International Journal of Production Research, 2009
Updating planned lead times in response to changing workload levels leads to erratic ordering beh... more Updating planned lead times in response to changing workload levels leads to erratic ordering behavior, resulting in even larger variability in the workload levels and flow times. This phenomenon is called lead time syndrome, and describes the cyclic interaction between adaptive planned lead times and order sizes. Although it has been conceptually defined and intuitively accepted, formal analysis with analytical evaluation of the phenomenon has not been conducted. The objective of this paper is to provide a stronger understanding of the lead time syndrome, and to give new insights into the effects of frequently updating planned lead times. We develop a two-dimensional Markov process to model a single-item production process with orders released sensitive to the planned lead time. Using matrix-geometric methods, analytical results on the utilization level and the variability in the system are presented in relation to the frequency of updating the planned lead time. Although the average utilization level is always retained, the lead time syndrome causes an increase in the average workload level and the actual flow times of the completed orders. The variability of the planned lead time increases with the update frequency except at the utilization boundaries, where the relative effect of the update frequency diminishes.
International Journal of Production Research, 2009
Updating planned lead times in response to changing workload levels leads to erratic ordering beh... more Updating planned lead times in response to changing workload levels leads to erratic ordering behavior, resulting in even larger variability in the workload levels and flow times. This phenomenon is called lead time syndrome, and describes the cyclic interaction between adaptive planned lead times and order sizes. Although it has been conceptually defined and intuitively accepted, formal analysis with analytical evaluation of the phenomenon has not been conducted. The objective of this paper is to provide a stronger understanding of the lead time syndrome, and to give new insights into the effects of frequently updating planned lead times. We develop a two-dimensional Markov process to model a single-item production process with orders released sensitive to the planned lead time. Using matrix-geometric methods, analytical results on the utilization level and the variability in the system are presented in relation to the frequency of updating the planned lead time. Although the average utilization level is always retained, the lead time syndrome causes an increase in the average workload level and the actual flow times of the completed orders. The variability of the planned lead time increases with the update frequency except at the utilization boundaries, where the relative effect of the update frequency diminishes.
We consider a system in which customers join upon arrival the shortest of two single-server queue... more We consider a system in which customers join upon arrival the shortest of two single-server queues. The interarrival times between customers are Erlang distributed and the service times of both servers are exponentially distributed. Under these assumptions, this system gives rise to a Markov chain on a multi-layered quarter plane. For this Markov chain we derive the equilibrium distribution using the compensation approach. The obtained expression for the equilibrium distribution matches and refines heavy-traffic approximations and tail asymptotics obtained earlier in the literature.
We develop accurate approximations of the delay distribution of the MArP/G/1 queue that cap-ture ... more We develop accurate approximations of the delay distribution of the MArP/G/1 queue that cap-ture the exact tail behavior and provide bounded relative errors. Motivated by statistical analysis, we consider the service times as a mixture of a phase-type and a heavy-tailed distribution. With the aid of perturbation analysis, we derive corrected phase-type approximations as a sum of the delay in an MArP/PH/1 queue and a heavy-tailed component depending on the perturbation parameter. We exhibit their performance with numerical examples. 1.
DOI to the publisher's website. • The final author version and the galley proof are versions of t... more DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:
We study a polling model where we want to achieve a balance between the fairness of the waiting t... more We study a polling model where we want to achieve a balance between the fairness of the waiting times and the efficiency of the system. For this purpose, we introduce the κ-gated service discipline. It is a hybrid of the classical gated and exhausted disciplines, and consists of using κi gated service phases at queue i before the server switches to the next queue. We derive the distributions and means of the waiting times, a pseudo conservation law for the weighted sum of the mean waiting times, and the fluid limits of the waiting times. Our goal is to optimize the κi’s so as to minimize the differences in the mean waiting times, i.e. to achieve maximal fairness, without giving up too much on the efficiency of the system. From the fluid limits we derive a heuristic rule for setting the κi’s. In a numerical study the heuristic is shown to perform well.
