Dmitry Krushinsky

The share-a-ride problem : people and parcels sharing taxis

New city logistics approaches are needed to ensure efficient urban mobility for both people and goods. Usually, these are handled independently in dedicated networks. This paper considers conceptual and mathematical models in which people and parcels are handled in an integrated way by the same taxi network. From a city perspective, this system has a potential to alleviate urban congestion and environmental pollution. From the perspective of a taxi company, new benefits from the parcel delivery service can be obtained. We propose two multi-commodity sharing models. The Share-a-Ride Problem (SARP) is discussed and defined in detail. A reduced problem based on the SARP is proposed: the Freight Insertion Problem (FIP) starts from a given route for handling people requests and inserts parcel requests into this route. We present MILP formulations and perform a numerical study of both static and dynamic scenarios. The obtained numerical results provide valuable insights into successfully implementing a taxi sharing service.

An adaptive large neighborhood search heuristic for the share-a-ride problem

The Share-a-Ride Problem (SARP) aims at maximizing the profit of serving a set of passengers and parcels using a set of homogeneous vehicles. We propose an adaptive large neighborhood search (ALNS) heuristic to address the SARP. Furthermore, we study the problem of determining the time slack in a SARP schedule. Our proposed solution approach is tested on three sets of realistic instances. The performance of our heuristic is benchmarked against a mixed integer programming (MIP) solver and the Dial-a-Ride Problem (DARP) test instances. Compared to the MIP solver, our heuristic is superior in both the solution times and the quality of the obtained solutions if the CPU time is limited. We also report new best results for two out of twenty benchmark DARP instances. HighlightsWe propose an adaptive large neighborhood search (ALNS) heuristic.The performance of our heuristic is benchmarked against an MIP solver and Dial-a-Ride (DARP) test instances.The ALNS-based heuristic can solve medium size instances of the Share-a-Ride Problem.

An exact model for cell formation in group technology

Despite the long history of the cell formation problem (CF) and availability of dozens of approaches, very few of them explicitly optimize the objective of cell formation. These scarce approaches usually lead to intractable formulations that can be solved only heuristically for practical instances. In contrast, we show that CF can be explicitly modelled via the minimum multicut problem and solved to optimality in practice (for moderately sized instances). We consider several real-world constraints that can be included into the proposed formulations and provide experimental results with real manufacturing data.

Flexible PMP Approach for Large-Size Cell Formation

Lately, the problem of cell formation CF has gained a lot of attention in the industrial engineering literature. Since it was formulated more than 50 years ago, the problem has incorporated additional industrial factors and constraints while its solution methods have been constantly improving in terms of the solution quality and CPU times. However, despite all the efforts made, the available solution methods including those for a popular model based on the p-median problem, PMP are prone to two major types of errors. The first error the modeling one occurs when the intended objective function of the CF as a rule, verbally formulated is substituted by the objective function of the PMP. The second error the algorithmic one occurs as a direct result of applying a heuristic for solving the PMP. In this paper we show that for instances that make sense in practice, the modeling error induced by the PMP is negligible. We exclude the algorithmic error completely by solving the adjusted pseudo-Boolean formulation of the PMP exactly, which takes less than one second on a general-purpose PC and software. Our experimental study shows that the PMP-based model produces high-quality cells and in most cases outperforms several contemporary approaches.

An approach to the asymmetric multi-depot capacitated arc routing problem

Despite the fact that the Capacitated Arc Routing Problems (CARPs) received substantial attention in the literature, most of the research concentrates on the symmetric and single-depot version of the problem. In this paper, we fill this gap by proposing an approach to solving a more general version of the problem and analysing its properties. We present an MILP formulation that accommodates asymmetric multi-depot case and consider valid inequalities that may be used to tighten its LP relaxation. A symmetry breaking scheme for a single-depot case is also proposed. An extensive numerical study is carried to investigate the properties of the problem and the proposed solution approach.

A computational study of the pseudo-Boolean approach to the p-median problem applied to cell formation

In this study we show by means of computational experiments that a pseudo-Boolean approach leads to a very compact presentation of p-Median problem instances which might be solved to optimality by a general purpose solver like CPLEX, Xpress, etc. Together with p-Median benchmark instances from OR and some other libraries we are able to solve to optimality many benchmark instances from cell formation in group technology which were tackled in the past only by means of different types of heuristics. Finally, we show that this approach is flexible to take into account many other practically motivated constraints in cell formation.

The Problem of Cell Formation: Ideas and Their Applications

This chapter provides a general overview of the cell formation problem, including the origins of the problem, a discussion on the relevance of a cellular layout together with its advantages and drawbacks, and an overview of the solution approaches. The notions of dissimilarity and performance measures are also considered in this chapter. Furthermore, the outline of the book is provided at the end of this chapter.

Synchronization of Movement for a Large-Scale Crowd

Real world models of large-scale crowd movement lead to computationally intractable problems implied by various classes of non-linear stochastic differential equations. Recently, cellular automata (CA) have been successfully applied to model the dynamics of vehicular traffic, ants and pedestrians’ crowd movement and evacuation without taking into account mental properties. In this paper we study a large-scale crowd movement based on a CA approach and evaluated by the following three criteria: the minimization of evacuation time, maximization of instantaneous flow of pedestrians, and maximization of mentality-based synchronization of a crowd. Our computational experiments show that there exist interdependencies between the three criteria.

Application of the PMP to Cell Formation in Group Technology

This chapter focuses on the p-median problem based approach to cell formation. A PMP-based model is described in detail and its performance is analysed theoretically and experimentally, both in terms of the solution quality and running times.

The p-Median Problem

This chapter focuses on the p-median problem (PMP) and its properties. We consider a pseudo-Boolean formulation of the PMP, demonstrate its advantages and derive the most compact MILP formulation for the PMP within the class of mixed-Boolean linear programming formulations. Further, we develop two applications of the pseudo-Boolean approach: a construction of PMP instances that are expected to be complex for any solution algorithm and a definition of an equivalence relation for PMP instances. By equivalence we mean that solving one instance gives a solution for all the instances from its equivalence class. The proposed equivalence relation can be extended to any other problem modelled via the PMP, for example, the cell formation problem.