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To solve the model, we propose a local search procedure that reroutes flow of multiple commodities at once. This is reconfirmed with a look atFigure 10.16 shows that the cost increases for a pure milk run system areconsiderably smaller for the small instances and even turn into significancost savings compared to an exclusive AF system for the biggerthe latter cases, it is beneficial to have the whole set of vehicle types – alsoIn phase III we analyse the advantage of the TC-MRS compared to the wheuristic allocates supplier relations to a transport concept depset of all vehicle types in order to compare the smallest possible cost in bothThe charts of Figure 10.17 confirm the results of Chapter 9:the size and the weight structure, a significant cost increase of up to 60%time, the results of the heuristic are strongly deviating both over instance sizeIn 5 out of these 8 scenarios it is beneficial to apply the Wis possible to reach significant cost savings of up to 11% in the w=1 scenarioscrucial for yielding these results, with none of it dominating the others.different thresholds need to be tested for realising these savings.planning process for the MRS is prohibitively time consuming.to the model since for the two big scenarios another 4 percentage points– summing up to 15% – and 6 percentage points – summing up to 24% –As already mentioned, the TC-MRS – using the a priori column generationapproach – could be solved to optimality for all scenarios of our use case.and, hence, by the weight structure and the geographic distribution.Figure 10.18 shows the run times for generating the columns ovof orders, that means, for the four different instance sizes defined by the cvcauses shorter run times since the search can be pruned heavily by the capacitresult from the maximum tour duration and hence the run times are almostThe longest resulting tours have 3 to 4 stops in the smallest scenario andbetween 40 for cv=0.3 and up to 200,000 tours for the cv=1.33 scenarios.In general, the column generation run times for the biggest instances of ourset (vc=1.33, BIG, w=1) it drops from 600 to 300 seconds if the numstops is restricted to 6, and to 70 seconds if it is restricted to 5.interesting since in practice more than 5 or 6 stops on a milk run tour arewhich corresponds to the default value of the applied Gurobi vAnother factor which seems to influence the run times of the set covcv=1.33 scenarios, the average run time for the w=1 scenario is around 170seconds and the average proportion of milk run orders is 20%.run time for the w=2 case is around 1900 seconds – even if in the w=2 caseof 100% are solved within less than a minute of run time.confirmed by the fact that the milk run only scenarios cause the longest runEven if there is some room for improving the performance of our algorithmfor the a priori column generation phase, the general picture is clear:As shown, the maximal number of stops – either restricted by the vcapacity or restricted due to operational reasons – influences the run timealso impacts the run time of the second stage, the set cover phase, the runon hand – the literature shows that there exist other use cases where theproposed approach, yielding optimal results, seems to be applicable:a planning problem of weekly milk runs for a distribution netwAmerica of a home appliances producer incorporating 75 regular clients.containing between 13 to 109 daily supplier relations.Especially for small and medium sized companies it might be beneficial tohave an easy to calculate parameter indicating if wIn order to judge if a supplier relation is a potential milk run candidate, oneneeds to trade off the AF against the milk run cost.easy to determine since they only depend on the distance and weight classdistance and operation time of the tour and can be only determined if the tourcan be easily calculated by determining the driving distance and operationduced in Chapter 9 for determining consistent AF cost parameters – for eachgenerated if on this milk run other suppliers “on the way” to the plancient tour including this supplier along with other stops on the wative scenarios with potential cost savings compared to the basebecomes clear with a look at the charts of Figure 10.21:by the assigned transport concept in the optimal solution for two scenarios.The upper chart of Figure 10.22 shows the relationship between the aratio over all supplier relations and the resulting TC-MRS cost differenmight not be beneficial in scenarios with a lower maximum geographical situations than the one considered here, this threshold might beclose to one or even above can be considered as a clear indicator that theintroduction of milk runs as an alternative to the AF netwAfter summarizing the most important insights of the case study we concludethis chapter by critically discussing the results with respect to their impact onthe planning situation of the receiving plant and the changes of the conThe analysis of the historical transport data showed, as expected, that weeklyprocess improvements and, at the same time, reduce variabiltone needs to keep in mind that there is an effort for planning and operatingthe milk runs, as well as for adapting the order policies to reach levelledfrequencies and reasonably levelled shipment sizes.emphasized since substantial cost savings of up to 15% for