Motivated by queues with multi-type servers and multi-type customers, we consider an infinite seq... more Motivated by queues with multi-type servers and multi-type customers, we consider an infinite sequence of items of types C = {c1,. .. , cI }, and another infinite sequence of items of types S = {s1,. .. , sJ }, and a bipartite graph G of allowable matches between the types. We assume that the types of items in the two sequences are i.i.d. with given probability vectors α, β. Matching the two sequences on a first come first served basis defines a unique infinite matching between the sequences. For (ci, sj) ∈ G we define the matching rate rc i ,s j as the long term fraction of (ci, sj) matches in the infinite matching, if it exists. We describe this system by a multi-dimensional countable Markov chain, obtain conditions for ergodicity, and derive its stationary distribution which is, most surprisingly, of product-form. We show that if the chain is ergodic, then the matching rates exist almost surely, and give a closed form formula to calculate them. We point out the connection of this model to some queueing models.
The curriculum of Applied Mathematics at the Eindhoven University of Technology (TU/e) in the Net... more The curriculum of Applied Mathematics at the Eindhoven University of Technology (TU/e) in the Netherlands includes a series of modelling projects: the so-called Modelling Track. This track was introduced in the curriculum fifteen years ago and has a specific educational approach. Mathematics that may be useful in the projects is not necessarily taught in courses preceding the modelling projects. Moreover, during the projects, students have to use their current skills and knowledge or even have to learn (or discover) new techniques by themselves. Overall, this teaching method has been quite successful in terms of students ‟ results and satisfaction. Project coaches have always been recruited from the entire department and gradually, the majority of the staff has become pleased with this method of modeling education. Throughout fifteen years, the structure and content of the series of projects have evolved. This article is based on reflections concerning these changes expressed by the...
Abstract: Motivated by the ABO issue of the blood banks system, in which the portions stored have... more Abstract: Motivated by the ABO issue of the blood banks system, in which the portions stored have constant shelf life, we consider two subsystems of per-ishable inventory. The two Perishable Inventory Subsystems – PIS A and PIS B, are correlated to each other through a so-called one-way substitution of demands. Specifically, the input streams and the demand streams applied to each subsys-tem are four Poisson processes which are independent of one another. However, if the shelf of PIS A (blood of type O) is empty of items an arriving demand of type A is unsatisfied, since demand of type A cannot be satisfied by an item of type B (blood portions of type AB), but if the shelf of PIS B is empty of items an arriving demand of type B is applied to PIS A, since demands of type B can be satisfied by both types. Such a one-way substitution of the issuing policy gen-erates for PIS A a modulated Poisson demand process operating in a two-state non-Markovian environment. The performance analysis...
In this paper we consider a single-server polling system with switch-over times. We introduce a n... more In this paper we consider a single-server polling system with switch-over times. We introduce a new service discipline, mixed gated/exhaustive service, that can be used for queues with two types of customers: high and low priority customers. At the beginning of a visit of the server to such a queue, a gate is set behind all customers. High priority customers receive priority in the sense that they are always served before any low priority customers. But high priority customers have a second advantage over low priority customers. Low priority customers are served according to the gated service discipline, i.e. only customers standing in front of the gate are served during this visit. In contrast, high priority customers arriving during the visit period of the queue are allowed to pass the gate and all low priority customers before the gate. We study the cycle time distribution, the waiting time distributions for each customer type, the joint queue length distribution of all priority ...
Abstract: In this paper we present an approximation for the performance analysis of single-server... more Abstract: In this paper we present an approximation for the performance analysis of single-server tandem queues with small buffers and generally distributed service times. The approximation is based on decomposition of the tandem queue in subsystems, the parameters of which are determined by an iterative algorithm. By employing a detailed description of the service process of each subsystem, we obtain an accurate approximation of performance characteristics such as throughput and mean sojourn time, which substantially outperforms former methods.
A typical polling system consists of a number of queues, attended by a single server in a fixed o... more A typical polling system consists of a number of queues, attended by a single server in a fixed order. The present study derives closed-form approximations for the mean waiting times and mean marginal queue lengths of polling systems with renewal arrival processes, which can be computed by simple calculations. The results of the present research may be very suitable for the design and optimisation phase in many application areas, such as telecommunication, maintenance, manufacturing and transportation.
