SLOPPGEN: A Problem Generator for the Two-Dimensional Rectangular Single Large Object Placement Problem With a Single Defect

In this paper, a problem generator for the Two-Dimensional Rectangular Single Large Object Placement Problem is presented. The parameters defining this problem are identified and described. The fea-tures of the problem generator are pointed out, and it is shown how the program can be used for the generation of reproducible random problem instances.two-dimensional cutting, defect, problem generator

Linear Programming for a Cutting Problem in the Wood Processing Industry – A Case Study

In this paper the authors present a case study from the wood-processing industry. It focuses on a cutting process in which material from stock is cut down in order to provide the items required by the customers in the desired qualities, sizes, and quantities. In particular, two aspects make this cutting process special. Firstly, the cutting process is strongly interdependent with a preceding handling process, which, consequently, cannot be planned independently. Secondly, if the trim loss is of a certain minimum size, it can be returned into stock and used as input to subsequent cutting processes. In order to reduce the cost of the cutting process, a decision support tool has been developed which incorporates a linear programming model as a central feature. The model is described in detail, and experience from the application of the tool is reported.one-dimensional cutting, linear programming, wood-processing industry

Container Loading Problems: A State-of-the-Art Review

Container loading is a pivotal function for operating supply chains efficiently. Underperformance results in unnecessary costs (e.g. cost of additional containers to be shipped) and in an unsatisfactory customer service (e.g. violation of deadlines agreed to or set by clients). Thus, it is not surprising that container loading problems have been dealt with frequently in the operations research literature. It has been claimed though that the proposed approaches are of limited practical value since they do not pay enough attention to constraints encountered in practice.In this paper, a review of the state-of-the-art in the field of container loading will be given. We will identify factors which - from a practical point of view - need to be considered when dealing with container loading problems and we will analyze whether and how these factors are represented in methods for the solution of such problems. Modeling approaches, as well as exact and heuristic algorithms will be reviewed. This will allow for assessing the practical relevance of the research which has been carried out in the field. We will also mention several issues which have not been dealt with satisfactorily so far and give an outlook on future research opportunities

A Solution Approach for the Joint Order Batching and Picker Routing Problem in a Two-Block Layout

Order Batching and Picker Routing Problems arise in warehouses when articles have to be retrieved from their storage location in order to satisfy a given demand specified by customer orders. The Order Batching Problem includes the grouping of a given set of customer orders into feasible picking orders such that the total length of all picker tours is minimized. The problem of determining the sequence according to which articles have to be picked is known as the Picker Routing Problem. Although these problems occur at the same planning level, it is common to solve these problems not simultaneously, but separately and in sequence. As for the batching problem it is usually assumed that the order pickers, when making their ways through the warehouse, follow a certain, simple routing strategy. Based on this routing strategy, the customer orders are grouped into picking orders. The advantage of this approach can be seen in the fact that – in particular for single-block warehouse layouts – the corresponding order picker tours are very straightforward and can be memorized easily by the order pickers. This advantage diminishes, however, when more complex, multi-block layouts have to be dealt with. Furthermore, in such case, the approach may result in picker tours that can be far from optimal. Therefore, for multi-block layouts, we develop a new approach, namely an iterated local search algorithm into which different routing algorithms have been integrated and which allows for solving the Order Batching Problem and the Picker Routing Problem simultaneously. By means of numerical experiments it is shown that this approach results in a substantial improvement of the solution quality without increasing computing times

SLOPPGEN: A Problem Generator for the Two-Dimensional Rectangular Single Large Object Placement Problem With a Single Defect

In this paper, a problem generator for the Two-Dimensional Rectangular Single Large Object Placement Problem is presented. The parameters defining this problem are identified and described. The fea-tures of the problem generator are pointed out, and it is shown how the program can be used for the generation of reproducible random problem instances

Tabu Search Heuristics for the Order Batching Problem in Manual Order Picking Systems