the original wscenario can be only realised if most of the daily and weekly supplier relationsEven if this could not be shown in the problem instances of the original weighwhich has in general more beneficial weight structures for milk runs than theto the best cases considering just one vehicle type.pure milk run system caused less cost than the AF network base case for theEven if we produced optimal MRS results after allocating the transport con-cept in accordance with the weight allocation heuristic – which is difficult todepending on distance and weight classes, as well as an upper bound of costan order on its own is a good seed stop for a milk run tour.If a milk run system is not considered as an alternative for operational reasons,leads to rather high transport cost compared to planning tours ad hoc.Independently from the concrete results of the case studycan be used to generate input data for the TC-MRS model.for a first analysis assessing the potential of cost savings by ineffort for the production and order planning to reach more levelled transportThe introduced a priori column generation approach clearly has its limits interms of the instance sizes which can be solved in acceptable run times.able to do what-if analysis – for example, playing around with different AFor vehicle cost parameters – solving only the set covperiodic vehicle routing problems considering a heterogeneous fleet with thebigger instances, the a priori approach might be used to generate startingsearch based heuristics – for example, for choosing seed vand operating effort for these milk runs for the receiving plant.and operating the tours – even if they are operated by vehicles of a logisticsing milk runs went up to 20 per week in a mixed system and up to 44 inand they need to be monitored in order to identify the moment when they arethat there exists one milk run, one calculates for the actual orders the virtualAF costs for all stops and relates them to the actual milk run costs.ratio is above one, the milk run is cost efficient compared to the AF netIf the vehicle capacity is not exceeded, the actual milk run cost corresponds tofor the following example that an order can be split and, hence, the exceedingcost for the shipments of all suppliers of a milk run tour are usually belowthe cost for the pure virtual AF shipments since the cost advThese relationships become clear with a look at the simplified,column), normal demand (middle) and high demand (right col-AF cost for the exceeding volume is added to the actual milk run cost showof the low demand realisations, the execution through the AF netwrealisation, it becomes clear that the pure AF costs are usually not reachedmight be better to adapt the milk run if the demand is assumed to be precourse or repair strategies in case of capacity violations during the MRD.measuring the cost efficiency of a running mixed AF and milk run system:It is better than measuring only the capacity usage of milk runs which iscommon in practice but which does not contain any information on the costefficiency relative to alternative transport concepts.Whenever suppliers are serviced in different milk runs with differing suppliers,only such a milk run it would be better in terms of cost to assign the relatedcluster it is beneficial to assign all suppliers to the milk run concept.between the receiving plant and the AF logistics prosolved, this can be considered as “cherry picking” from the perspective of asulting from the solution of the TC-MRS model for instanceposition are served by milk runs, planned and controlled by the receivingthe potential for building cost efficient tours in the affected area decreases forIf the shifted volumes are relatively small compared to the total shippingvolume of the receiving plant or compared to the total shipping vthe logistics provider in the area, it does not affect the general cost structureof the logistics provider significantly and, hence, the AF tariffs offered to thecost structure forces the logistics provider in the medium-term to raise theIn such a case it might be of interest for both parties that the milk runs and thenot decrease and it would be even possible to leave it to the logistics proto fill up a milk run tour with additional stops if it can be guaranteed that thethe master tour concept introduced in Section 2.1.2).for the daily and weekly supplier relations and optimization potential forAnother possible scenario could be that a logistics provider offers better condi-can offer milk runs with fixed schedules serving different cliengreater optimization potential and reduces the cost and at the same time thethesis with respect to the goal from a practical point of view – to providemodels and indicators to manage the planning complexity of milk runs – andwith respect to the research questions formulated in Section 1.1.this thesis with an outlook on opportunities for future research.and indicators to manage the planning complexity of milk runs.shows the three main contributions of this thesis, and it shows whicmapped to a distinct chapter or a single set of research questions, we use thethree key contributions of Figure 11.1 as a structure to discuss and summarizeThe first part of this thesis is dedicated to defining milk runs as a trans-research questions 1 and 2 from a conceptual point of view abstracting fromDue to the ambiguous use of the term milk