Flexible servers in tandem lines with setup costs

Abstract

We study the dynamic assignment of flexible servers to stations in the presence of setup costs that are incurred when servers move between stations. The goal is to maximize the long-run average profit. We provide a general problem formulation and some structural results, and then concentrate on tandem lines with two stations, two servers, and a finite buffer between the stations. We investigate how the optimal server assignment policy for such systems depends on the magnitude of the setup costs, as well as on the homogeneity of servers and tasks. More specifically, for systems with either homogeneous servers or homogeneous tasks, small buffer sizes, and constant setup cost, we prove the optimality of "multiple threshold" policies (where servers' movement between stations depends on both the number of jobs in the system and the locations of the servers) and determine the values of the thresholds. For systems with heterogeneous servers and tasks, small buffers, and constant setup cost, we provide results that partially characterize the optimal server assignment policy. Finally, for systems with larger buffer sizes and various service rate and setup cost configurations, we present structural results for the optimal policy and provide numerical results that strongly support the optimality of multiple threshold policies.

Dynamic Control of Non‐Collaborative Workers When Reassignment Is Costly

“…One can also contrast the structure of the optimal policy characterized in Theorem 1 to the partial characterization of the optimal worker allocation policy in the collaborative setting provided by Andradóttir et al. (2012). Their results show that for systems with small buffer sizes (i.e., and ), the collaborative optimal policy uses the non‐collaborative worker assignment that maximizes the product of the service rates whenever the workers are not collaborating (so the alternative non‐collaborative assignment is never used), reassigns at most one worker at a time, only reassigns a worker to initiate or to end collaboration, and depending on the magnitude of the reassignment costs, may never reassign one or both workers.…”

“…As far as we are aware, the only paper that considers a system with multiple cross‐trained servers, finite buffers and setups is Andradóttir et al. (2012). Furthermore, previous work on allocation of flexible servers in the presence of setup costs considers either single‐server systems or assumes servers are collaborative.…”

Optimal control policies in service systems with limited information on the downstream stage

“…More recently, Baumann and Sandmann () study multiserver tandem queues where both stages have a finite buffer and service times are assumed to follow phase‐type distribution. Two‐stage systems with multiple flexible servers are also studied by Andradóttir, Ayhan, and Kırkızlar (), Schiefermayr and Weichbold (), and Wu, Lewis, and Veatch (). In contrast to our paper, returning jobs is not considered in the setting of these studies and authors assume that the state information is fully known to all servers when they make the decisions of which queue to serve next.…”

Dynamic control of a flexible server in an assembly-type queue with setup costs

“…The articles that we are aware of are Andradottir, Ayhan, and Down [2,3], Andradottir, Ayhan, and Kırkızlar [4], Duenyas, Gupta, and Olsen [7], Iravani, Posner, and Buzacott [15], Mayorga, Taaffe, and Arumugam [19], and Sennott, Van Oyen, and Iravani [22]. Among these, the most relevant to our work are Duenyas et al [7] and Iravani et al [15], which consider a tandem queueing network where all stations are attended by a single server.…”