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## Multi-product systems with both setup times and costs: Fluid bounds and schedules (2004)

Venue: | Operations Research |

Citations: | 18 - 0 self |

### Citations

1167 |
Nonlinear Programming: Theory and Algorithms.
- Bazaraa, Sherali, et al.
- 2006
(Show Context)
Citation Context ...t result in the optimal sequence described above. The data set contains 4 queues, the workload backlogging costs and setup costs are ci = 1 and ki = 50 for all 1 ≤ i ≤ 4. Further µ1 =9,µi = 1 for i ∈ =-=[2, 4]-=-, λ1 =1.125, 1.575, or 2.025, and λi =0.125, 0.175, or 0.225 for i ∈ [2, 4] with ρ equal to 0.5, 0.7, or 0.9, respectively. We simulate a periodic exhaustive service system with a polling table equal ... |

464 |
Stochastic modeling and the theory of queues
- Wolff
- 1989
(Show Context)
Citation Context .... Remark 3: It is shown in the numerical study that the lower bound is not a lower bound for systems under dynamic scheduling schemes. One reason for this lies with the inspection paradox (see, e.g., =-=[79]-=-). For example, if one could show that the probability that a type i job does not see the machine cruising in queue i is (1 − dπ i ) (as one may intuitively expect), then the lower bound would follow ... |

350 | On positive harris recurrence of multiclass queueing networks: A unified approach via fluid limit models. The Annals of Applied Probability
- Dai
- 1995
(Show Context)
Citation Context ...rmance approximations because in simple systems without setups strong-law scalings often result in a zero limit. However, such a zero limit is often highly useful in proving stability (see, e.g., Dai =-=[19]-=- and Rybko and Stolyar [69]). Indeed, Dai and Jennings [20] and Jennings [38] explicitly use fluid models of systems with setups to prove stability. In systems with setups, strong-law scalings, where ... |

209 |
Analysis of Polling Systems
- Takagi
(Show Context)
Citation Context ...r the server changes product class are known as polling models. Polling models have been heavily studied in the queueing and telecommunications literature. The interested reader is referred to Takagi =-=[71]-=-, [72], and [73] for surveys of this literature and Levy and Sidi [46] for a survey of polling model applications. 1In general, polling table work considers setup times but not costs; whereas there i... |

139 |
Ergodicity of stochastic processes describing the operation of open queueing networks
- Rybko, Stolyar
- 1992
(Show Context)
Citation Context ...se in simple systems without setups strong-law scalings often result in a zero limit. However, such a zero limit is often highly useful in proving stability (see, e.g., Dai [19] and Rybko and Stolyar =-=[69]-=-). Indeed, Dai and Jennings [20] and Jennings [38] explicitly use fluid models of systems with setups to prove stability. In systems with setups, strong-law scalings, where both work and time are scal... |

137 |
Production and Operations Analysis
- Nahmias
- 1997
(Show Context)
Citation Context ...y is that, in FBk, the average setup costs equals the average workload backlogging costs in each production run for each product. This is similar to the results in a traditional EOQ model (see, e.g., =-=[55]-=-) in which average setup costs equals average inventory costs for a single product system. Note that, without cruising, it would not be possible to let the backlogging costs equal setup costs for each... |

93 |
Stochastic decompositions in the M/G/1 queue with generalized vacations
- Fuhrmann, Cooper
- 1985
(Show Context)
Citation Context ...[L µi i=1 π N∑ ci i ] ≥ E[L µi i=1 π∗ N∑ i i ]= ciρiE[W i=1 π∗ i i ], where the last equivalence follows from Little’s law. are all well defined. The requirements of the Fuhrmann-Cooper decomposition =-=[30]-=- for M/G/1 queues with generalized vacations and exhaustive service hold for queue i under π∗ i . In particular, the number of customers that arrive during an intervisit time is, by definition, indepe... |

59 |
Queueing analysis of polling models: an update, in: H
- Takagi
- 1990
(Show Context)
Citation Context ...server changes product class are known as polling models. Polling models have been heavily studied in the queueing and telecommunications literature. The interested reader is referred to Takagi [71], =-=[72]-=-, and [73] for surveys of this literature and Levy and Sidi [46] for a survey of polling model applications. 1In general, polling table work considers setup times but not costs; whereas there is a la... |

