Branch-and-price and heuristic column generation for the generalized truck-and-trailer routing problem

The generalized truck-and-trailer routing problem (GTTRP) constitutes a uni¯ed model for vehicle routing problems with trailers and a fixed lorry-trailer assignment. The GTTRP is a generalization of the truck-and-trailer routing problem (TTRP), which itself is an extension of the well-known vehicle routing problem (VRP). In the GTTRP, the vehicle fleet consists of single lorries and lorry-trailer combinations. Some customers may be visited only by a single lorry or by a lorry without its trailer, some may also be visited by a lorry-trailer combination. In addition to the customer locations, there is another relevant type of location, called transshipment location, where trailers can be parked and where a load transfer from a lorry to its trailer can be performed. In this paper, two mixed-integer programming (MIP) formulations for the GTTRP are presented. Moreover, an exact solution procedure for the problem, a branch-and-price algorithm, and heuristic variants of this algorithm are described. Computational experiments with the algorithms are presented and discussed. The experiments are performed on randomly generated instances structured to resemble real-world situations and on TTRP benchmark instances from the literature. The results of the experiments show that instances of realistic structure and size can be solved in short time and with high solution quality by a heuristic algorithm based on column generation

Scheduling of project networks by job assignment

A recurring problem in project management involves the allocation of scarce resources to the individual jobs comprising the project. In many situations such as audit scheduling, the resources correspond to individuals (skilled labour). This naturally leads to an assignment type project scheduling problem, i.e. a project has to be processed by assigning one of several individuals (resources) to each job. In this paper we consider the nonpreemptive variant of a resource-constrained project job-assignment problem, where job durations as well as costs depend upon the assigned resource. Regarding precedence relations as well as release dates and deadlines, the question arises, to which jobs resources should be assigned in order to minimize overall costs. For solving this time-resource-cost-tradeoff problem we present a hybrid branch and bound / dynamic programming algorithm with a (rather efficient Monte Carlo type) heuristic upper bounding technique as well as various relaxation procedures for determining lower bounds. Computational results are presented as well

A comparison of logic and mixed-integer programming solvers for batch sequencing with sequence-dependent setups

A batch sequencing model with sequence-dependent setup-times and -costs is used to compare modelling and solving with two different general solvers. "Conceptual models" are implemented in the constraint propagation / logic programming language CHARME and solved with the PROLOG inference engine. The mixed-integer-programming (MIP) formulation of the same problem is solved with OSL, a state-of-the-art MIP solver. Modelling is easier in CHARME and computational results show, that the first approach outperforms the second one for instances with high capacity utilization

The Development of a Single Frequency Place in the Mammalian Cochlea: The Cochlear Resonance in the Mustached Bat Pteronotus parnellii

Cochlear microphonic potentials (CMs) were recorded from the sharply tuned, strongly resonant auditory foveae of 1- to 5-week-old mustached bats that were anesthetized with Rompun and Ketavet. The fovea processes Doppler-shifted echo responses of the constant-frequency component of echolocation calls. During development, the frequency and tuning sharpness of the cochlear resonance increases, and CM ringing persists for longer after the tone. CM is relatively insensitive at tone onset and grows linearly with increased stimulus level. During the tone, the CM is more sensitive and grows compressively with increased stimulus level and phase leads onset CM by 90° for frequencies below the resonance. CM during the ringing is also sensitive and compressive and phase leads onset CM by 180° below the resonance and lags it by 180° above the resonance. Throughout postnatal development, CMs measured during the tone and in the ringing increase both in sensitivity and compression. The cochlear resonance appears to be attributable to interaction between two oscillators. The more broadly tuned oscillator dominates the onset response, and the narrowly tuned oscillator dominates the ringing. Early in development, mechanical coupling between the oscillators results in a relatively broadly tuned system with several frequency modes in the CM at tone onset and in the CM ringing. Beating occurs between the resonance and the stimulus response during the tone and between two components of the narrowly tuned oscillator at tone offset. At maturity, the CM has three modes for frequencies within 10 kHz of the resonance at tone onset and a single, sharply tuned mode in the ringing

Local search for nonpreemptive multi-mode resource-constrained project scheduling

This paper addresses a general class of nonpreemptive resource-constrained project scheduling problems in which activity durations are discrete functions of committed renewable and nonrenewabe resources. We provide a 0-1 problem formulation and stress the importance of the outlined model by giving applications within production and operations management. Furthermore, we prove that even the problem to derive a feasible solution is NP-complete. As a consequence, solution procedures proposed so far suffer from severe drawbacks: Exact procedures can only solve very small instances to optimality, while heuristic solution approaches fail to generate feasible solutions when problems become highly resource-constrained. Hence, we propose a new local search methodology which first tries to find a feasible solution and second performs a single-neighbourhood search on the set of feasible mode-assignments. In order to evaluate the new procedura we perform a rigorous computational study on the ProGen benchmark-set which is available in the open literature. The experiment includes a comparison of our procedure with other recently proposed heuristics

Fuzzy multicriteria flight gate assignment

This paper addresses the multiple criteria flight gate assignment problem under uncertainty, which is naturally modeled by fuzzy numbers. The problem examined is a special kind of multicriteria multi-mode resource-constrained project scheduling problem with generalized precedence constraints or time windows. Fuzziness is introduced for basic problem parameters, that is, arrival and departure times, in order to cover possible earliness and tardiness of flights. We solve the problem directly by a special multicriteria metaheuristic, known as fuzzy Pareto simulated annealing, in order to get a representative approximation of the Pareto front

A new type of model for multi-item capacitated dynamic lotsizing and scheduling

Three types of multi-item capacitated dynamic lotsizing and scheduling models are well established until now: The capacitated lotsizing problem, the discrete lotsizing and scheduling problem as well as the continuous setup lotsizing problem. An analysis of the underlying fundamental assumptions provides the basis for introducing a new model type, the proportional lotsizing and scheduling problem. This model type is well suited for incorporating some of the extensions relevant with respect to practice: Setup times, sequence dependent setup costs (times), multiple machines as well as multiple stages. Last but not least we show how make-or-buy decisions may be modelled within this framework. This is relevant regarding three important aspects: First it is more general, second it is of practical relevance, third it provides the basis for overcoming difficulties associated with feasibility problems. The last fact opens up new avenues especially for the development of efficient local search procedures

Hybrid biased random sampling for multiple resourse-constrained project scheduling problems

In this paper we propose a new heuristic to solve the well-known multiple resource-constrained project scheduling problem. The method is basically a biased random sampling procedure which shows extremely good results by use of the following features: A problem-based selection of the solution space, a sample-size-based guidance of the search, application of a priority rule superior to so-far existing rules, and finally the application of global and local (lower) bounds. Evaluating this new heuristic on a set of widely used benchmark-instances we show that it derives superior results than all other existing polynomially bounded algorithms

Project scheduling with multiple modes: A comparison of exact algorithms

This paper is devoted to a comparison of all available branch-and-bound algorithms that can be applied to solve resource-constrained project scheduling problems with multiple execution modes for each activity. After summarizing the two exact algorithms that have been suggested in the literature, we propose an alternative exact approach based on the concepts of mode and extension alternatives to solve this problem. Subsequently, we compare it to the two procedures available in the literature. Therefore, the three algorithms as well as all available bounding criteria and dominance rules are summarized in a unified framework. In addition to a theoretical comparison of the procedures, we present the results of our computational studies in order to determine the most efficient algorithm