The Lagrangean Relaxation for the Flow Shop Scheduling Problem with Precedence Constraints, Release Dates and Delivery Times

This work aims to present a methodology to support a company in the automotive business on scheduling the jobs on its final processes. These processes are: (i) checking the final product and (ii) loading the dispatch trucks. These activities are usually found in the outbound area of any manufacturing company. The problem faced is defined as the flow shop problem with precedence constraints, release dates, and delivery times. The major objective is to minimize the latest date a client receives its products. We present a time-indexed integer mathematical model to compute feasible solutions for the presented problem. Moreover, we take advantage of the Lagrangean Relaxation procedure to compute valid lower and upper bounds. The experiments were held based on the company’s premises. As a conclusion, the results showed that the methodology proposed was able to compute feasible solutions for all the instances tested. Also, the Lagrangean Relaxation approach was able to calculate better bounds in a shorter computational time than the Mathematical problem for the more complicated instances.

Optimizing Capacity Assignment in Multiservice MPLS Networks

The general Multiprotocol Label Switch (MPLS) topology optimisation problem is complex and concerns the optimum selection of links, the assignment of capacities to these links and the routing requirements on these links. Ideally, all these are jointly optimised, leading to a minimum cost network which continually meets given objectives on network delay and throughput. In practice, these problems are often dealt with separately and a solution iterated. In this paper, we propose an algorithm that computes the shortest routes, assigns optimal flows to these routes and simultaneously determines optimal link capacities. We take into account the dynamic adaptation of optimal link capacities by considering the same Quality of Service (QoS) measure used in the flow assignment problem in combination with a blocking model for describing call admission controls (CAC) in multiservice broadband telecommunication networks. The main goal is to achieve statistical multiplexing advantages with multiple traffic and QoS classes of connections that share a common trunk present. We offer a mathematical programming model of the problem and proficient solutions which are founded on a Lagrangean relaxation of the problem. Experimental findings on 2-class and 6-class models are reported.