55 | Sequencing and routing in multiclass queueing networks. part i: Feedback regulation
- Meyn
- 2001
(Show Context)
Citation Context ...has been described above in the context of bounds. There is also work that views the fluid model as the limit of a stochastic system. For example, fluid limit models are explicitly considered in Meyn =-=[52]-=- and [53]. The optimal policy for the fluid model provides a policy for a stochastic network model that is “almost optimal in heavy traffic” (see [53] for details). Also, Maglaras [48] uses fluid limi... |

53 |
Scheduling with batching: a review
- Potts, Kovalyov
- 2000
(Show Context)
Citation Context ...ure for deterministic capacitated systems where demand may change over time (but is known). Surveys of batching decisions are provided by Kuik, Salomon, and van Wassenhove [42] and Potts and Kovalyov =-=[66]-=-. Baker [1] reviews the deterministic scheduling literature for scheduling job families with setups and due dates as well as presenting new heuristic procedures. Here we focus on systems that are both... |

50 |
Discrete-review policies for scheduling stochastic networks: trajectory tracking and fluid-scale asymptotic optimality
- Maglaras
- 2000
(Show Context)
Citation Context ...sidered in Meyn [52] and [53]. The optimal policy for the fluid model provides a policy for a stochastic network model that is “almost optimal in heavy traffic” (see [53] for details). Also, Maglaras =-=[48]-=- uses fluid limits that result from heavy-traffic limits to derive schedules for a system without setups. Recent surveys of the use of fluid models for scheduling may be found in Bertsimas et al. [4] ... |

40 |
The economic lot scheduling problem (ELSP): Review and extensions
- Elmaghraby
- 1978
(Show Context)
Citation Context ..., the majority of this literature is for deterministic environments. In particular, solution techniques for the Economic Lot Scheduling Problem (ELSP) consume a large portion of this work. Elmaghraby =-=[26]-=- and Carstensen [16] provide surveys of the ELSP. In addition, Drexl and Kimms [22] survey the lot sizing and scheduling literature for deterministic capacitated systems where demand may change over t... |

38 |
Queueing analysis of polling models: progress in 1990–1994
- Takagi
- 1997
(Show Context)
Citation Context ...nges product class are known as polling models. Polling models have been heavily studied in the queueing and telecommunications literature. The interested reader is referred to Takagi [71], [72], and =-=[73]-=- for surveys of this literature and Levy and Sidi [46] for a survey of polling model applications. 1In general, polling table work considers setup times but not costs; whereas there is a large operat... |

36 |
On the optimal control of two queues with server set-up times and its analysis
- Hofri, Ross
(Show Context)
Citation Context ...ched. Optimal dynamic schedules for polling systems are extremely difficult to obtain. Even systems with only two queues present significant challenges (see, e.g., Boxma and Down [11], Hofri and Ross =-=[34]-=-, Koole [41], Nobel [56] [57], Nobel and Tijms [58], and Reiman and Wein [68]). For systems with more than two queues one is struck by the “curse of dimensionality.” While there has been some numerica... |

36 | Dynamic scheduling of a two class queue with setups
- Reiman, Wein
- 1998
(Show Context)
Citation Context ...o obtain. Even systems with only two queues present significant challenges (see, e.g., Boxma and Down [11], Hofri and Ross [34], Koole [41], Nobel [56] [57], Nobel and Tijms [58], and Reiman and Wein =-=[68]-=-). For systems with more than two queues one is struck by the “curse of dimensionality.” While there has been some numerical work on solving such systems (see, e.g., Kim et al. [40]), the schedules th... |

34 |
sizing and scheduling - survey and extensions
- Drexl, Kimms
- 1997
(Show Context)
Citation Context ... solution techniques for the Economic Lot Scheduling Problem (ELSP) consume a large portion of this work. Elmaghraby [26] and Carstensen [16] provide surveys of the ELSP. In addition, Drexl and Kimms =-=[22]-=- survey the lot sizing and scheduling literature for deterministic capacitated systems where demand may change over time (but is known). Surveys of batching decisions are provided by Kuik, Salomon, an... |

28 | A fluid heuristic for minimizing makespan in job-shops
- Dai, Weiss
(Show Context)
Citation Context ... of the idling conditions derived by Chase and Ramadge. Perkins and Kumar [65] (but not Chase and Ramadge [17]) present a scheduling heuristic for the fluid system based on their bound. Dai and Weiss =-=[21]-=- present bounds and schedules utilizing a fluid system for minimizing makespan in jobshops. Bounds for systems with both setups times and costs in stochastic systems have been considered by Federgruen... |

