Workload-dependent capacity control (original) (raw)
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Workload-dependent capacity control in production-to-order systems
IIE Transactions, 2009
The development of job intermediation and the increasing use of the Internet allow companies to carry out ever quicker capacity changes. In many cases, capacity can be adapted rapidly to the actual workload, which is especially important in production-to-order systems, where inventory cannot be used as a buffer for demand variation. We introduce a set of Markov chain models to represent workload-dependent capacity control policies. We present two analytical approaches to evaluate the policies' due-date performance based on stationary analysis. One provides an explicit expression of throughput time distribution, the other is a fixed-point iteration method that calculates the moments of the throughput time. We compare due-date performance, capacity, capacity switching, and lost sales costs to select optimal policies. We also give insight into which situations a workload-dependent policy is beneficial to introduce. Our results can be used by manufacturing and service industries when establishing a static policy for dynamic capacity planning.
1Workload-dependent capacity control in production-to-order systems
2016
The development of job intermediation and the increasing use of the Internet allow companies to carry out ever quicker capacity changes. In many cases, capacity can be adapted rapidly to the actual workload, which is especially important in production-to-order systems, where inventory cannot be used as a buffer for demand variation. We introduce a set of Markov chain models to represent workload-dependent capacity control policies. We present two analytical approaches to evaluate the policies ’ due-date performance based on stationary analysis. One provides an explicit expression of throughput time distribution, the other is a fixed-point iteration method that calculates the moments of the throughput time. We compare due-date performance, capacity, capacity switching, and lost sales costs to select optimal policies. We also give insight into which situations a workload-dependent policy is beneficial to introduce. Our results can be used by manufacturing and service industries when e...
Modeling Load and Overwork E ects in Queueing Systems with Adaptive Service Rates
Servers in many real queueing systems do not work at a constant speed. They adapt to the system state by speeding up when the system is highly loaded or slowing down when load has been high for an extended time period. Their speed can also be constrained by other factors, such as geography or a downstream blockage. We develop a state-dependent queueing model in which the service rate depends on the system "load" and "overwork." Overwork refers to a situation where the system has been under a heavy load for an extended time period. We quantify load as the number of users in the system and we operationalize overwork with a state variable that is incremented with each service completion in a high-load period and decremented with each service completion in a low-load period. Our model is a quasi-birth-and-death process with a special structure that we exploit to develop efficient and easy-to- implement algorithms to compute system performance measures. We use the analytical model and simulation to demonstrate how using models that ignore adaptive server behavior can result in inconsistencies between planned and realized performance and can lead to suboptimal, unstable, or oscillatory staffing decisions.
On A Two-Dimensional Markov Chain Model for Performance Analysis of Systems with Varying Capacities
2021
In many systems, service capacities vary over time as a result of capital and technology investment, as well as demand fluctuation. In this paper, we analyze a simple two dimensional Markov chain for queueing system to model the behavior of such systems. In our model, servers are added to the system to increase its service capacity, and a server can depart if it has been idle for too long. Multi-dimensional Markov chains such as the one in the paper are in general difficult to analyze. Our focus is on an approximation method of stationary performance of the system via the Stein method. For this purpose, innovative methods are developed to estimate the moments of the Markov chain, as well as the solution to the Poisson equation with a partial differential operator.
