Dirk Cattrysse

A guided local search heuristic for the capacitated arc routing problem

Abstract This paper presents a new local search algorithm for the capacitated arc routing problem (CARP). The procedure uses single vehicle moves and moves that operate on two routes, both derived from a node routing context but properly adapted to work well for arc routing problems. We combine the algorithm with the meta-heuristic guided local search and further use the mechanisms of neighbor lists and edge marking to improve the solution quality and to save computation time. Experiments on standard benchmark problems from the literature show that our algorithm outperforms the existing heuristics for the CARP. On a set of new test problems, the local search approach consistently produces high quality solutions and often detects an optimal solution within limited computation time.

Multi-item spare parts systems with lateral transshipments and waiting time constraints

This paper deals with the analysis of a multi-item, continuous review model of two-location inventory systems for repairable spare parts, used for expensive technical systems with high target availability levels. Lateral and emergency shipments occur in response to stockouts. A continuous review basestock policy is assumed for the inventory control of the spare parts. The objective is to minimize the total costs for inventory holding, lateral transshipments and emergency shipments subject to a target level for the average waiting time per demanded part at each of the two locations. A solution procedure based on Lagrangian relaxation is developed to obtain both a lower bound and an upper bound on the optimal total cost. The upper bound follows from a heuristic solution. An extensive numerical experiment shows an average gap of only 0.31% between the lower and upper bounds. The experiment also gives insights into the relative improvement achieved by applying lateral transshipments and or the system approach. We also apply the proposed model to actual data from an air carrier company.

Districting for salt spreading operations

Abstract The districting problem presented in this paper involves the partitioning of the road network in a region into sub-networks (or districts), to facilitate the organization of the operations to be performed within the region. Typically, each district contains one local center (depot) whose location is given, while the operations involve different types of routing, with routes starting and ending at the depot. For public sector applications like salt spreading and road maintenance, this partitioning is a real distinct stage in the organization and planning of services, and as is the case with location, districting is of a non-operational nature. Relevant characteristics of well-designed districts are: ability to support good routing, balance in workload, compactness of the sub-areas, centrality of the depot, etc. We present a heuristic procedure for our districting problem. First we partition the road network into small cycles, then we aggregate them into districts in two phases. Phase 1 uses an approach based on bin packing principles, while in Phase 2 a multi criteria approach is used. We illustrate the procedure and discuss its merits for the salt spreading operations in the province of Antwerp.

A set partitioning heuristic for the generalized assignment problem

This paper discusses a heuristic for the generalized assignment problem (GAP). The objective of GAP is to minimize the costs of assigning J jobs to M capacity constrained machines, such that each job is assigned to exactly one machine. The problem is known to be NP-Hard, and it is hard from a computational point of view as well. The heuristic proposed here is based on column generation techniques, and yields both upper and lower bounds. On a set of relatively hard test problems the heuristic is able to find solutions that are on average within 0.13% from optimality.

Simple, efficient heuristics for multi-item multi-location spare parts systems with lateral transshipments and waiting time constraints

This paper deals with the analysis of a multi-item, continuous review model of a multi-location inventory system of repairable spare parts, in which lateral and emergency shipments occur in response of stock-outs. The objective is to determine close-to-optimal stocking policies minimizing the total cost for inventory holding, lateral transshipments, and emergency shipments subject to a target level for the average waiting times at all locations. We structure the optimization problem as a combinatorial problem and four different heuristics are developed and evaluated in terms of their total costs and computation times. It is shown that the greedy-type heuristic has the best performance. A numerical study is carried out to look at the relative cost savings obtained from the use of multi-item approach and lateral transshipments.

Efficient heuristics for two-echelon spare parts inventory systems with an aggregate mean waiting time constraint per local warehouse

This paper presents solution procedures for determining close- to-optimal base stock policies in a multi-item two-echelon spare parts inventory system. The system consists of a central warehouse and multiple local warehouses, and there is a target for the aggregate mean waiting time per local warehouse. We develop four different heuristics and derive a lower bound on the optimal total cost. The effectiveness of each heuristic is assessed by the relative gap between the heuristic’s total cost and the lower bound. The results of the computational experiments show that a greedy procedure performs most satisfactorily. It is accurate as indicated by relatively small gaps, easy to implement, and the computational requirements are limited. Its computational efficiency can be increased by using Graves’ approximate evaluation method instead of an exact evaluation method, while the results remain accurate. That results in a feasible algorithm for real-life cases with many items and local warehouses.

District design for arc-routing applications

In this paper we address the problem of district design for the organisation of arc-routing activities. In particular, the focus is on operations like winter gritting and road maintenance. The problem involves how to allocate the road network edges to a set of depots with given locations. The collection of edges assigned to a facility forms a district in which routes have to be designed that start and end at the facility. Apart from the ability to support good arc routing, well-designed districts for road-maintenance operations should have the road network to be serviced connected and should define clear geographical boundaries. We present three districting heuristics and evaluate the quality of the partitions by solving capacitated arc routing problems in the districts, and by comparing the solution values with a multi-depot CARP cutting plane lower bound. Our experiments reveal that based on global information about the distribution system (ie the number of facilities or districts, the average edge demand and the vehicle capacity) and by using simple guidelines, an adequate districting policy may be selected.

Exploring Variants of 2-Opt and 3-Opt for the General Routing Problem

The general routing problem (GRP) is the problem of finding a minimum length tour, visiting a number of specified vertices and edges in an undirected graph. In this paper, we describe how the well-known 2-opt and 3-opt local search procedures for node routing problems can be adapted to solve arc and general routing problems successfully. Two forms of the 2-opt and 3-opt approaches are applied to the GRP. The first version is similar to the conventional approach for the traveling salesman problem; the second version includes a dynamic programming procedure and explores a larger neighborhood at the expense of higher running times. Extensive computational tests, including ones on larger instances than previously reported in the arc routing literature, are performed with variants of both algorithms. In combination with the guided local search metaheuristic and the mechanisms of marking and neighbor lists, the procedures systematically detect optimal or high-quality solutions within limited computation time.

Automatic production planning of press brakes for sheet metal bending

This paper discusses the planning module of system that has been developed in a research project investigating the possibilities for automatic planning of press brakes. Only limited attention has been given to production-planning problems for bending processes in the sheet-metal industry. A well-considered production-planning module provides an important opportunity for cost saving and flow-time reduction. The module will support and may replace an experienced planner. Under certain assumptions, the planning problem can be modelled both ways as a Travelling Purchaser Problem (TPP) and as a Generalized Travelling Salesperson Problem (GTSP). A hierarchical decomposition approach is presented to solve the TPP, while the GTSP is solved using guided local search (GLS). These methods are compared based on a set of problems from a real production environment and perform well.

A Holonic Chain Conveyor Control System: An Application

The control of the flow of goods through an extensive chain conveyor system is a complex task. The currently used control system (based on dispatching rules) is robust but does not take advantage of all opportunities. An alternative approach makes use of a planning algorithm to determine the routing decisions. This requires however an ad hoc algorithm and regular maintenance. The paper examines how the concepts and principles of Holonic Manufacturing Execution Systems can be used to control the product flow. This holonic multi-agent approach makes the control system adaptive and reactive and requires less maintenance. To illustrate how disturbances are handled, the holonic approach is applied to a cross-dock distribution center equipped with chain conveyors.