run in practice and literaturewe proposed an extended classification scheme characterising differentransport concepts typically applied within the German automotive sector.Therefore, we added the tariff structure – defined by the cost structure andthe type of contract, the degree of consolidation, the planning horizon, andthe responsibility for the tour planning task as further classification criteria.Based on the discussion of the road transport concepts we defined the termrepeated according to a fixed schedule, with a fixed sequence and fixed arrivalon a daily basis by a pull or push based order policyRegarding the regularity – and the resulting reliability – as a kcompared to ad hoc concepts, a reduced operational complexity, and a betterMilk Runs and HEIJUNKA Levelled Supplier KANBAN CyclesBesides reflecting milk runs as a general transport concept, we discussed thelogic of supplier milk runs within lean manufacturing principles.world, milk run schedules are usually repeated on a daily basis.are picked up at the respective supplier sites up to 8 times per daycycle times for every supplier plant relation are approIf milk runs are repeated on a weekly basis, the resulting inter arrivto supplier KANBAN cycles in order to reach levelled transport lots in spitethere exists no description of such a system in lean manufacturing literature.Ensuing from the previous results, we defined the milk run design problem asa tactical decision considering simultaneously the assignment of a transportconcept and a frequency to every supplier plant relation, and the solution ofthe milk run scheduling problem for the suppliers assigned to the milk runconsidering the capacity of vehicles and storage areas.features can be required to further reduce the operational complexity.On the basis of the definition of the milk run design problem we turnedproaches from literature and proposed models addressing the problem in ancial instances and a real-world instance for addressing the research questionproaches from literature coming from different researcand which types of regularity and consistency the resulting scture considered the transport concept assignment, the frequency assignment,and the milk run scheduling decision simultaneouslyformance estimation concepts and performance indicator existed for the milkrun concept relating it to the cost for alternative transport concepts.tory routing model considering consistency, outsourcing, and a heterogeneousThe basic milk run scheduling model consists of an explicit deterministic cyclicsponding cost for every supplier, are taken as input.can be either determined by an economic lower bound or by the afrequency if that results in lower operational cost.In the following we describe the model (components), the results of the com-putational experiments and the solution approach in more depth.timal delivery pattern for every frequency and the corresponding invfrom literature for both constant cycle schedules (continmodels) and delivery profile schedules (discrete time invresources, we proposed a new model describing order pSince the optimality property for patterns cannot be expressed explicitly byfects on the consistency of shipping volumes and the compatibility with timethe cost of the solution without asking for arrival time consistency are onlysignificant routing cost increase for the test instances.cost is in most cases not compensated by considerably lower inules are operationally complex in case of a cycle time of one week.times during the night and in the early morning are in conflict with night drivbans and with the opening hours of logistics providers and suppliers.The experimental results furthermore showed that arrivthe routing cost increase is in most cases moderate if all suppliers are alwaysWhenever driver consistency is not strictly necessarydriver consistency is very promising since a high levthe same consistency level could be reached on our instances by applyingduring the solution of the MRS, we reassign the tours in a second step in aassignment to a transport concept simultaneously was tested on both artifi-incorporated area forwarding, point-to-point transports,tigated the behaviour in case of varying milk run cost parameters not beingof a production site of Bosch automotive in Homburg the application of theTC-MRS model resulted in significant cost savings of up to 15% compared toThis was especially surprising since the weight structure is – due to the lofor the instances considering 44 out of the 54 regular suppliers and all 54are incorporated, the higher is the cost savings potential.the use case data that there exist situations in which significant additionalcost savings can be realised by considering vehicle classes with differenand capacity parameters instead of a single vehicle tAs a benchmark we also tested the performance of rule based transport con-run design problem and not necessarily a solution approach scaling to largeproach, which could be applied to all model configurations and which yieldedoptimal results for nearly all models on all instances.generation procedure grows exponentially with the number of suppliers.the number of tours is high, also the solution process of the set cover or par-for configurations in which time consistency is considered.time consistency could be solved to optimality for all instances of our real-world use case containing up to 54 