An optimal scheduling problem for a system with finite buffers and non-negligible setup times and costs

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

“…Equations (20) and (22) agree with intuition: l * is a function of the setup cost K s going to infinity as K s goes to infinity. Also, if K s = 0, we expect l * = 0, since this is the optimal solution of the case with negligible setup costs.…”

“…8 and 9 we report the limit cycle for K s = 2000, 500 and 350 respectively. From equations (20) and (22) we get l * = 7.6, 0.36 and 0 respectively. These values agree with the values which can be observed in the figures, in particular the optimal steady state trajectory approaches the limit cycle optimal in the case of negligible setup costs (see Fig.…”

“…Based on a model similar to the one defined in [18], we considered non negligible setup times in [19] and non negligible setup times and costs in [20] deriving results about systems with finite buffers, with particular attention to the transient optimization problem. For this objective, we considered a cost index, similar to the one defined in [21], which allows to optimize the transient behavior.…”

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

“…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.…”