Periodic capacity management under a lead-time performance constraint
OR Spectrum, 2011
In this paper, we study a production system that operates under a leadtime performance constraint which guarantees the completion of an order before a predetermined lead-time with a certain probability. The demand arrival times and the service requirements for the orders are random. To reduce the capacity-related operational costs, the production system under study has the option to use flexible capacity. We focus on periodic capacity policies and model the production system as a queuing system that can change its capacity periodically and choose to operate in one of the two levels: a permanent capacity level and a permanent plus contingent capacity level. Contingent capacity is supplied if needed at the start of a period, and is available during that period, at a cost rate that is decreasing in period length in different functional forms. Next, we propose a search algorithm that finds the capacity levels and the switching point that minimizes the capacity-related costs for a given period length. The behaviour of the capacity-related costs changes drastically under different period lengths and cost structures. In our computational study, we observe that the periodic capacity flexibility can reduce the capacity-related operational costs
Modeling Load and Overwork Effects in Queueing Systems with Adaptive Service Rates
Operations Research, 2016
Servers in many real queueing systems do not work at a constant speed. They adapt to the system state by speeding up when the system is highly loaded or slowing down when load has been high for an extended time period. Their speed can also be constrained by other factors, such as geography or a downstream blockage. We develop a state-dependent queueing model in which the service rate depends on the system “load” and “overwork.” Overwork refers to a situation where the system has been under a heavy load for an extended time period. We quantify load as the number of users in the system, and we operationalize overwork with a state variable that is incremented with each service completion in a high-load period and decremented at a rate that is proportional to the number of idle servers during low-load periods. Our model is a quasi-birth-and-death process with a special structure that we exploit to develop efficient and easy-to-implement algorithms to compute system performance measures....
Modelling flow and jobbing shops as a queueing network for workload control
International Journal of Production Economics, 2002
Workload control is an approach for production planning and control that attempts to manage manufacturing lead times rather than treat them as a forecasting problem. It is particularly appropriate for jobbing and #ow shops in the make-to-order sector of industry. It is based on Little's well known formula in queueing theory that the time an arrival spends in the system is the average number in the system divided by the arrival rate. However, the workload control approach treats the jobbing shop as a single entity and thus ignores the complexities caused by competing jobs arriving at a work station at the same time thus forming queues. This paper describes how the job shop environment may be formulated as an open queueing network. It is computationally impossible to solve the model exactly if there are more than three or four work stations. Results for an exact Markov process model for a triangular con"guration of work stations are described. Initial results suggest that treating each work station as an independent queueing system leads to signi"cant underestimation of the manufacturing lead times, even for such a simple manufacturing system. Some initial ideas on deriving an approximation of the exact model to cover larger systems are also discussed.
Staffing to Stabilize the Tail Probability of Delay in Service Systems with Time-Varying Demand
Operations Research, 2018
Analytic formulas are developed to set the time-dependent number of servers to stabilize the tail probability of customer waiting times for the Gt/GI/st + GI queueing model, which has a nonstationary non-Poisson arrival process (the Gt), nonexponential service times (the first GI), and allows customer abandonment according to a nonexponential patience distribution (the +GI). Specifically, for any delay target w > 0 and probability target α ∈ (0, 1), we determine appropriate staffing levels (the st) so that the time-varying probability that the waiting time exceeds a maximum acceptable value w is stabilized at α at all times. In addition, effective approximating formulas are provided for other important performance functions such as the probabilities of delay and abandonment, and the means of delay and queue length. Many-server heavy-traffic limit theorems in the efficiency-driven regime are developed to show that (i) the proposed staffing function achieves the goal asymptotically...
Impact of ramp-up on the optimal capacity-related reconfiguration policy
International Journal of Flexible Manufacturing Systems, 2007
This paper presents an optimal solution, based on Markov Decision Theory, for the problem of optimal capacity-related reconfiguration of manufacturing systems, under stochastic market demand. Both capacity expansion and reduction are considered. The solution quantitatively takes into account the effect of the ramp-up phenomenon, following each reconfiguration, on the optimal policy. A closed-form solution is presented in the case product demand is independently and generally distributed over time. A real case concerning a flexible manufacturing line in the automotive sector is shown, to prove that ignoring the ramp-up effect in the decision process can lead to significant increases in the overall costs.
International Journal of Science and Research (IJSR)
The ultimate objective of the analysis of queuing systems is to understand the behaviour of their underlying process so that informed and intelligent decisions can be made by the management. The application of queuing concepts is an attempt to minimize cost through minimization of inefficiency and delays in a system. Various methods of solving queuing problems have been proposed. In this study we have explored single –server Markovian queuing model with both interarrival and service times following exponential distribution with parameters and , respectively, and unlimited queue size with FIFO queuing discipline and unlimited customer population. We apply this model to catering data and estimate parameters for the same. A sensitivity analysis is the carried out to evaluate stability of the system.