28 |
Assigning a single server to inhomogeneous queues with switching costs. Theoretical Computer Science
- Koole
- 1997
(Show Context)
Citation Context ...l dynamic schedules for polling systems are extremely difficult to obtain. Even systems with only two queues present significant challenges (see, e.g., Boxma and Down [11], Hofri and Ross [34], Koole =-=[41]-=-, Nobel [56] [57], Nobel and Tijms [58], and Reiman and Wein [68]). For systems with more than two queues one is struck by the “curse of dimensionality.” While there has been some numerical work on so... |

23 | From fluid relaxations to practical algorithms for job shop scheduling: the makespan objective
- Bertsimas, Sethuraman
(Show Context)
Citation Context ...[48] uses fluid limits that result from heavy-traffic limits to derive schedules for a system without setups. Recent surveys of the use of fluid models for scheduling may be found in Bertsimas et al. =-=[4]-=- and Hasenbein [32]. There have been some limited optimality results for multi-queue systems like those in this paper. For example, Liu et al. [47] show that for symmetric single machine systems, with... |

22 | Optimization of multiclass queueing networks with changeover times via the achievable region method: Part I, the single-station case
- Bertsimas, Nino-Mora
- 1999
(Show Context)
Citation Context ...bed above and the bounds in this paper are for stochastic systems under static service policies. Lower bounds for weighted mean delay under dynamic policies have been found in Bertsimas and Niño-Mora =-=[6]-=-. In this work, external arrivals are assumed to be Poisson but Bernoulli routing is allowed. Setups are sequence-dependent. Using the achievable region approach, Bertsimas and Niño-Mora provide a ser... |

22 |
Batching Decisions: Structure and Models
- Kuik, Salomon, et al.
- 1994
(Show Context)
Citation Context ...izing and scheduling literature for deterministic capacitated systems where demand may change over time (but is known). Surveys of batching decisions are provided by Kuik, Salomon, and van Wassenhove =-=[42]-=- and Potts and Kovalyov [66]. Baker [1] reviews the deterministic scheduling literature for scheduling job families with setups and due dates as well as presenting new heuristic procedures. Here we fo... |

21 | Polling systems in heavy-traffic: a Bessel process limit - Coffman, Puhalskii, et al. - 1998 |

21 | Optimality of index policies for stochastic scheduling with switching penalties
- Oyen, Pandelis, et al.
- 1992
(Show Context)
Citation Context ...e: Setups in the context of lotsizing (see, e.g., Hodgson et al. [33], Karmarkar et al. [39], and references there-in), models with no arrivals but some stochastic element (see, e.g., Van Oyen et al. =-=[77]-=- and Van Oyen and Pichitlamken [78]), polling systems with fixed times for beginning and ending service (see, e.g., Borst et al. [10]), polling systems where the queues are in sequence and the custome... |

19 |
Heavy traffic analysis of dynamic cyclic policies: a unified treatment of the single machine scheduling problem
- Markowitz, Wein
(Show Context)
Citation Context ...ns are on an ongoing basis, based on the state of the system. Stochastic make-to-stock systems are often referred to as the stochastic ELSP (see, e.g., Federgruen and Katalan [28], Markowitz and Wein =-=[50]-=-, and Sox et al. [70]). Here we focus on systems that are make-to-order rather than make-to-stock. Single-server make-to-order queueing systems where a setup time is incurred whenever the server chang... |

17 |
Determining production schedules under base-stock policies in single facility multi-item production systems
- Federgruen, Katalan
- 1998
(Show Context)
Citation Context ...ndom fashion) and decisions are on an ongoing basis, based on the state of the system. Stochastic make-to-stock systems are often referred to as the stochastic ELSP (see, e.g., Federgruen and Katalan =-=[28]-=-, Markowitz and Wein [50], and Sox et al. [70]). Here we focus on systems that are make-to-order rather than make-to-stock. Single-server make-to-order queueing systems where a setup time is incurred ... |

16 |
On real-time scheduling policies for flexible manufacturing systems
- Chase, Ramadge
- 1992
(Show Context)
Citation Context ... particular, Perkins and Kumar [65] provided a lower bound on the average production cost per unit time for a similar type of fluid model to the one that we consider in Section 4.1. Chase and Ramadge =-=[17]-=- extended this work by introducing the notion of idling and gave a refined lower bound. Our fluid bound extends this previous work to cases where setup times are allowed to be different for each produ... |