suppliers within less than an hour.authors report on more producing companies having only between 20 and upto smaller real-world instances yielding optimal results.The set of research questions 4 is treated within the case studyThe procedures to generate the necessary input data for solving a milk rundesign model are transferable to other companies since they are based onSolving the milk run design problem based on the derived input parametersdecide if more detailed, usually difficult to gather, data such as net demandsthe order policy can be adapted in a way that the frequency and the shippingfined by the share of AF cost for an order and the milk run cost accrued ifthe corresponding supplier is served on an exclusive milk run.values can be easily determined without solving a vehicle routing problem.it is not very likely that milk runs are a cost efficienis above one, at least one milk run results in cost savings and an in depthbe also used to assess AF tariff tables compared to exclusive milk runs orthe actual milk run cost including potential extra cost accrued if the demandmeasuring the performance of a milk run cluster with respect to alternativethe AF tariffs the fewer milk runs are cost efficient but the better the milkdesign problem corresponds to “cherry picking” with respect to the freightThe results of our experiments showed that the TC-MRS is adequate to modelthe milk run design decision if the receiving plant aims for weekly recurringmilk runs consisting of a pre- and a main-leg or a pre-, main- and sub-legsuppliers is located far away from the receiving planreverse flows of parts to suppliers – for example in case of metal finishingprocesses executed by a supplier – the routing model should consider pickIf the AF tariffs differentiate between pre- and main-leg tables, the AF costcannot be determined before the orders are assigned to days since the tariffsfor the main-leg depend on the resulting volumes per dayEven if it is assumed that sufficiently stable frequencies and vreached in general, in practice the capacity of milk runs will be exceeded ondays with a higher demand and the capacity usage rate will be low on dadifferent parts for the same plant are often correlated.considering different possible recourse strategies for exceeding demands.with exact or heuristic subprocedures seems promising.cases the time synchronisation resulting from time consistency requirementscomplicates the approach since one must assure that compatible tours withA heuristic approach successfully applied to other vehicle routing problemsproblems is the adaptive large neighbourhood search.a helpful indicator for selecting suppliers for relaxing the solution and forAkturk, M. and F. Erhun (1999).
To solve the model, we propose a local search procedure that reroutes flow of multiple commodities at once. This is reconfirmed with a look atFigure 10.16 shows that the cost increases for a pure milk run system areconsiderably smaller for the small instances and even turn into significancost savings compared to an exclusive AF system for the biggerthe latter cases, it is beneficial to have the whole set of vehicle types – alsoIn phase III we analyse the advantage of the TC-MRS compared to the wheuristic allocates supplier relations to a transport concept depset of all vehicle types in order to compare the smallest possible cost in bothThe charts of Figure 10.17 confirm the results of Chapter 9:the size and the weight structure, a significant cost increase of up to 60%time, the results of the heuristic are strongly deviating both over instance sizeIn 5 out of these 8 scenarios it is beneficial to apply the Wis possible to reach significant cost savings of up to 11% in the w=1 scenarioscrucial for yielding these results, with none of it dominating the others.different thresholds need to be tested for realising these savings.planning process for the MRS is prohibitively time consuming.to the model since for the two big scenarios another 4 percentage points– summing up to 15% – and 6 percentage points – summing up to 24% –As already mentioned, the TC-MRS – using the a priori column generationapproach – could be solved to optimality for all scenarios of our use case.and, hence, by the weight structure and the geographic distribution.Figure 10.18 shows the run times for generating the columns ovof orders, that means, for the four different instance sizes defined by the cvcauses shorter run times since the search can be pruned heavily by the capacitresult from the maximum tour duration and hence the run times are almostThe longest resulting tours have 3 to 4 stops in the smallest scenario andbetween 40 for cv=0.3 and up to 200,000 tours for the cv=1.33 scenarios.In general, the column generation run times for the biggest instances of ourset (vc=1.33, BIG, w=1) it drops from 600 to 300 seconds if the numstops is restricted to 6, and to 70 seconds if it is restricted to 5.interesting since in practice more than 5 or 6 stops on a milk run tour arewhich corresponds to the default value of the applied Gurobi vAnother factor which seems to influence the run times of the set covcv=1.33 scenarios, the average run time for the w=1 scenario is around 170seconds and the average proportion of milk run orders is 20%.run time for the w=2 case is around 1900 seconds – even if in the w=2 caseof 100% are solved within less than a minute of run time.confirmed