The curriculum of Applied Mathematics at the Eindhoven University of Technology (TU/e) in the Net... more The curriculum of Applied Mathematics at the Eindhoven University of Technology (TU/e) in the Netherlands includes a series of modelling projects: the so-called Modelling Track. This track was introduced in the curriculum fifteen years ago and has a specific educational approach. Mathematics that may be useful in the projects is not necessarily taught in courses preceding the modelling projects. Moreover, during the projects, students have to use their current skills and knowledge or even have to learn (or discover) new techniques by themselves. Overall, this teaching method has been quite successful in terms of students’ results and satisfaction. Project coaches have always been recruited from the entire department and gradually, the majority of the staff has become pleased with this method of modeling education. Throughout fifteen years, the structure and content of the series of projects have evolved. This article is based on reflections concerning these changes expressed by the ...
Mobile Shelf-based Order Pick (MSOP) systems are gaining significant interest for e-commerce fulf... more Mobile Shelf-based Order Pick (MSOP) systems are gaining significant interest for e-commerce fulfillment due to their rapid deployment capability and dynamic organization of storage pods based on item demand profiles. In this research, we model the MSOP system with class-based storage strategies and alternate pod storage policies using multi-class closed queuing networks. We observe that though closest-open location pod storage policy do not allow to efficiently use the storage spaces in comparison to random location pod storage policy in an aisle, it increases the system throughput for all item classes.
In this paper we analyze continuous- ow production lines consisting of a number of machines or se... more In this paper we analyze continuous- ow production lines consisting of a number of machines or servers in series and a finite buffer between each pair of machines. Each machine suffers from breakdowns, for instance because of failures, cleaning, changeover, etcetera. The resulting up- and downtime periods are generally distributed. Because of breakdowns and non-identical machine speeds, the machines are in uenced by each other, resulting in starvation, blocking, and speed adaption. We are interested in throughput and mean buffer content of this production line. The newly developed method relies on decomposition of the production line into two-stage, one-buffer subsystems. The parameters for each subsystem are determined iteratively. A crucial feature of the model is that we deal with generally distributed up- and downtimes. The use of aggregation techniques on the subsystem level is important to be able to analyze larger production lines of up to 16 machines. The proposed method per...
ing (e.g., Ozmantar & Monaghan, 2008). The activity of concretising probably is more characterist... more ing (e.g., Ozmantar & Monaghan, 2008). The activity of concretising probably is more characteristic for Applied Mathematics than for pure mathematics. We acknowledge that in a process of acting and thinking all four categories can occur, but we will treat those as four equally important and independent activities. We do not regard analysing synthesising or even abstracting concretising as opposites. We will show that for the above definitions engaging in the activity of abstracting does not automatically imply that one is also de-concretising, and vice versa. The independence of abstracting and concretising can be illustrated with an example from the classical mechanics of a pendulum. In high school, a pendulum is considered as a point mass, suspended on an infinitely strong (non-elastic) rope, moving at small amplitudes, leading to a simple linear, second order differential equation. In a first-year mechanics course in university, the abstraction is made where the 'point mass&#...
In the poultry processing industry demand and supply are still growing in volume and diversity, w... more In the poultry processing industry demand and supply are still growing in volume and diversity, which requires more processing capacity, flexibility and smarter control. This paper focuses on the fillet batching process. To minimize the giveaway of fixed-weight fillet batching the right choices on layout, buffer sizes, batch sizes and batch allocation policies are of great importance. We develop a simulation model to support such decisions on design and control. The model is used (i) to determine buffer and grader sizes, (ii) to optimize batch allocation in a dedicated layout, (iii) to compare a dedicated to a flexible layout and (iv) to assess the impact of smart allocation policies. In particular we find that significant reductions in giveaway can be achieved by employing so-called index policies in a flexible layout.