In manual order picking systems, order pickers walk or ride through a distribution warehouse in order to collect items requested by (internal or external) customers. In order to perform these operations efficiently, it is usually required that customer orders are combined into (more substantial) picking orders of limited size. The Order Batching Problem considered in this paper deals with the question of how a given set of customer orders should be combined such that the total length of all tours necessary to collect all items is minimized. For the solution of this problem the authors suggest two approaches based on the tabu search principle. The first one is a straightforward classic Tabu Search algorithm (TS), the second one is the Attribute-Based Hill Climber (ABHC). In a series of extensive numerical experiments, the newly developed approaches are benchmarked against different solution methods from literature. It is demonstrated that the proposed methods are superior to existing methods and provide solutions which may allow for operating distribution warehouses significantly more efficiently

A Grouping Genetic Algorithm for the Order Batching Problem in Distribution Warehouses

Order picking is a warehouse function that deals with the retrieval of articles from their storage locations in order to satisfy certain customer demands. Combining several single customer orders into one (more substantial) picking order can increase the efficiency of warehouse operations. The Order Batching Problem considered in this paper deals with the question of how different customer orders should be grouped into picking orders, such that the total length of all tours through the warehouse is minimized, which are necessary to collect all requested articles. For the solution of this problem, the authors introduce a Grouping Genetic Algorithm. This genetic algorithm is combined with a local search procedure which results in a highly competitive hybrid algorithm. In a series of extensive numerical experiments, the algorithm is benchmarked against a genetic algorithm with a standard item-oriented encoding scheme. The results show that the new genetic algorithm based on the group-oriented encoding scheme is preferable for the Order Batching Problem, and that the algorithm provides high quality solutions in reasonable computing times

A Grouping Genetic Algorithm for the Order Batching Problem in Distribution Warehouses

Order picking is a warehouse function that deals with the retrieval of articles from their storage locations in order to satisfy certain customer demands. Combining several single customer orders into one (more substantial) picking order can increase the efficiency of warehouse operations. The Order Batching Problem considered in this paper deals with the question of how different customer orders should be grouped into picking orders, such that the total length of all tours through the warehouse is minimized, which are necessary to collect all requested articles. For the solution of this problem, the authors introduce a Grouping Genetic Algorithm. This genetic algorithm is combined with a local search procedure which results in a highly competitive hybrid algorithm. In a series of extensive numerical experiments, the algorithm is benchmarked against a genetic algorithm with a standard item-oriented encoding scheme. The results show that the new genetic algorithm based on the group-oriented encoding scheme is preferable for the Order Batching Problem, and that the algorithm provides high quality solutions in reasonable computing times.Warehouse Management, Order Picking, Order Batching, Genetic Algorithms

A hybrid solution approach for the 3L-VRP with simultaneous delivery and pickups

This paper deals with a special vehicle routing problem with backhauls where each customer receives items from a depot and, at the same time, returns items back to the depot. Moreover, time windows are assumed and three-dimensional loading constraints are to be observed, i.e. the items are three-dimensional boxes and packing constraints, e.g. regarding load stability, are to be met. The resulting problem is the vehicle routing problem with simultaneous delivery and pickup (VRPSDP), time windows, and three-dimensional loading constraints (3L-VRPSDPTW). This problem occurs, for example, if retail stores are supplied by a central warehouse and wish to return packaging material.A particular challenge of the problem is to transport delivery and pickup items simultaneously on the same vehicle. In order to avoid any reloading effort during a tour, we consider two different loading approaches of vehicles: (i) loading from the back side with separation of the loading space into a delivery section and a pickup section and (ii) loading at the long side. A hybrid algorithm is proposed for the 3L-VRPSDPTW consisting of an adaptive large neighbourhood search for the routing and different packing heuristics for the loading part of the problem. Extensive numerical experiments are conducted with VRPSDP instances from the literature and newly generated instances for the 3LVRPSDPTW

Linear Programming for a Cutting Problem in the Wood Processing Industry: A Case Study

In this paper the authors present a case study from the wood-processing industry. It focuses on a cutting process in which material from stock is cut down in order to provide the items required by the customers in the desired qualities, sizes, and quantities. In particular, two aspects make this cutting process special. Firstly, the cutting process is strongly interdependent with a preceding handling process, which, consequently, cannot be planned independently. Secondly, if the trim loss is of a certain minimum size, it can be returned into stock and used as input to subsequent cutting processes. In order to reduce the cost of the cutting process, a decision support tool has been developed which incorporates a linear programming model as a central feature. The model is described in detail, and experience from the application of the tool is reported