by the fact that the milk run only scenarios cause the longest runEven if there is some room for improving the performance of our algorithmfor the a priori column generation phase, the general picture is clear:As shown, the maximal number of stops – either restricted by the vcapacity or restricted due to operational reasons – influences the run timealso impacts the run time of the second stage, the set cover phase, the runon hand – the literature shows that there exist other use cases where theproposed approach, yielding optimal results, seems to be applicable:a planning problem of weekly milk runs for a distribution netwAmerica of a home appliances producer incorporating 75 regular clients.containing between 13 to 109 daily supplier relations.Especially for small and medium sized companies it might be beneficial tohave an easy to calculate parameter indicating if wIn order to judge if a supplier relation is a potential milk run candidate, oneneeds to trade off the AF against the milk run cost.easy to determine since they only depend on the distance and weight classdistance and operation time of the tour and can be only determined if the tourcan be easily calculated by determining the driving distance and operationduced in Chapter 9 for determining consistent AF cost parameters – for eachgenerated if on this milk run other suppliers “on the way” to the plancient tour including this supplier along with other stops on the wative scenarios with potential cost savings compared to the basebecomes clear with a look at the charts of Figure 10.21:by the assigned transport concept in the optimal solution for two scenarios.The upper chart of Figure 10.22 shows the relationship between the aratio over all supplier relations and the resulting TC-MRS cost differenmight not be beneficial in scenarios with a lower maximum geographical situations than the one considered here, this threshold might beclose to one or even above can be considered as a clear indicator that theintroduction of milk runs as an alternative to the AF netwAfter summarizing the most important insights of the case study we concludethis chapter by critically discussing the results with respect to their impact onthe planning situation of the receiving plant and the changes of the conThe analysis of the historical transport data showed, as expected, that weeklyprocess improvements and, at the same time, reduce variabiltone needs to keep in mind that there is an effort for planning and operatingthe milk runs, as well as for adapting the order policies to reach levelledfrequencies and reasonably levelled shipment sizes.emphasized since substantial cost savings of up to 15% for the original wscenario can be only realised if most of the daily and weekly supplier relationsEven if this could not be shown in the problem instances of the original weighwhich has in general more beneficial weight structures for milk runs than theto the best cases considering just one vehicle type.pure milk run system caused less cost than the AF network base case for theEven if we produced optimal MRS results after allocating the transport con-cept in accordance with the weight allocation heuristic – which is difficult todepending on distance and weight classes, as well as an upper bound of costan order on its own is a good seed stop for a milk run tour.If a milk run system is not considered as an alternative for operational reasons,leads to rather high transport cost compared to planning tours ad hoc.Independently from the concrete results of the case studycan be used to generate input data for the TC-MRS model.for a first analysis assessing the potential of cost savings by ineffort for the production and order planning to reach more levelled transportThe introduced a priori column generation approach clearly has its limits interms of the instance sizes which can be solved in acceptable run times.able to do what-if analysis – for example, playing around with different AFor vehicle cost parameters – solving only the set covperiodic vehicle routing problems considering a heterogeneous fleet with thebigger instances, the a priori approach might be used to generate startingsearch based heuristics – for example, for choosing seed vand operating effort for these milk runs for the receiving plant.and operating the tours – even if they are operated by vehicles of a logisticsing milk runs went up to 20 per week in a mixed system and up to 44 inand they need to be monitored in order to identify the moment when they arethat there exists one milk run, one calculates for the actual orders the virtualAF costs for all stops and relates them to the actual milk run costs.ratio is above one, the milk run is cost efficient compared to the AF netIf the vehicle capacity is not exceeded, the actual milk run cost corresponds tofor the following example that an order can be split and, hence, the exceedingcost for the shipments of all suppliers of a milk run tour are usually belowthe cost for the pure virtual AF shipments since the cost advThese relationships become clear with a look at the simplified,column), normal demand (middle) and high demand (right col-AF cost for the exceeding volume is added to the actual milk run cost showof the low demand realisations, the execution through the AF netwrealisation, it becomes clear that the pure AF costs are usually not reachedmight be better to adapt the milk