Some results on Bellman equations of optimal production control in a stochastic manufacturing system.
This paper studies scheduling problems which include a combination of nonlinear job deterioration and a time-dependent learning effect. We use past sequence dependent (p-s-d) setup times, which is first introduced by Koulamas and Kyparisis [Eur. J. Oper. Res.187 (2008) 1045–1049]. They considered a new form of setup times which depend on all already scheduled jobs from the current batch. Job deterioration and learning co-exist in various real life scheduling settings. By the effects of learning...
A production inventory problem with limited backlogging and with stockouts is described in a discrete time, stochastic optimal control framework with finite horizon. It is proved by dynamic programming methods that an optimal policy is of (s,S)-type. This means that in every period the policy is completely determined by two fixed levels of the stochastic inventory process considered.
We consider a strong NP-hard single-machine scheduling problem with deadlines and minimizing the total weight of late jobs on a single machine (). Processing times are deterministic values or random variables having Erlang distributions. For this problem we study the tolerance to random parameter changes for solutions constructed according to tabu search metaheuristics. We also present a measure (called stability) that allows an evaluation of the algorithm based on its resistance to random parameter...
Congestion control in the ABR class of ATM network presents interesting challenges due to the presence of multiple uncertain delays. Recently, probabilistic methods and statistical learning theory have been shown to provide approximate solutions to challenging control problems. In this paper, using some recent results by the authors, an efficient statistical algorithm is used to design a robust, fixed-structure, controller for a high-speed communication network with multiple uncertain propagation...
In a general model (AIMD) of transmission control protocol (TCP) used in internet traffic congestion management, the time dependent data flow vector x(t) > 0 undergoes a biased random walk on two distinct scales. The amount of data of each component xi(t) goes up to xi(t)+a with probability 1-ζi(x) on a unit scale or down to γxi(t), 0 < γ < 1 with probability ζi(x) on a logarithmic scale, where ζi depends on the joint state of the system x. We investigate the long time behavior, mean field...