Dynamic Scheduling for a Single Machine System Under Different Setup and Buffer Capacity Scenarios

Abstract

The problem of dynamic scheduling for single machine manufacturing systems has been extensively studied in the past under different setup scenarios, mainly for systems with infinite buffer capacity. This paper addresses a general framework and investigates similarities and differences between policies optimal if setup times and costs are or are not negligible, if buffers have a finite or an infinite capacity. The cost function takes into account of backlog and surplus, but also includes a demand loss component if buffers have a finite capacity and a setup cost if not negligible. Both a steady state and a transient optimization problem are considered and already known results are compared and extended to complete the analysis.

Optimal steady-state and transient trajectories of multi-queue switching servers with a fixed service order of queues

“…The time average costs are commonly used as performance indicator, also referred to as time average weighted work in process for manufacturing systems or time average weighted queue lengths. In [1,4,8,11,14], this performance indicator is also considered. The time average costs, given a fixed cycle time T , are given by…”

“…Therefore, the trajectory can include slow-modes at both queues. A special case of this model, with µ 1 = µ 2 and c 1 = c 2 has been studied in [1,4,7,8,11] and it is shown that the optimal policy is a clearing policy, i.e., the server empties a queue and then switches to serve the other queue.…”

“…For the trajectory depicted in Figure 9b, it is clearly shown that a trade-off exists between a build-up of the much more expensive queue 1 and switching before emptying queue 2. This behavior is not present in symmetric systems, as a clearing policy is optimal for symmetric systems, see for instance [1,11].…”

“…Optimal scheduling of systems with switching behavior is a problem of great importance. This problem, for even the most simple system, i.e., a server attending two queues, has been investigated by many researchers, see for example [1,4,5,6,7,8,10,11,14], and references therein. We follow the general framework introduced by [9] and model the production flow as continuous rather than discrete.…”

“…In the aforementioned literature, the two queue switching servers are restricted in the sense that either setup times, setup costs, backlog or limited queue contents are required, omitted or not allowed. Also, most studies assume the simplifying condition that the system is symmetric, see [1,4,8,11]. In the current work, a two queue switching server is considered without restrictions on any parameters and with the flexibility of allowing setup times, setup costs and backlog, as well as constraints on cycle time, service time and queue contents.…”