Manolis N. Kritikos

A greedy look-ahead heuristic for the vehicle routing problem with time windows

In this paper we consider the problem of physically distributing finished goods from a central facility to geographically dispersed customers, which pose daily demands for items produced in the facility and act as sales points for consumers. The management of the facility is responsible for satisfying all demand, and promises deliveries to the customers within fixed time intervals that represent the earliest and latest times during the day that a delivery can take place. We formulate a comprehensive mathematical model to capture all aspects of the problem, and incorporate in the model all critical practical concerns such as vehicle capacity, delivery time intervals and all relevant costs. The model, which is a case of the vehicle routing problem with time windows, is solved using a new heuristic technique. Our solution method, which is based upon Atkinsons greedy look-ahead heuristic, enhances traditional vehicle routing approaches, and provides surprisingly good performance results with respect to a set of standard test problems from the literature. The approach is used to determine the vehicle fleet size and the daily route of each vehicle in an industrial example from the food industry. This actual problem, with approximately two thousand customers, is presented and solved by our heuristic, using an interface to a Geographical Information System to determine inter-customer and depot–customer distances. The results indicate that the method is well suited for determining the required number of vehicles and the delivery schedules on a daily basis, in real life applications.

Map-Route: a GIS-based decision support system for intra-city vehicle routing with time windows

This paper presents a Decision Support System (DSS) that enables dispatchers–schedulers to approach intra-city vehicle routing problems with time windows interactively, using appropriate computational methods and exploiting a custom knowledge base that contains information about traffic and spatial data. The DSS, named Map-Route, generates routes that satisfy time and vehicle capacity constraints. Its computational engine is based on an effective heuristic method for solving the underlying optimization problem, while its implementation is developed using MapInfo, a popular Geographical Information System (GIS) platform. Map-Route provides very efficient solutions, is particularly user-friendly, and can reach answers for a wide variety of ‘what if’ scenarios with potentially significant cost implications. We have implemented Map-Route in an actual industrial environment and we report on the experience gained from this real-life application.

Corporate Real Estate Analysis:Evaluating Telecom Branch Efficiency in Greece

This article proposes productivity analysis for evaluating the relative efficiency in corporate real estate usage across decision-making units. Using data from the Greek Telecommunications Organization (GTO), we measure the productivity of 127 branches using the number of employees and the total area covered per building as inputs and the number of telephony access lines as outputs. We apply three nonparametric Data Envelopment Analysis (DEA) models assuming: Constant Returns to Scale (CRS), Variable Returns to Scale (VRS) and Slacks-Based Measures (SBM), respectively. We discuss how the proposed approach can provide real estate managers and analysts a multi-informational tool that allows the quantification of targets and may serve as a guide tool for the efficient employment of real estate assets.

Optimization of material handling in production and warehousing facilities

In this paper we consider the problem of minimizing material handling costs in manufacturing systems or warehousing facilities, subject to constraints that restrict the start and end time of each production or picking/packaging activity, according to pre-specified daily operational schedules and process planning information. The underlying decision problem is modeled using an integer programming formulation similar to the vehicle routing problem with time windows. Since the problem isNP-complete, we develop an efficient heuristic to solve it in short processing time. The method, called penalty-based heuristic, allows routes to be constructed by exploiting the tradeoff between material handling and resource starvation costs. The steps of the method are illustrated via a comprehensive example.

A synthesis of assignment and heuristic solutions for vehicle routing with time windows

This paper proposes a three-stage method for the vehicle-routing problem with time window constraints (VRPTW). Using the Hungarian method the optimal customer matching for an assignment approximation of the VRPTW, which is a travel time-based relaxation that partially respects the time windows, is obtained. The assignment matching is transformed into feasible routes of the VRPTW via a simple decoupling heuristic. The best of these routes, in terms of travelling and vehicle waiting times, form part of the final solution, which is completed by the routes provided by heuristic methods applied to the remainder of the customers. The proposed approach is tested on a set of standard literature problems, and improves the results of the heuristic methods with respect to total travel time. Furthermore, it provides useful insights into the effect of employing optimal travel time solutions resulting from the assignment relaxation to derive partial route sets of the VRPTW.

Sequencing material handling equipment in production facilities

In this article we consider the problem of sequencing material handling equipment in manufacturing systems, subject to constraints that restrict the start and end time of each production activity, according to pre-specified daily resource operational schedules and process planning information. The underlying decision problem is modeled using an integer programming formulation similar to vehicle routing with time windows (VRPTW). To take advantage of standard approaches for the VRPTW, we develop a transformation schema that allows a one-to-one mapping between the manufacturing problem and VRPTW. An efficient heuristic to solve the resulting transformed problem is proposed. The method, which is a penalty-based sequential insertion heuristic, allows routes to be constructed by exploiting the tradeoff between material handling and resource starvation costs. The steps of the method are illustrated via a comprehensive example and results on benchmark problems are reported.

A greedy heuristic for the capacitated minimum spanning tree problem

This paper develops a greedy heuristic for the capacitated minimum spanning tree problem (CMSTP), based on the two widely known methods of Prim and of Esau–Williams. The proposed algorithm intertwines two-stages: an enhanced combination of the Prim and Esau–Williams approaches via augmented and synthetic node selection criteria, and an increase of the feasible solution space by perturbing the input data using the law of cosines. Computational tests on benchmark problems show that the new heuristic provides extremely good performance results for the CMSTP, justifying its effectiveness and robustness. Furthermore, excluding the feasible space expansion, we show that we can still obtain good quality solutions in very short computational times.

Two heuristics for the capacitated minimum spanning tree problem with time windows

Abstract We consider the capacitated minimum spanning tree problem with time windows (CMSTPTW) and propose an enhancement of greedy heuristic for the uncapacitated version of it, showing that our algorithm significantly outperforms Solomon’s one based on the R7 test problem. To examine the performance of our approach, we convert the vehicle routing data sets to appropriately model CMSTPTW instances and provide solutions for all of them; in addition, we compare the solutions we reach for the uncapacitated version of all instances and those obtained by Solomon to demonstrate the consistent superiority of the proposed method. Finally, we develop a second solution approach, the local domain priority heuristic, which when applied to the same data sets results in better solutions for the majority of the CMSTPTW instances, without excessive computational effort.

An introduction to decision making using the elimination method of Fourier-Motzkin

Abstract The paper introduces the decision-making through a system of inequalities for high-school students and first-year undergraduate students. The objective of this paper is to enable the students to understand the importance of mathematics in real business application problems. Moreover, we present a production problem and highlight the set of solutions for the problem. The set of solutions is defined by the system of inequalities resulting from available resources for production, storage, and consumption. Furthermore, we introduce the elimination method of Fourier-Motzkin. The method helps us to find the optimum solution for the production problem by solving systems of inequalities without using linear programming.

A Two-phase Solution Algorithm for the Inventory Routing Problem with Time Windows

The main objective of this paper is to propose a two-phase solution algorithm for solving the Inventory Routing Problem with Time Windows (IRPTW), which has not been excessively researched in the literature. The solution approach is based on (a) a simple simulation for the planning phase (Phase I) and (b) the Variable Neighborhood Search Algorithm (VNS) for the routing phase (Phase II). Testing instances are established to investigate algorithmic performance, and the computational results are then reported. The computational study underscores the importance of integrating the inventory and vehicle routing decisions. Graphical presentation formats are provided to convey meaningful insights into the problem.