16 |
A two-stage tandem queue attended by a moving server with holding and switching costs. Queueing Systems
- Iravani, Posner, et al.
- 1997
(Show Context)
Citation Context ...ing service (see, e.g., Borst et al. [10]), polling systems where the queues are in sequence and the customer is routed through each station in turn (see, e.g., Duenyas et al. [25] and Iravani et al. =-=[36]-=-), scheduling systems with finite buffers (see, e.g., Browne and Yechiali [15], Hwang and Chang [35], Kim and Van Oyen [40], and Marsan et al. [51]), optimization within cyclic 7schedules (see, e.g.,... |

15 | Stochastic scheduling of parallel queues with set-up costs, Queueing Systems 19
- Duenyas, Oyen
- 1995
(Show Context)
Citation Context ...Yechiali [14] derive quasi-dynamic index policies where each queue is visited exactly once per cycle but the order in which queues are visited within a cycle changes dynamically. Duenyas and Van Oyen =-=[23]-=- provide a dynamic heuristic for scheduling systems with setup costs that is based on a dynamic programming formulation and Duenyas and Van Oyen [24] provides similar results for systems with setup ti... |

13 | The stochastic economic lot scheduling problem: heavy traffic analysis of dynamic cyclic policies
- Markowitz, Reiman, et al.
(Show Context)
Citation Context ...em at any time. Duenyas and Van Oyen [24] show that in order to minimize total expected throughput it is optimal to serve exhaustively at the class with the smallest processing time. Markowitz et al. =-=[49]-=- show that, in cyclic service systems under heavy-traffic, it is optimal to serve all but the lowest priority class exhaustively. Van der Mei and Levy [76] analyze cyclic systems under branching-type ... |

12 | Dynamic server assignment in a twoqueue model
- Boxma, Down
- 1997
(Show Context)
Citation Context ...se-stock level is reached. Optimal dynamic schedules for polling systems are extremely difficult to obtain. Even systems with only two queues present significant challenges (see, e.g., Boxma and Down =-=[11]-=-, Hofri and Ross [34], Koole [41], Nobel [56] [57], Nobel and Tijms [58], and Reiman and Wein [68]). For systems with more than two queues one is struck by the “curse of dimensionality.” While there h... |

12 |
distributed, real-time scheduling of flexible manufacturing/assembly/disassembly systems
- Stable
- 1989
(Show Context)
Citation Context ...e research. 2 Literature Due to the fact that fluid systems are interesting in their own right, there has been some work on bounding the performance of fluid systems. In particular, Perkins and Kumar =-=[65]-=- provided a lower bound on the average production cost per unit time for a similar type of fluid model to the one that we consider in Section 4.1. Chase and Ramadge [17] extended this work by introduc... |

11 |
Multi-item batching heuristics for minimization of queueing delays
- US, Kekre, et al.
- 1992
(Show Context)
Citation Context ... designed to produce flow times with a light tailed distribution and moderate mean. Other relevant models include: Setups in the context of lotsizing (see, e.g., Hodgson et al. [33], Karmarkar et al. =-=[39]-=-, and references there-in), models with no arrivals but some stochastic element (see, e.g., Van Oyen et al. [77] and Van Oyen and Pichitlamken [78]), polling systems with fixed times for beginning and... |

11 |
Polling systems with periodic server routing in heavy-traffic: renewal arrivals
- Olsen, Mei
(Show Context)
Citation Context ...ere queues are evenly spaced. Recently, Olsen and van der Mei have provided heavy-traffic limit theorems for the behavior of polling tables under exhaustive (and gated) service. Olsen and van der Mei =-=[62]-=- prove results for systems in steady-state with Poisson arrivals and Olsen and van der Mei [63] (OVDM) conjecture results for both transient and steady-state systems with renewal arrivals. These conje... |

10 |
Op[imization of polling systems with Bernoulli schedules
- Blanc, Mei
- 1992
(Show Context)
Citation Context ...ith finite buffers (see, e.g., Browne and Yechiali [15], Hwang and Chang [35], Kim and Van Oyen [40], and Marsan et al. [51]), optimization within cyclic 7schedules (see, e.g., Blanc and van der Mei =-=[9]-=- and Levy [45]), transportation applications (see, e.g., Gandhi and Cassandras [31]), workload allocation or customer routing across parallel polling models (see, e.g., Benjaafar and Gupta [3] and Raj... |