A new concept in automated storage and retrieval systems is the full roaming shuttle system, the ... more A new concept in automated storage and retrieval systems is the full roaming shuttle system, the distinguishing feature of which is that its material handling shuttles are not aisle-captive, but can easily switch aisles and levels in the storage area. A consequence of this flexibility is that shuttles more often overtake each other and deliver product totes in a different sequence than they are requested. In case of strict sequence requirements for delivered totes, this leads to more waiting time of shuttles and thus to loss of throughput capacity. In this paper we propose heuristics to assign tasks to shuttles that aim at minimizing the number of out-of-sequence occurrences and at maximizing the throughput capacity. These heuristics are evaluated through simulation. The results suggest that, in comparison to first-in first-out task assignment, substantial throughput improvement can be achieved by employing smart task assignment heuristics.
To increase a 3D printer's throughput and decrease the print objects' lead times, composing good ... more To increase a 3D printer's throughput and decrease the print objects' lead times, composing good batches for 3D printers in high-volume 3D printing environments is of great importance. Since manual planners cannot oversee the whole production planning, they tend to make sub-optimal decisions. This paper presents a two-stage procedure that automatically generates batches for multiple 3D printers. The first stage consists of allocating objects to a batch. This problem is an extension of the classical one-dimensional bin packing problem by including lateness and object size mixture requirements. In the second stage, the positions of the print objects in a tray are determined by using third party three-dimensional packing software. By simulating the production planning of Shapeways, a popular 3D printing marketplace, model parameters are calibrated and the performance of the two-stage procedure is evaluated. The results show an increase of the throughput of the 3D-printers by approximately 10% in comparison with manually created batches.
The present paper deals with the problem of calculating mean delays in polling systems with eithe... more The present paper deals with the problem of calculating mean delays in polling systems with either exhaustive or gated service. We develop a mean value analysis (MVA) to compute these delay figures. The merits of MVA are in its intrinsic simplicity and its intuitively appealing derivation. As a consequence, MVA may be applied, both in an exact and approximate manner, to a large variety of models.
International Journal of Production Research, 2009
Updating planned lead times in response to changing workload levels leads to erratic ordering beh... more Updating planned lead times in response to changing workload levels leads to erratic ordering behavior, resulting in even larger variability in the workload levels and flow times. This phenomenon is called lead time syndrome, and describes the cyclic interaction between adaptive planned lead times and order sizes. Although it has been conceptually defined and intuitively accepted, formal analysis with analytical evaluation of the phenomenon has not been conducted. The objective of this paper is to provide a stronger understanding of the lead time syndrome, and to give new insights into the effects of frequently updating planned lead times. We develop a two-dimensional Markov process to model a single-item production process with orders released sensitive to the planned lead time. Using matrix-geometric methods, analytical results on the utilization level and the variability in the system are presented in relation to the frequency of updating the planned lead time. Although the average utilization level is always retained, the lead time syndrome causes an increase in the average workload level and the actual flow times of the completed orders. The variability of the planned lead time increases with the update frequency except at the utilization boundaries, where the relative effect of the update frequency diminishes.
International Journal of Production Research, 2009
Updating planned lead times in response to changing workload levels leads to erratic ordering beh... more Updating planned lead times in response to changing workload levels leads to erratic ordering behavior, resulting in even larger variability in the workload levels and flow times. This phenomenon is called lead time syndrome, and describes the cyclic interaction between adaptive planned lead times and order sizes. Although it has been conceptually defined and intuitively accepted, formal analysis with analytical evaluation of the phenomenon has not been conducted. The objective of this paper is to provide a stronger understanding of the lead time syndrome, and to give new insights into the effects of frequently updating planned lead times. We develop a two-dimensional Markov process to model a single-item production process with orders released sensitive to the planned lead time. Using matrix-geometric methods, analytical results on the utilization level and the variability in the system are presented in relation to the frequency of updating the planned lead time. Although the average utilization level is always retained, the lead time syndrome causes an increase in the average workload level and the actual flow times of the completed orders. The variability of the planned lead time increases with the update frequency except at the utilization boundaries, where the relative effect of the update frequency diminishes.
