Network Scheduling Problems Research Articles

Network scheduling problem with cross-docking and loading constraints

Cross-docking is a logistic strategy which can increase rates of consolidation, and reduce distribution and storage costs and delivery times. The optimization literature on cross-docking has mostly focused on the modeling and solution of problems considering a single cross-docking facility. Networks with multiple cross-docks remain rather unexplored and the few papers that deal with the problem do this by simplifying the geometry of the goods. We intend to shorten this gap by proposing a mixed-integer linear programming model for optimizing distribution and delay costs for the transportation of goods in open networks with multiple cross-docks considering the three-dimensional aspects of the cargo. Also, we propose a logic-based Benders decomposition strategy which allow for the solution of larger instances when compared with those that can be handled by a branch-and-cut MIP solver. Experiments showed that the decomposition can handle instances with two times more nodes and five times more boxes than a direct use of the solver. Also, the framework is flexible enough to accommodate other features of practical cases.

Adaptive Traffic Management and Energy Cooperation in Renewable-Energy-Powered Cellular Networks

In this paper, we consider a cellular system, in which base stations (BSs) are powered by both on-grid and renewable energy sources. To efficiently utilize the harvested energy of the BSs, we study adaptive traffic management (TM) and energy cooperation (EC) that aim at minimizing the on-grid energy consumption, while guaranteeing minimum average throughputs. To achieve this, we develop an adaptive TM and EC algorithm that jointly decides the energy sharing among BSs, the user association to BSs, and the sub-channel and power allocation in BSs. Within the algorithm, a network scheduling problem, which is mixed-integer non-linear programming (MINLP), should be solved in each timeslot. To efficiently solve it, we develop a network scheduling algorithm applying generalized Benders decomposition (GBD) that optimally solves the MINLP problem. In addition, we also develop a heuristic network scheduling algorithm that has a much lower computational complexity than the GBD algorithm, while providing comparable performance. Through the numerical results, we show that our algorithms always outperform the algorithms that use only one of TM or EC regardless of the system conditions.

Improved response-time bounds in fixed priority scheduling with arbitrary deadlines

We consider fixed priority sporadic tasks with arbitrary deadlines to be executed upon a uni-processor platform. Efficient schedulability tests for this task model are required for both online task admission in dynamic systems and interactive design of complex embedded real-time systems. The paper derives novel continuous upper bounds on the worst-case response times which runs in linear complexity. These bounds are not comparable to the tightest existing continuous upper bound of Bini et al. (in: Proceedings of the IEEE international conference on real-time systems symposium (RTSS’15), San Antonio, 2015) and strictly tighter under some parameters configurations. Moreover, the proposed approach allows to combine various existing methods to produce the tightest known continuous response time bounds. These results are extended to be applicable to a wide range of processor and network scheduling problems, including: release jitters, blocking times and cache related preemption delay (CRPD). Response time upper bounds are also given for tasks that are scheduled pre-emptively, co-operatively with intervals where pre-emption is deferred, and non-preemptively. Lastly, the quality of the method is analyzed and various recommendations are provided by means of numerical experiments.

Comparison of deterministic and heuristic optimization solvers for water network scheduling problems

This paper presents a novel approximate dynamic programming technique for solving the pump schedule optimization of real-water distribution networks. The method is based on the significant decreasing of the search space by splitting the optimization problem into smaller units. In addition, the state space of the main distribution system was further reduced to the most important reservoirs. The capabilities of the proposed technique are demonstrated on a real-life problem, the water distribution system of the town of Sopron, Hungary. Nine test cases were defined which represent different initial water level scenarios, thus the new application was easy to compare to a former developed genetic algorithm and to some world-leading optimization solvers which are available on the NEOS Server. The benefits and drawbacks of these deterministic and heuristic methods are highlighted.