9 |
Binomial-gated service: A method for effective operation and optimization of polling systems
- Levy
- 1991
(Show Context)
Citation Context ...ffers (see, e.g., Browne and Yechiali [15], Hwang and Chang [35], Kim and Van Oyen [40], and Marsan et al. [51]), optimization within cyclic 7schedules (see, e.g., Blanc and van der Mei [9] and Levy =-=[45]-=-), transportation applications (see, e.g., Gandhi and Cassandras [31]), workload allocation or customer routing across parallel polling models (see, e.g., Benjaafar and Gupta [3] and Rajan and Agrawal... |

9 |
On optimal polling policies. Queueing Systems Theory and Applications
- Liu, Nain, et al.
- 1992
(Show Context)
Citation Context ...odels for scheduling may be found in Bertsimas et al. [4] and Hasenbein [32]. There have been some limited optimality results for multi-queue systems like those in this paper. For example, Liu et al. =-=[47]-=- show that for symmetric single machine systems, with some 6mild independence assumptions, policies that are exhaustive and serve the next class as that with the most work stochastically minimize the... |

9 |
Delay in polling systems with large switch-over times
- Mei
- 1999
(Show Context)
Citation Context ... scalings with respect to setup times. In other words, mean setup times are increased to infinity while both work and time are scaled down in proportion to mean setup time. Olsen [60] and van der Mei =-=[75]-=- consider such heavy-setup scalings. Most relevant to the work here, [60] considers systems with polling tables under exhaustive service in steady-state. By noting that the waiting time distribution f... |

7 | Heuristic procedures for scheduling job families with setups and due dates. Naval Research Logistic
- Baker
- 1999
(Show Context)
Citation Context ...rministic capacitated systems where demand may change over time (but is known). Surveys of batching decisions are provided by Kuik, Salomon, and van Wassenhove [42] and Potts and Kovalyov [66]. Baker =-=[1]-=- reviews the deterministic scheduling literature for scheduling job families with setups and due dates as well as presenting new heuristic procedures. Here we focus on systems that are both stochastic... |

7 | Optimization of polling systems and dynamic vehicle routing problems on networks. Working paper, Operations Research
- Bertsimas, Xu
- 1993
(Show Context)
Citation Context ...duct variety, they use their bounds to provide insights on the growth rate of system cost. One of these 4insights is described in Section 4.3. Perhaps most related to the work here, Bertsimas and Xu =-=[8]-=- have provided a lower bound for systems with sequence-dependent setup times and no setup costs. Assuming Poisson arrivals they derive a lower bound on weighted mean delay over all static policies. Th... |

7 |
A practical scheduling method for multiclass production systems with setups
- Olsen
- 1999
(Show Context)
Citation Context ...cheduling heuristics for these systems and shows how these bounds lead to good heuristic schedules. Examples of appropriate production environments for such models may be found, for example, in Olsen =-=[59]-=-. The scheduling of systems with setups has a vast literature. However, the majority of this literature is for deterministic environments. In particular, solution techniques for the Economic Lot Sched... |

7 |
Limit theorems for polling models with increasing setups
- Olsen
- 2001
(Show Context)
Citation Context ...rform strong-law type scalings with respect to setup times. In other words, mean setup times are increased to infinity while both work and time are scaled down in proportion to mean setup time. Olsen =-=[60]-=- and van der Mei [75] consider such heavy-setup scalings. Most relevant to the work here, [60] considers systems with polling tables under exhaustive service in steady-state. By noting that the waitin... |

7 |
H.: Polling systems in heavy traffic: exhaustiveness of service policies. Queueing Syst
- Mei, Levy
- 1997
(Show Context)
Citation Context ...e smallest processing time. Markowitz et al. [49] show that, in cyclic service systems under heavy-traffic, it is optimal to serve all but the lowest priority class exhaustively. Van der Mei and Levy =-=[76]-=- analyze cyclic systems under branching-type service. They derive closed form expressions for the expected delay under standard heavy-traffic scalings in terms of a single “exhaustiveness” parameter. ... |

6 |
Efficient visit orders for polling systems
- Boxma, Levy, et al.
- 1993
(Show Context)
Citation Context ...me that the machine spends cruising in queue i, respectively. We use the word “intuitive” because under our definition of stability we have not proven that such fractions exist. In Boxma et al. [12], =-=[13]-=- and Federgruen and Katalan [28], polling tables are determined by first finding appropriate ni, 1 ≤ i ≤ N. Our solution to ni can serve this purpose as well. This idea is explored further in Section ... |