run if the demand is assumed to be precourse or repair strategies in case of capacity violations during the MRD.measuring the cost efficiency of a running mixed AF and milk run system:It is better than measuring only the capacity usage of milk runs which iscommon in practice but which does not contain any information on the costefficiency relative to alternative transport concepts.Whenever suppliers are serviced in different milk runs with differing suppliers,only such a milk run it would be better in terms of cost to assign the relatedcluster it is beneficial to assign all suppliers to the milk run concept.between the receiving plant and the AF logistics prosolved, this can be considered as “cherry picking” from the perspective of asulting from the solution of the TC-MRS model for instanceposition are served by milk runs, planned and controlled by the receivingthe potential for building cost efficient tours in the affected area decreases forIf the shifted volumes are relatively small compared to the total shippingvolume of the receiving plant or compared to the total shipping vthe logistics provider in the area, it does not affect the general cost structureof the logistics provider significantly and, hence, the AF tariffs offered to thecost structure forces the logistics provider in the medium-term to raise theIn such a case it might be of interest for both parties that the milk runs and thenot decrease and it would be even possible to leave it to the logistics proto fill up a milk run tour with additional stops if it can be guaranteed that thethe master tour concept introduced in Section 2.1.2).for the daily and weekly supplier relations and optimization potential forAnother possible scenario could be that a logistics provider offers better condi-can offer milk runs with fixed schedules serving different cliengreater optimization potential and reduces the cost and at the same time thethesis with respect to the goal from a practical point of view – to providemodels and indicators to manage the planning complexity of milk runs – andwith respect to the research questions formulated in Section 1.1.this thesis with an outlook on opportunities for future research.and indicators to manage the planning complexity of milk runs.shows the three main contributions of this thesis, and it shows whicmapped to a distinct chapter or a single set of research questions, we use thethree key contributions of Figure 11.1 as a structure to discuss and summarizeThe first part of this thesis is dedicated to defining milk runs as a trans-research questions 1 and 2 from a conceptual point of view abstracting fromDue to the ambiguous use of the term milk run in practice and literaturewe proposed an extended classification scheme characterising differentransport concepts typically applied within the German automotive sector.Therefore, we added the tariff structure – defined by the cost structure andthe type of contract, the degree of consolidation, the planning horizon, andthe responsibility for the tour planning task as further classification criteria.Based on the discussion of the road transport concepts we defined the termrepeated according to a fixed schedule, with a fixed sequence and fixed arrivalon a daily basis by a pull or push based order policyRegarding the regularity – and the resulting reliability – as a kcompared to ad hoc concepts, a reduced operational complexity, and a betterMilk Runs and HEIJUNKA Levelled Supplier KANBAN CyclesBesides reflecting milk runs as a general transport concept, we discussed thelogic of supplier milk runs within lean manufacturing principles.world, milk run schedules are usually repeated on a daily basis.are picked up at the respective supplier sites up to 8 times per daycycle times for every supplier plant relation are approIf milk runs are repeated on a weekly basis, the resulting inter arrivto supplier KANBAN cycles in order to reach levelled transport lots in spitethere exists no description of such a system in lean manufacturing literature.Ensuing from the previous results, we defined the milk run design problem asa tactical decision considering simultaneously the assignment of a transportconcept and a frequency to every supplier plant relation, and the solution ofthe milk run scheduling problem for the suppliers assigned to the milk runconsidering the capacity of vehicles and storage areas.features can be required to further reduce the operational complexity.On the basis of the definition of the milk run design problem we turnedproaches from literature and proposed models addressing the problem in ancial instances and a real-world instance for addressing the research questionproaches from literature coming from different researcand which types of regularity and consistency the resulting scture considered the transport concept assignment, the frequency assignment,and the milk run scheduling decision simultaneouslyformance estimation concepts and performance indicator existed for the milkrun concept relating it to the cost for alternative transport concepts.tory routing model considering consistency, outsourcing, and a heterogeneousThe basic milk run scheduling model consists of an explicit deterministic cyclicsponding cost for every supplier, are taken as input.can be either determined by an economic lower bound or by the afrequency if that results in lower operational cost.In the following