We consider a system in which customers join upon arrival the shortest of two single-server queue... more We consider a system in which customers join upon arrival the shortest of two single-server queues. The interarrival times between customers are Erlang distributed and the service times of both servers are exponentially distributed. Under these assumptions, this system gives rise to a Markov chain on a multi-layered quarter plane. For this Markov chain we derive the equilibrium distribution using the compensation approach. The obtained expression for the equilibrium distribution matches and refines heavy-traffic approximations and tail asymptotics obtained earlier in the literature.
We develop accurate approximations of the delay distribution of the MArP/G/1 queue that cap-ture ... more We develop accurate approximations of the delay distribution of the MArP/G/1 queue that cap-ture the exact tail behavior and provide bounded relative errors. Motivated by statistical analysis, we consider the service times as a mixture of a phase-type and a heavy-tailed distribution. With the aid of perturbation analysis, we derive corrected phase-type approximations as a sum of the delay in an MArP/PH/1 queue and a heavy-tailed component depending on the perturbation parameter. We exhibit their performance with numerical examples. 1.
DOI to the publisher's website. • The final author version and the galley proof are versions of t... more DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:
We study a polling model where we want to achieve a balance between the fairness of the waiting t... more We study a polling model where we want to achieve a balance between the fairness of the waiting times and the efficiency of the system. For this purpose, we introduce the κ-gated service discipline. It is a hybrid of the classical gated and exhausted disciplines, and consists of using κi gated service phases at queue i before the server switches to the next queue. We derive the distributions and means of the waiting times, a pseudo conservation law for the weighted sum of the mean waiting times, and the fluid limits of the waiting times. Our goal is to optimize the κi’s so as to minimize the differences in the mean waiting times, i.e. to achieve maximal fairness, without giving up too much on the efficiency of the system. From the fluid limits we derive a heuristic rule for setting the κi’s. In a numerical study the heuristic is shown to perform well.
Motivated by queues with multi-type servers and multi-type customers, we consider an infinite seq... more Motivated by queues with multi-type servers and multi-type customers, we consider an infinite sequence of items of types C = {c1,. .. , cI }, and another infinite sequence of items of types S = {s1,. .. , sJ }, and a bipartite graph G of allowable matches between the types. We assume that the types of items in the two sequences are i.i.d. with given probability vectors α, β. Matching the two sequences on a first come first served basis defines a unique infinite matching between the sequences. For (ci, sj) ∈ G we define the matching rate rc i ,s j as the long term fraction of (ci, sj) matches in the infinite matching, if it exists. We describe this system by a multi-dimensional countable Markov chain, obtain conditions for ergodicity, and derive its stationary distribution which is, most surprisingly, of product-form. We show that if the chain is ergodic, then the matching rates exist almost surely, and give a closed form formula to calculate them. We point out the connection of this model to some queueing models.
The curriculum of Applied Mathematics at the Eindhoven University of Technology (TU/e) in the Net... more The curriculum of Applied Mathematics at the Eindhoven University of Technology (TU/e) in the Netherlands includes a series of modelling projects: the so-called Modelling Track. This track was introduced in the curriculum fifteen years ago and has a specific educational approach. Mathematics that may be useful in the projects is not necessarily taught in courses preceding the modelling projects. Moreover, during the projects, students have to use their current skills and knowledge or even have to learn (or discover) new techniques by themselves. Overall, this teaching method has been quite successful in terms of students ‟ results and satisfaction. Project coaches have always been recruited from the entire department and gradually, the majority of the staff has become pleased with this method of modeling education. Throughout fifteen years, the structure and content of the series of projects have evolved. This article is based on reflections concerning these changes expressed by the...