5 | Decomposition results for general polling systems and their applications. Queueing Systems
- Bertsimas, Mourtzinou
- 1999
(Show Context)
Citation Context ...cheduling policy. ✷ Remark 1: The only place the proof hinges on the assumption of Poisson arrivals is in applying the Fuhrmann-Cooper decomposition in equation (3). However, Bertsimas and Mourtzinou =-=[5]-=- have generalized the Fuhrmann-Cooper decomposition results. Therefore this result also extends to systems with Mixed Generalized Erlang arrival process using Theorem 4 in [5] or, as in Theorem 7 in [... |

5 |
Control of a single-server tandem queueing system with setups
- Duenyas, Gupta, et al.
- 1998
(Show Context)
Citation Context ...es for beginning and ending service (see, e.g., Borst et al. [10]), polling systems where the queues are in sequence and the customer is routed through each station in turn (see, e.g., Duenyas et al. =-=[25]-=- and Iravani et al. [36]), scheduling systems with finite buffers (see, e.g., Browne and Yechiali [15], Hwang and Chang [35], Kim and Van Oyen [40], and Marsan et al. [51]), optimization within cyclic... |

4 |
Workload allocation in multi-product, multi-facility production systems
- Benjaafar, Gupta
- 1999
(Show Context)
Citation Context ...der Mei [9] and Levy [45]), transportation applications (see, e.g., Gandhi and Cassandras [31]), workload allocation or customer routing across parallel polling models (see, e.g., Benjaafar and Gupta =-=[3]-=- and Rajan and Agrawal [67]) and practical applications of setup scheduling (see, e.g., Fransoo et al. [29], Olson and Schniederjans [64], and Tayur [74]). 3 Notation and Assumptions The systems we co... |

4 |
A hierarchical approach for capacity coordination in multiple products single-machine production systems with stationary stochastic demands
- Fransoo, Sridharan, et al.
- 1995
(Show Context)
Citation Context ...allocation or customer routing across parallel polling models (see, e.g., Benjaafar and Gupta [3] and Rajan and Agrawal [67]) and practical applications of setup scheduling (see, e.g., Fransoo et al. =-=[29]-=-, Olson and Schniederjans [64], and Tayur [74]). 3 Notation and Assumptions The systems we consider are composed of N types of product (classes of jobs) served by a single machine (server) in a make-t... |

4 |
Cassandras. Optimal control of polling models for transportation applications
- Gandhi, G
- 1996
(Show Context)
Citation Context ... and Van Oyen [40], and Marsan et al. [51]), optimization within cyclic 7schedules (see, e.g., Blanc and van der Mei [9] and Levy [45]), transportation applications (see, e.g., Gandhi and Cassandras =-=[31]-=-), workload allocation or customer routing across parallel polling models (see, e.g., Benjaafar and Gupta [3] and Rajan and Agrawal [67]) and practical applications of setup scheduling (see, e.g., Fra... |

4 |
Dynamic lot size/sequencing policies in a multi-product, single-machine system
- Hodgson, Ge, et al.
- 1997
(Show Context)
Citation Context ...namic heuristic that is designed to produce flow times with a light tailed distribution and moderate mean. Other relevant models include: Setups in the context of lotsizing (see, e.g., Hodgson et al. =-=[33]-=-, Karmarkar et al. [39], and references there-in), models with no arrivals but some stochastic element (see, e.g., Van Oyen et al. [77] and Van Oyen and Pichitlamken [78]), polling systems with fixed ... |

4 | General Dynamic Programming Algorithms Applied to Polling Systems
- Kim, Oyen, et al.
- 1998
(Show Context)
Citation Context ...nd Reiman and Wein [68]). For systems with more than two queues one is struck by the “curse of dimensionality.” While there has been some numerical work on solving such systems (see, e.g., Kim et al. =-=[40]-=-), the schedules that are produced are often not very implementable. For example, if there are few items the queue might be cleared, for a medium number of items a switch might occur, and for a large ... |

4 |
Improving operations and quoting accurate lead times in a laminate plant. Interfaces Forthcoming
- Tayur
- 1998
(Show Context)
Citation Context ... polling models (see, e.g., Benjaafar and Gupta [3] and Rajan and Agrawal [67]) and practical applications of setup scheduling (see, e.g., Fransoo et al. [29], Olson and Schniederjans [64], and Tayur =-=[74]-=-). 3 Notation and Assumptions The systems we consider are composed of N types of product (classes of jobs) served by a single machine (server) in a make-to-order fashion. Orders for product i arrive a... |

