In this article, we develop a novel role for the initial function v 0 in the value iteration algorithm. In case the optimal policy of a countable state Markovian queueing control problem has a threshold or switching curve structure, we conjecture, that one can tune the choice of v 0 to generate monotonic sequences of n-stage threshold or switching curve optimal policies. We will show this for three queueing control models, the M/M/1 queue with admission and with service control, and the two-competing queues model with quadratic holding cost. As a consequence, we obtain increasingly tighter upper and lower bounds. After a finite number of iterations, either the optimal threshold, or the optimal switching curve values in a finite number of states is available. This procedure can be used to increase numerical efficiency. KEYWORDSderiving bounds, optimal policies, value iteraton 1 638This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Abstract:In this article, we study a class of Quasi-Skipfree (QSF) processes where the transition rate submatrices in the skipfree direction have a column times row structure. Under homogeneity and irreducibility assumptions we show that the stationary distributions of these processes have a product form as a function of the level. For an application, we will discuss the Cox(k)/M Y /1 -queue that can be modeled as a QSF process on a two-dimensional state space. In addition, we study the properties of the stationary distribution and derive monotonicity of the mean number of the customers in the queue, their mean sojourn time and the variance as a function of k for fixed mean arrival rate.

In a minimization problem, there are some operational costs, such as transportation costs which are not negligible. In this research we discuss a transportation problem and propose a comparison of the generalized unified tabu search and the branch and bound algorithms. One of our concerns is the geographical condition of Indonesia, which is an archipelago country. To minimize these costs, the decision maker needs to determine the best route. In a distribution cycle, the goods from the supplier are picked up by the transporter and then sent to the processing factory. Several issues were highlighted in the actual process of designing contracts such as the use of historical data. In determining the route, an approach based on scenario analysis is used which consists of revising the steps and information. In this case, the generalized unified tabu search algorithm is used to find the best route and its performance is compared using the branch and bound method. As a numerical simulation, this research is applied on ginger distributions in Java, Indonesia.