Abstract: Motivated by the ABO issue of the blood banks system, in which the portions stored have... more Abstract: Motivated by the ABO issue of the blood banks system, in which the portions stored have constant shelf life, we consider two subsystems of per-ishable inventory. The two Perishable Inventory Subsystems – PIS A and PIS B, are correlated to each other through a so-called one-way substitution of demands. Specifically, the input streams and the demand streams applied to each subsys-tem are four Poisson processes which are independent of one another. However, if the shelf of PIS A (blood of type O) is empty of items an arriving demand of type A is unsatisfied, since demand of type A cannot be satisfied by an item of type B (blood portions of type AB), but if the shelf of PIS B is empty of items an arriving demand of type B is applied to PIS A, since demands of type B can be satisfied by both types. Such a one-way substitution of the issuing policy gen-erates for PIS A a modulated Poisson demand process operating in a two-state non-Markovian environment. The performance analysis...
In this paper we consider a single-server polling system with switch-over times. We introduce a n... more In this paper we consider a single-server polling system with switch-over times. We introduce a new service discipline, mixed gated/exhaustive service, that can be used for queues with two types of customers: high and low priority customers. At the beginning of a visit of the server to such a queue, a gate is set behind all customers. High priority customers receive priority in the sense that they are always served before any low priority customers. But high priority customers have a second advantage over low priority customers. Low priority customers are served according to the gated service discipline, i.e. only customers standing in front of the gate are served during this visit. In contrast, high priority customers arriving during the visit period of the queue are allowed to pass the gate and all low priority customers before the gate. We study the cycle time distribution, the waiting time distributions for each customer type, the joint queue length distribution of all priority ...
Abstract: In this paper we present an approximation for the performance analysis of single-server... more Abstract: In this paper we present an approximation for the performance analysis of single-server tandem queues with small buffers and generally distributed service times. The approximation is based on decomposition of the tandem queue in subsystems, the parameters of which are determined by an iterative algorithm. By employing a detailed description of the service process of each subsystem, we obtain an accurate approximation of performance characteristics such as throughput and mean sojourn time, which substantially outperforms former methods.
A typical polling system consists of a number of queues, attended by a single server in a fixed o... more A typical polling system consists of a number of queues, attended by a single server in a fixed order. The present study derives closed-form approximations for the mean waiting times and mean marginal queue lengths of polling systems with renewal arrival processes, which can be computed by simple calculations. The results of the present research may be very suitable for the design and optimisation phase in many application areas, such as telecommunication, maintenance, manufacturing and transportation.
The curriculum of Applied Mathematics at the Eindhoven University of Technology (TU/e) in the Net... more The curriculum of Applied Mathematics at the Eindhoven University of Technology (TU/e) in the Netherlands includes a series of modelling projects: the so-called Modelling Track. This track was introduced in the curriculum fifteen years ago and has a specific educational approach. Mathematics that may be useful in the projects is not necessarily taught in courses preceding the modelling projects. Moreover, during the projects, students have to use their current skills and knowledge or even have to learn (or discover) new techniques by themselves. Overall, this teaching method has been quite successful in terms of students’ results and satisfaction. Project coaches have always been recruited from the entire department and gradually, the majority of the staff has become pleased with this method of modeling education. Throughout fifteen years, the structure and content of the series of projects have evolved. This article is based on reflections concerning these changes expressed by the ...
Mobile Shelf-based Order Pick (MSOP) systems are gaining significant interest for e-commerce fulf... more Mobile Shelf-based Order Pick (MSOP) systems are gaining significant interest for e-commerce fulfillment due to their rapid deployment capability and dynamic organization of storage pods based on item demand profiles. In this research, we model the MSOP system with class-based storage strategies and alternate pod storage policies using multi-class closed queuing networks. We observe that though closest-open location pod storage policy do not allow to efficiently use the storage spaces in comparison to random location pod storage policy in an aisle, it increases the system throughput for all item classes.
