Optimal control of queueing systems with non-collaborating servers

Isik, Tugce; Andradóttir, Sigrún; Ayhan, Hayriye

doi:10.1007/s11134-016-9481-2

Cited by 8 publications

(13 citation statements)

References 59 publications

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“…For systems with N tasks and N workers without any reassignment costs, Işık et al. (2016) characterized a special case in which each worker is the most skilled worker at a different task and showed that in this case, a dedicated worker assignment policy is optimal. The following proposition generalizes that result for systems with positive worker reassignment costs.…”

Section: Structural Results: When Cross‐training Is Not Beneficialmentioning

confidence: 99%

“…Proposition 4 shows that the optimal policy identified by Işık et al. (2016) for systems with no reassignment costs can perform arbitrarily bad when worker reassignments are costly. We perform a similar numerical comparison between the collaborative and non‐collaborative settings by using the partial results by Andradóttir et al.…”

Section: Two‐station Systems With Homogeneous Tasksmentioning

confidence: 95%

“…Note that in the system without reassignment costs, the location of the faster worker does not need to be kept track of and the corresponding MDP has a smaller state space (see Işık et al. 2016). We use the policy iteration algorithm to compute these long‐run average throughput values for systems with N ∈{3, 4} workstations and buffer sizes B ∈{1, 2, 3, 4, 5} since at larger buffer sizes the computation once again becomes challenging.…”

Section: Longer Lines With a Dominant Servermentioning

confidence: 99%

“…If there are no reassignment costs and the tasks are homogeneous, then it is shown that the optimal policy is threshold type and the optimal threshold is

s^{*} \in false{⌊ \frac{B_{1} + 3}{2} ⌋, ⌈ \frac{B_{1} + 3}{2} ⌉ false}

(see Theorem 2 and the proof of Proposition 4 in Işık et al. (2016). Note that this earlier result corresponds to the optimality of the decision rule

δ_{⌊ \frac{B_{1} + 3}{2} ⌋}

for c = 0 in our model, meaning that faster worker is assigned to the upstream station immediately when the buffer is less than half full and is assigned to the downstream station immediately when the buffer is more than half full , which implies that worker reassignments happen more frequently when there are no reassignment costs as one would expect.…”

Section: Two‐station Systems With Homogeneous Tasksmentioning

confidence: 99%

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Dynamic Control of Non‐Collaborative Workers When Reassignment Is Costly

Isik

Andradóttir

Ayhan

2022

Production and Operations Management

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C ross-training is an important tool to improve the performance of manufacturing and service systems through dynamic worker allocation. This study investigates how cross-training can be leveraged when worker collaboration is not possible and frequent worker reassignment is undesirable. We consider a tandem queueing system with finite buffers between tasks. We show that if each worker is the fastest at a different task, then the optimal policy is always dedicated, regardless of the magnitude of the reassignment costs. Otherwise, if the system is Markovian with two homogeneous tasks and a faster and a slower worker, we completely characterize how the profit-optimal policy depends on the (constant) reassignment cost. We also prove that for any given reassignment cost, dedicated worker allocation policies are strictly suboptimal for large enough buffer sizes. Instead, the faster worker should move to the downstream task only if there are enough jobs in the intermediate buffer and return to the upstream task when the buffer is sufficiently empty. Furthermore, the benefit of task switching increases as the buffer size becomes larger. We use our theoretical results to develop worker allocation heuristics both for more general systems with two tasks and for systems with more tasks. Numerical experimentation provides insights on how the profit depends on the buffer sizes and reassignment costs, shows that policies that are optimal when workers are collaborative result in excessive switching for non-collaborative workers, and indicates that our pick-the-best heuristics perform well in all settings.

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Section: Structural Results: When Cross‐training Is Not Beneficialmentioning

confidence: 99%

Section: Two‐station Systems With Homogeneous Tasksmentioning

confidence: 95%

Section: Longer Lines With a Dominant Servermentioning

confidence: 99%

“…If there are no reassignment costs and the tasks are homogeneous, then it is shown that the optimal policy is threshold type and the optimal threshold is

s^{*} \in false{⌊ \frac{B_{1} + 3}{2} ⌋, ⌈ \frac{B_{1} + 3}{2} ⌉ false}

(see Theorem 2 and the proof of Proposition 4 in Işık et al. (2016). Note that this earlier result corresponds to the optimality of the decision rule

δ_{⌊ \frac{B_{1} + 3}{2} ⌋}

Section: Two‐station Systems With Homogeneous Tasksmentioning

confidence: 99%

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Dynamic Control of Non‐Collaborative Workers When Reassignment Is Costly

Isik

Andradóttir

Ayhan

2022

Production and Operations Management

Self Cite

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“…Ahn and Lewis (2013) study the dynamic allocation of two flexible servers in a two-station parallel network, along with the dynamic routing decisions, for revenue management purposes. Flexible server allocation is commonly studied in tandem networks (Farrar, 1993;Ahn et al, 1999;Andradóttir et al, 2001;Ahn et al, 2002;Schhiefermayr and Weichbold, 2005;Andradóttir and Ayhan, 2005;Dobson et al, 2012;Işık et al, 2016;Papachristos and Pandelis, 2019;Lim et al, 2020). Among these, some study a clearing tandem network with no external arrivals (Ahn et al, 1999;Schhiefermayr and Weichbold, 2005;Farrar, 1993;Papachristos and Pandelis, 2019;Lim et al, 2020).…”

Section: Literature Reviewmentioning

confidence: 99%

Capacity management for personalized services in education

Aslan¹

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Operational Tactical Strategic O.1 How many sessions T.1 How much teaching capacity S.1 How many teachers to plan per activity ? to allocate to activities to hire per subject? O.2 Which teachers to assign on each subject, or to learners? S.2 How many classrooms to sessions? T.2 How many classrooms to build? O.3 Which classrooms to assign to allocate to activities S.3 Which seating capacity to sessions? on each subject? to consider for classrooms? O.4 Which time blocks to assign S.4 How frequently to perform to sessions? competency assessments? O.5 Which learners to assign to sessions?In providing these capacity management tools, we use a variety of OR frameworks. Among these are meta-heuristics, simulation, integer programming, stochastic programming, model predictive control, queueing theory and Markov decision processes. In numerically validating and demonstrating the effectiveness of the presented planning tools, we mainly rely on the data coming from Dutch secondary education schools, through collaborating with the Zo.Leer.Ik! schools network.In summary, this thesis has two overarching goals: showing the impact that an Operations Research perspective can make in the transition toward personalization of services in education, and introducing novel operational planning problems on capacity management to the OR literature and providing new solution methods for them. Capacity management tools for service providersWhen educational service providers manage their available resource capacity (i.e., teaching capacity, classrooms and time blocks) to serve the personalized learning demands of many learners, they face several logistics planning decision problems. We identify these in Table 1.1 at operational (O.1-O.4), tactical (T.1-T.2) and strategic (S.1-S.4) decisionmaking levels for a service system that takes a demand-driven planning approach.The operational-level decision problems facilitate the organization of learning activities on subjects (e.g., Mathematics, English) to serve the personalized learning demands that are directly provided by learners. It must be noted that the problems O.2-O.4 are also relevant for one-size-fits-all systems. However, for PL systems these decisions cannot be fixed in the beginning of an academic year, instead they have to be remade depending on the changes in learning demands throughout the year. Moreover, the decision problems O.1 and O.5 are not relevant at all for one-size-fits-all systems.

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