M-Balanced words: A generalization of balanced words

Consider to construct an infinite sequence, or an infinite word, from a finite set of letters such as each letter is distributed with “good balance,” that is, as evenly as possible, when the densities of letters are provided. Such words have been applied to many scheduling and routing problems in various areas. Concerning the balancedness of words, the notions of regularity and balanced words have been exploited. However, it is known that there does not always exist a balanced word for given densities of letters. In this paper, we introduce a new notion called m- balanced words, which gives a measure of “well balancedness” for any words with any densities of letters. We derive some properties of m-balanced words and give a set of algorithms generating well balanced words. We further give a few examples of applications to simple network scheduling problems.

Using a GAMS Modelling Environment to Solve Network Scheduling Problems

Using a GAMS Modelling Environment to Solve Network Scheduling Problems

Heavy traffic analysis of a system with parallel servers: asymptotic optimality of discrete-review policies

This paper is concerned with dynamic scheduling in a queueing system that has two independent Poisson input streams, two servers, deterministic service times and linear holding costs. One server can process both classes of incoming jobs, but the other can process only one class, and the service time for the shared job class is different depending on which server is involved. A bound on system performance is developed in terms of a single pooled resource, or super-server, whose capabilities combine those of the original two servers. Thereafter, attention is focused on the heavy traffic regime, where the combined capacity of the two servers is approximately equal to the total input rate. We construct a discrete-review control policy and show that if its parameters are chosen correctly as one approaches the heavy traffic limit, then its cost performance approaches the bound associated with a single pooled resource. Thus the discrete-review policy is proved to be asymptotically optimal in the heavy traffic limit. Although resource pooling in heavy traffic has been observed to occur in other network scheduling problems, there have been very few studies that rigorously proved the pooling phenomenon, or that proved the asymptotic optimality of a specific policy. Our discrete-review policy is obtained by applying a general method, called the BIGSTEP method in an earlier paper, to the parallel-server model.

Brownian Networks with Discretionary Routing

Motivated by scheduling problems that arise in flexible manufacturing systems, we develop a heuristic procedure to obtain effective flow control (sequencing, routing, and input control) policies for multiclass queueing networks. The procedure employs a Brownian model of J. M. Harrison that approximates a multiclass queueing network with dynamic scheduling capability, if the total load imposed on each station in the queueing network is approximately equal to that station's capacity. In this paper, each customer class may be served at any of several different stations, and thus dynamic routing decisions are added to the sequencing and input control decisions already present in Harrison's model. Using previous heavy traffic results as a guide, we observe that, under heavy traffic conditions, a queueing network routing its customers to the queue where they will incur the shortest expected delay behaves very much like the reduced queueing network formed by pooling the appropriate servers. This observation leads to a proposed reduction of a Brownian network with discretionary routing to a simpler Brownian network without discretinary routing. Computational results indicate that combining this reduction with previous analysis of Brownian networks without discretionary routing leads to effective flow control policies for many moderately sized queueing network scheduling problems.

A branch-and-bound algorithm for the solution of two network scheduling problems

A branch-and-bound algorithm for the solution of two network scheduling problems

Optimal Solution of Scheduling Problems Using Lagrange Multipliers: Part I

This paper presents an algorithm for solving resource-constrained network scheduling problems, a general class of problems that includes the classical job-shop-scheduling problem. It uses Lagrange multipliers to dualize the resource constraints, forming a Lagrangian problem in which the network constraints appear explicitly, while the resource constraints appear only in the Lagrangian function. Because the network constraints do not interact among jobs, the problem of minimizing the Lagrangian decomposes into a subproblem for each job. Algorithms are presented for solving these subproblems. Minimizing the Lagrangian with fixed multiplier values yields a lower bound on the cost of an optimal solution to the scheduling problem. The paper gives procedures for adjusting the multipliers iteratively to obtain strong bounds, and it develops a branch-and-bound algorithm that uses these bounds in the solution of the scheduling problem. Computational experience with this algorithm is discussed.