In this paper we analyze continuous- ow production lines consisting of a number of machines or se... more In this paper we analyze continuous- ow production lines consisting of a number of machines or servers in series and a finite buffer between each pair of machines. Each machine suffers from breakdowns, for instance because of failures, cleaning, changeover, etcetera. The resulting up- and downtime periods are generally distributed. Because of breakdowns and non-identical machine speeds, the machines are in uenced by each other, resulting in starvation, blocking, and speed adaption. We are interested in throughput and mean buffer content of this production line. The newly developed method relies on decomposition of the production line into two-stage, one-buffer subsystems. The parameters for each subsystem are determined iteratively. A crucial feature of the model is that we deal with generally distributed up- and downtimes. The use of aggregation techniques on the subsystem level is important to be able to analyze larger production lines of up to 16 machines. The proposed method per...
ing (e.g., Ozmantar & Monaghan, 2008). The activity of concretising probably is more characterist... more ing (e.g., Ozmantar & Monaghan, 2008). The activity of concretising probably is more characteristic for Applied Mathematics than for pure mathematics. We acknowledge that in a process of acting and thinking all four categories can occur, but we will treat those as four equally important and independent activities. We do not regard analysing synthesising or even abstracting concretising as opposites. We will show that for the above definitions engaging in the activity of abstracting does not automatically imply that one is also de-concretising, and vice versa. The independence of abstracting and concretising can be illustrated with an example from the classical mechanics of a pendulum. In high school, a pendulum is considered as a point mass, suspended on an infinitely strong (non-elastic) rope, moving at small amplitudes, leading to a simple linear, second order differential equation. In a first-year mechanics course in university, the abstraction is made where the 'point mass&#...
In the poultry processing industry demand and supply are still growing in volume and diversity, w... more In the poultry processing industry demand and supply are still growing in volume and diversity, which requires more processing capacity, flexibility and smarter control. This paper focuses on the fillet batching process. To minimize the giveaway of fixed-weight fillet batching the right choices on layout, buffer sizes, batch sizes and batch allocation policies are of great importance. We develop a simulation model to support such decisions on design and control. The model is used (i) to determine buffer and grader sizes, (ii) to optimize batch allocation in a dedicated layout, (iii) to compare a dedicated to a flexible layout and (iv) to assess the impact of smart allocation policies. In particular we find that significant reductions in giveaway can be achieved by employing so-called index policies in a flexible layout.
A new concept in automated storage and retrieval systems is the full roaming shuttle system, the ... more A new concept in automated storage and retrieval systems is the full roaming shuttle system, the distinguishing feature of which is that its material handling shuttles are not aisle-captive, but can easily switch aisles and levels in the storage area. A consequence of this flexibility is that shuttles more often overtake each other and deliver product totes in a different sequence than they are requested. In case of strict sequence requirements for delivered totes, this leads to more waiting time of shuttles and thus to loss of throughput capacity. In this paper we propose heuristics to assign tasks to shuttles that aim at minimizing the number of out-of-sequence occurrences and at maximizing the throughput capacity. These heuristics are evaluated through simulation. The results suggest that, in comparison to first-in first-out task assignment, substantial throughput improvement can be achieved by employing smart task assignment heuristics.
To increase a 3D printer's throughput and decrease the print objects' lead times, composing good ... more To increase a 3D printer's throughput and decrease the print objects' lead times, composing good batches for 3D printers in high-volume 3D printing environments is of great importance. Since manual planners cannot oversee the whole production planning, they tend to make sub-optimal decisions. This paper presents a two-stage procedure that automatically generates batches for multiple 3D printers. The first stage consists of allocating objects to a batch. This problem is an extension of the classical one-dimensional bin packing problem by including lateness and object size mixture requirements. In the second stage, the positions of the print objects in a tray are determined by using third party three-dimensional packing software. By simulating the production planning of Shapeways, a popular 3D printing marketplace, model parameters are calibrated and the performance of the two-stage procedure is evaluated. The results show an increase of the throughput of the 3D-printers by approximately 10% in comparison with manually created batches.
The present paper deals with the problem of calculating mean delays in polling systems with eithe... more The present paper deals with the problem of calculating mean delays in polling systems with either exhaustive or gated service. We develop a mean value analysis (MVA) to compute these delay figures. The merits of MVA are in its intrinsic simplicity and its intuitively appealing derivation. As a consequence, MVA may be applied, both in an exact and approximate manner, to a large variety of models.
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