = 5.12 for ABC vertical storage and 𝑓𝑓 = 6.03 for ABC horizontal storage). For medium and large warehouse dimensions the values are accordingly higher (medium: 𝑓𝑓 = 3.65, 𝑓𝑓 = 7.25, and 𝑓𝑓 = 7.24, resp.; large: 𝑓𝑓 = 4.38, 𝑓𝑓 = 8.95, and 𝑓𝑓 = 8.00, resp.) In view of those values it is assumed that especially for small warehouse dimensions and for warehouses using random storage assignment curves and turn manoeuvres could influence the choice of routing policy in terms of ergonomic aspects. When taking manoeuvres into account a minimization of travel distance does not necessarily results in minimal physical exposure for traveling. Besides the impact of manoeuvres on metabolic costs (absolute energy
8.5 8 7.5 7 6.5 6 5.5 5 1
3
5
7
9
Factor for additional force in curves/turn manoeuvres 𝒇𝒇 return largest gap optimal
traversal composite
midpoint combined
Fig. 2. Mean metabolic rate for small warehouse dimensions in relation to storage assignment and routing policy, varying factor for additional force in curves/turn manoeuvres ̅ according to eq. 4 The mean total time for the tours 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡,𝑅𝑅𝑅𝑅 depends on additional time for curves/turn manoeuvres as well as on factor for additional force. There is no empirical evidence on how additional time and additional force are interrelated. On the one hand it could be possible that for example in case of a cart difficult to handle the order picker exerts larger forces and is able to travel curves in comparable short times. On the other hand lower forces at the expense of higher additional times are possible, too. Therefore in fig. 3 the additional time for curve from which a heuristic routing policy provides shorter total tour times including rest allowance is shown as function of factor for additional force in curves/turn manoeuvres. The graphs show the results for small warehouse dimensions in relation to storage assignment policy. For all values of ∆𝑡𝑡𝑐𝑐 below the graphs the corresponding heuristic routing policy (combined or traversal, see above) leads to shorter total times than the optimal routing policy (represented by the arrows). There is again a lower bound for 𝑓𝑓 from which on this is the case (𝑓𝑓 = 4.34 for random storage, 𝑓𝑓 = 8.49 for ABC vertical storage and 𝑓𝑓 = 20.92 for ABC horizontal storage). From those values the graphs are rapidly rising so that even for small values of ∆𝑡𝑡𝑐𝑐 the heuristics outperform the optimal policy. However this effect only occurs for small warehouse dimensions and random or ABC vertical storage in a range of additional force which is assumed to be realisitic for realworld warehouses.
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Warehouse dimension small Additional time for curve ∆𝒕𝒕𝒄𝒄 [s]
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Fig. 3. Additional time for curve from which a heuristic routing policy provides shorter total tour times including rest allowance as function of factor for additional force in curves/turn manoeuvres Regarding RQ 2 it can be summarized that especially for small warehouse dimensions or warehouses using random storage assignment routing policies that reduce or minimize travel distance (like the optimal policy) does not guarntee minimal metabolic rates as well. Curves and turn manoeuvres should also be considered in evaluating the physical exposure for order pickers. 4. CONCLUSION In summary especially for small warehouse dimensions and random storage considering curves/turn manoeuvers in travel time calculation as well as in calculation of metabolic rates can influence decisions regarding the operating strategy. Since random storage is frequently used in real-world warehouses due to lower space requirements (de Koster et al., 2007) the results could be of high relevance for warehouse operators. The simplified assumption of constant additional times for curve/turn manoeuvres and of a constant factor for additional force together with a lack of empirical data for those parameters are limitations of this study. Therefore further research should systematically investigate which values for additional time and forces in curves/turn manoeuvres in relation to other influencing factors (resulting from task, design of the cart, environment, and operator) occur in practice. In a next step routing policies could be adapted for considering both travel distance and manoeuvres to realize further improvements regarding travel time and metabolic rates. REFERENCES Bartholdi, J.J., and Hackman, S.T. (2014). Warehouse and Distribution Science, Available at: www.warehousescience.com. Battini, D., Glock, C.H., Grosse, E.H., Persona, A., and Sgarbossa, F. (2015). Ergo-lot-sizing: Considering ergonomics in lot-sizing decisions. IFAC Proceedings Volumes (IFAC-PapersOnline), 48(3), pp.326–331. Battini, D., Faccio, M., Persona, A., and Sgarbossa, F.
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