3 |
Optimization of fixed time polling schemes
- Borst, Boxma, et al.
- 1994
(Show Context)
Citation Context ...o arrivals but some stochastic element (see, e.g., Van Oyen et al. [77] and Van Oyen and Pichitlamken [78]), polling systems with fixed times for beginning and ending service (see, e.g., Borst et al. =-=[10]-=-), polling systems where the queues are in sequence and the customer is routed through each station in turn (see, e.g., Duenyas et al. [25] and Iravani et al. [36]), scheduling systems with finite buf... |

3 |
Dynamic priority rules for cyclic type queues
- Browne, Yechiali
- 1989
(Show Context)
Citation Context ...er, we are aware of none that are available for both. Boxma et al. [12] find sequences for periodic service to minimize expected waiting cost where costs are assumed to be linear. Browne and Yechiali =-=[14]-=- derive quasi-dynamic index policies where each queue is visited exactly once per cycle but the order in which queues are visited within a cycle changes dynamically. Duenyas and Van Oyen [23] provide ... |

2 |
The economic lot scheduling problem - survey and LP-based method
- Carstensen
- 1999
(Show Context)
Citation Context ...is literature is for deterministic environments. In particular, solution techniques for the Economic Lot Scheduling Problem (ELSP) consume a large portion of this work. Elmaghraby [26] and Carstensen =-=[16]-=- provide surveys of the ELSP. In addition, Drexl and Kimms [22] survey the lot sizing and scheduling literature for deterministic capacitated systems where demand may change over time (but is known). ... |

2 |
The Effect of Product Variety on Manufacturing Performance.” Working Paper
- Federgruen, Gallego, et al.
- 2000
(Show Context)
Citation Context ... bounds and schedules utilizing a fluid system for minimizing makespan in jobshops. Bounds for systems with both setups times and costs in stochastic systems have been considered by Federgruen et al. =-=[27]-=- in parallel work to ours. However, their work focuses the effect of product variety for make-to-stock systems; they provide both upper and lower bounds for the performance of periodic base-stock poli... |

2 |
Generalized Round Robin Service Disciplines in Stochastic Networks with Setups: Stability Analysis and Diffusion Approximation
- Jennings
- 1999
(Show Context)
Citation Context ...pends on the visit frequencies, this optimization is a non-trivial non-convex optimization. One question that immediately arises is: how large is the class of policies that satisfy the HTAP? Jennings =-=[37]-=- hypothesizes, but does not prove, that his two-queue dynamic scheduling heuristic satisfies the HTAP. Even for cyclic systems with more than two queues the HTAP is just hypothesized to hold in CPR. F... |

2 |
Server allocation and routing in homogeneous queues with switching penalties
- Rajan, Agrawal
- 1996
(Show Context)
Citation Context ..., transportation applications (see, e.g., Gandhi and Cassandras [31]), workload allocation or customer routing across parallel polling models (see, e.g., Benjaafar and Gupta [3] and Rajan and Agrawal =-=[67]-=-) and practical applications of setup scheduling (see, e.g., Fransoo et al. [29], Olson and Schniederjans [64], and Tayur [74]). 3 Notation and Assumptions The systems we consider are composed of N ty... |

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Dynamic scheduling in single-server multiclass service systems with unit buffers
- Browne, Yechiali
- 1991
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Citation Context ...re in sequence and the customer is routed through each station in turn (see, e.g., Duenyas et al. [25] and Iravani et al. [36]), scheduling systems with finite buffers (see, e.g., Browne and Yechiali =-=[15]-=-, Hwang and Chang [35], Kim and Van Oyen [40], and Marsan et al. [51]), optimization within cyclic 7schedules (see, e.g., Blanc and van der Mei [9] and Levy [45]), transportation applications (see, e... |

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Stabilizing Queueing Networks with Setups. Working Paper
- Dai, Jennings
- 2002
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Citation Context ...ups strong-law scalings often result in a zero limit. However, such a zero limit is often highly useful in proving stability (see, e.g., Dai [19] and Rybko and Stolyar [69]). Indeed, Dai and Jennings =-=[20]-=- and Jennings [38] explicitly use fluid models of systems with setups to prove stability. In systems with setups, strong-law scalings, where both work and time are scaled by one minus utilization, can... |