we describe the model (components), the results of the com-putational experiments and the solution approach in more depth.timal delivery pattern for every frequency and the corresponding invfrom literature for both constant cycle schedules (continmodels) and delivery profile schedules (discrete time invresources, we proposed a new model describing order pSince the optimality property for patterns cannot be expressed explicitly byfects on the consistency of shipping volumes and the compatibility with timethe cost of the solution without asking for arrival time consistency are onlysignificant routing cost increase for the test instances.cost is in most cases not compensated by considerably lower inules are operationally complex in case of a cycle time of one week.times during the night and in the early morning are in conflict with night drivbans and with the opening hours of logistics providers and suppliers.The experimental results furthermore showed that arrivthe routing cost increase is in most cases moderate if all suppliers are alwaysWhenever driver consistency is not strictly necessarydriver consistency is very promising since a high levthe same consistency level could be reached on our instances by applyingduring the solution of the MRS, we reassign the tours in a second step in aassignment to a transport concept simultaneously was tested on both artifi-incorporated area forwarding, point-to-point transports,tigated the behaviour in case of varying milk run cost parameters not beingof a production site of Bosch automotive in Homburg the application of theTC-MRS model resulted in significant cost savings of up to 15% compared toThis was especially surprising since the weight structure is – due to the lofor the instances considering 44 out of the 54 regular suppliers and all 54are incorporated, the higher is the cost savings potential.the use case data that there exist situations in which significant additionalcost savings can be realised by considering vehicle classes with differenand capacity parameters instead of a single vehicle tAs a benchmark we also tested the performance of rule based transport con-run design problem and not necessarily a solution approach scaling to largeproach, which could be applied to all model configurations and which yieldedoptimal results for nearly all models on all instances.generation procedure grows exponentially with the number of suppliers.the number of tours is high, also the solution process of the set cover or par-for configurations in which time consistency is considered.time consistency could be solved to optimality for all instances of our real-world use case containing up to 54 suppliers within less than an hour.authors report on more producing companies having only between 20 and upto smaller real-world instances yielding optimal results.The set of research questions 4 is treated within the case studyThe procedures to generate the necessary input data for solving a milk rundesign model are transferable to other companies since they are based onSolving the milk run design problem based on the derived input parametersdecide if more detailed, usually difficult to gather, data such as net demandsthe order policy can be adapted in a way that the frequency and the shippingfined by the share of AF cost for an order and the milk run cost accrued ifthe corresponding supplier is served on an exclusive milk run.values can be easily determined without solving a vehicle routing problem.it is not very likely that milk runs are a cost efficienis above one, at least one milk run results in cost savings and an in depthbe also used to assess AF tariff tables compared to exclusive milk runs orthe actual milk run cost including potential extra cost accrued if the demandmeasuring the performance of a milk run cluster with respect to alternativethe AF tariffs the fewer milk runs are cost efficient but the better the milkdesign problem corresponds to “cherry picking” with respect to the freightThe results of our experiments showed that the TC-MRS is adequate to modelthe milk run design decision if the receiving plant aims for weekly recurringmilk runs consisting of a pre- and a main-leg or a pre-, main- and sub-legsuppliers is located far away from the receiving planreverse flows of parts to suppliers – for example in case of metal finishingprocesses executed by a supplier – the routing model should consider pickIf the AF tariffs differentiate between pre- and main-leg tables, the AF costcannot be determined before the orders are assigned to days since the tariffsfor the main-leg depend on the resulting volumes per dayEven if it is assumed that sufficiently stable frequencies and vreached in general, in practice the capacity of milk runs will be exceeded ondays with a higher demand and the capacity usage rate will be low on dadifferent parts for the same plant are often correlated.considering different possible recourse strategies for exceeding demands.with exact or heuristic subprocedures seems promising.cases the time synchronisation resulting from time consistency requirementscomplicates the approach since one must assure that compatible tours withA heuristic approach successfully applied to other vehicle routing problemsproblems is the adaptive large neighbourhood search.a helpful indicator for selecting suppliers for relaxing the solution and forAkturk, M. and F. Erhun (1999).