1 | Scheduling Multiclass Queueing Networks via Fluid Models. Tutorial given at
- Hasenbein
- 2002
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Citation Context ...mits that result from heavy-traffic limits to derive schedules for a system without setups. Recent surveys of the use of fluid models for scheduling may be found in Bertsimas et al. [4] and Hasenbein =-=[32]-=-. There have been some limited optimality results for multi-queue systems like those in this paper. For example, Liu et al. [47] show that for symmetric single machine systems, with some 6mild indepe... |

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Positive Harris Recurrence of Multiclass Queueing Networks with Setups. Working Paper
- Jennings
- 2000
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Citation Context ...lings often result in a zero limit. However, such a zero limit is often highly useful in proving stability (see, e.g., Dai [19] and Rybko and Stolyar [69]). Indeed, Dai and Jennings [20] and Jennings =-=[38]-=- explicitly use fluid models of systems with setups to prove stability. In systems with setups, strong-law scalings, where both work and time are scaled by one minus utilization, can result in systems... |

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Dynamic Scheduling of Multi-Product Systems: Bounds and Heuristics
- Lan
- 2000
(Show Context)
Citation Context ...nd derived by Chase and Ramadge in their Theorem 1. However, our ciρi cjρj CC1 is ≥ which corrects the first cruising condition from Chase and Ramadge [17]. 1 − ρi 1 − ρj Further, as described in Lan =-=[43]-=-, although there is a flaw in Chase and Ramadge’s proof that at most one queue should have cruising, the result is still true (unlike in systems with both setup times and costs or with setup costs alo... |

1 | Heuristics for the Stochastic Scheduling of Multi-Product Systems with - Lan, Olsen - 2001 |

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Dynamic polling orders in multiserver multiqueue systems
- Marsan, Donatelli, et al.
- 1995
(Show Context)
Citation Context ...n (see, e.g., Duenyas et al. [25] and Iravani et al. [36]), scheduling systems with finite buffers (see, e.g., Browne and Yechiali [15], Hwang and Chang [35], Kim and Van Oyen [40], and Marsan et al. =-=[51]-=-), optimization within cyclic 7schedules (see, e.g., Blanc and van der Mei [9] and Levy [45]), transportation applications (see, e.g., Gandhi and Cassandras [31]), workload allocation or customer rou... |

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Optimal control for two queues with one switching server. Working Paper, Vrije Universiteit, The
- Nobel
- 2001
(Show Context)
Citation Context ...hedules for polling systems are extremely difficult to obtain. Even systems with only two queues present significant challenges (see, e.g., Boxma and Down [11], Hofri and Ross [34], Koole [41], Nobel =-=[56]-=- [57], Nobel and Tijms [58], and Reiman and Wein [68]). For systems with more than two queues one is struck by the “curse of dimensionality.” While there has been some numerical work on solving such s... |

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Optimal control for two finite-buffer queues with one switching server. Working Paper, Vrije Universiteit, The Netherlands
- Nobel
- 2001
(Show Context)
Citation Context ...es for polling systems are extremely difficult to obtain. Even systems with only two queues present significant challenges (see, e.g., Boxma and Down [11], Hofri and Ross [34], Koole [41], Nobel [56] =-=[57]-=-, Nobel and Tijms [58], and Reiman and Wein [68]). For systems with more than two queues one is struck by the “curse of dimensionality.” While there has been some numerical work on solving such system... |

1 | On Multi-Item Production Systems with Setups: Review and Intuition - Olsen - 2001 |

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A heuristic scheduling system for ceramic industrial coatings
- Olson, Schniederjans
- 2000
(Show Context)
Citation Context ... across parallel polling models (see, e.g., Benjaafar and Gupta [3] and Rajan and Agrawal [67]) and practical applications of setup scheduling (see, e.g., Fransoo et al. [29], Olson and Schniederjans =-=[64]-=-, and Tayur [74]). 3 Notation and Assumptions The systems we consider are composed of N types of product (classes of jobs) served by a single machine (server) in a make-to-order fashion. Orders for pr... |

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Properties of optimal-weighted flowtime policies with a makespan constraint and set-up times
- Oyen, Pichitlamken
- 2000
(Show Context)
Citation Context ...ng (see, e.g., Hodgson et al. [33], Karmarkar et al. [39], and references there-in), models with no arrivals but some stochastic element (see, e.g., Van Oyen et al. [77] and Van Oyen and Pichitlamken =-=[78]-=-), polling systems with fixed times for beginning and ending service (see, e.g., Borst et al. [10]), polling systems where the queues are in sequence and the customer is routed through each station in... |