Bin Packing Problem

The present paper approaches the loading distribution of trucks for Product Transportation as a rich problem. This is formulated with the classic Bin Packing Problem and five variants associated with a real case of study. A state of the art review reveals that related work deals with three variants at the most. Besides, they do not consider its relation with the vehicle routing problem. For the solution of this new rich problem a heuristic-deterministic algorithm was developed. It works together with a metaheuristic algorithm to assign routes and loads. The results of solving a set of real world instances show an average saving of three vehicles regarding their manual solution; this last needed 180 minutes in order to solve an instance and the actual methodology takes two minutes. On average, the demand was satisfied in 97.45%. As future work the use of a non deterministic algorithm is intended.

Since the Bin Packing Problem (BPP) is one of the main NP-hard problems, a lot of approximation algorithms have been suggested for it. It has been proven that the best algorithm for BPP has the approximation ratio of and the time order of, unless. In the current paper, a linear-approximation algorithm is presented. The suggested algorithm not only has the best possible theoretical factors, approximation ratio, space order, and time order, but also outperforms the other approximation algorithms according to the experimental results; therefore, we are able to draw the conclusion that the algorithms is the best approximation algorithm which has been presented for the problem until now.

Today, there is almost no one person who is not interested in packaging. The packaging that its place and importance in our lives is increasing further, has been documented how to surround of mankind history by its 5000 years history. The increase of potential consumers can not be ignored at its acquiring of this much space in our daily lives, but manufacturer competition takes the lion’s share. Purchasing is often triggered by the allurement instinct of packaging of the products on the shelves like a fashion charm. Brand value, product quality, type and other factors are important details that consumers do not ignore. However, in this article has been tried to focus on the factors which trigger to customer ego as the allure of the packaging, lonely sales strategy and creating a sense of trust. Therefore, reasons for the importance of packaging in our daily life have been the subject of this research Design of packaging, form of packaging, psychological causes as their impact on ego, power that brings to the second class of product brand and quality value have been tried to demonstrate.

B.C. In 3000, Egyptians, Phoenicians, Iranians and Turks were able to make bottles by blowing glass, using containers such as jars and jars for liquid foods, and papyrus for packaging. With the development of humanity and the increase in needs, increases and changes in packaging types and materials have started to take place. Especially M.S. The discovery of paper in 105, and later in the 15th century, the innovation movements that began in Europe were the most important factors that accelerated the development of packaging. Paper bags, tin and corrugated cardboard boxes, high quality glass bottles for milk and other liquid beverages and other types of packaging have been introduced to humanity one after another. Furthermore, more durable and protective packages have been produced by increasing the resistance of these materials by tinning, coating and similar chemical and physical interactions. In addition to materials and production techniques, original and realistic packages were designed with the knowledge of contemporary structure of designers.

Together with the developing packaging technology, more useful and showy packages have been produced. Its superior ego has produced much more functional and flashy packages. The number of consumers who buy the products is not limited because they like their packaging. However, the production of so many packages brought about environmental problems and the packaging waste started to occupy the agenda. In many countries, municipalities felt the obligation to reuse waste by implementing packaging waste collection laws. Because after this stage, ego has started to be replaced by environmental awareness and common life concerns. It is the general aim of humanity to create a society and a world in which people can benefit equally from the welfare society, which constantly develops without overloading the environment. Especially after product developers, consumers and even anyone interested in packaging should make efforts. The purpose of the packaging has now changed for the third time. Since the creation of mankind, storage-protection in the first stage, protection-transportation-promotion in the second stage, and environment and living space creation in the third stage are the new points in the packaging. In other words, new concepts such as environmental protection, product responsibility and universal designs have started to prevail in the world of packaging.

This article has been demonstrated the characteristics of a successful packaging and has been described the fact that has been able to recognize packaging before the product via the designer’s right approach. It was explained that most of the time, the sense of allure of the consumer that is created by packaging how comes to forefront of the product and brand identity. With this study, which investigated the successful packaging forms and features, has been wanted to explain the effective design in packaging which means buying fast on the customer side.

In this article gives examples of how packaging reflects the place, the importance, the definition and the human qualities we have in our lives. It is told how packaging is a living soul, how talking with us, how print quality affects packaging, and what try to say us. In today when the packaging is not just a container and this value judgment is becoming more widespread, it has been revealed how people reflect their love, loneliness, and friendship and health worries to packaging. It was exemplified how we associate with a package when we receive a product, and how the product or its package directed us. In this study, living connective tissues between packages and humans were determined.

We consider problems requiring to allocate a set of rectangular items to larger rectangular standardized units by minimizing the waste. In two-dimensional bin packing problems these units are finite rectangles, and the objective is to pack all the items into the minimum number of units, while in two-dimensional strip packing problems there is a single standardized unit of given width,

High utilization of cargo volume is an essential factor in the success of modern enterprises in the market. Although mathematical models have been presented for container loading problems in the literature, there is still a lack of studies that consider practical constraints. In this paper, a Mixed Integer Linear Programming is developed for the problem of packing a subset of rectangular boxes inside a container such that the total value of the packed boxes is maximized while some realistic constraints, such as vertical stability, are considered. The packing is orthogonal, and the boxes can be freely rotated into any of the six orientations. Moreover, a sequence triple-based solution methodology is proposed, simulated annealing is used as modeling technique, and the situation where some boxes are preplaced in the container is investigated. These preplaced boxes represent potential obstacles. Numerical experiments are conducted for containers with and without obstacles. The results show that the simulated annealing approach is successful and can handle large number of packing instances.

Packing problems deal with loading of a set of items (objects) into a set of boxes (containers) in order to optimize a performance criterion under various constraints. With the advance of RFID technologies and investments in IT infrastructures companies now have access to the necessary data that can be utilized in cost reduction of packing processes. Therefore bin packing and container loading problems are becoming more popular in recent years. In this research we propose a beam search algorithm to solve a packing problem that we encountered in a real world project. The 3D-MBSBPP (Multiple Bin Sized Bin Packing Problem) that we present and solve has not been analyzed in literature before, to the best of our knowledge. We present the performance of our proposed beam search algorithm in terms of both cost and computational time in comparison to a greedy algorithm and a tree search enumeration algorithm.

The utilization bound for earliest deadline first (EDF) scheduling is extended from uniprocessors to homogeneous multiprocessor systems with partitioning strategies. First results are provided for a basic task model, which includes periodic and independent tasks with deadlines equal to periods. Since the multiprocessor utilization bounds depend on the allocation algorithm, different allocation algorithms have been considered, ranging from simple heuristics to optimal allocation algorithms. As multiprocessor utilization bounds for EDF scheduling depend strongly on task sizes, all these bounds have been obtained as a function of a parameter which takes task sizes into account. Theoretically, the utilization bounds for multiprocessor EDF scheduling can be considered a partial solution to the bin-packing problem, which is known to be NP-complete. The basic task model is extended to include resource sharing, release jitter, deadlines less than periods, aperiodic tasks, non-preemptive sections, context switches, and mode changes.

Wireless broadband networks are designed to provide high quality services to multiple mobile users using OFDMA schema for frame structure. This schema defines rectangular resource allocation schema of time slots and frequency carriers. This structure is used for arranging incoming user requests. Our goal was to increase bandwidth utilization while arranging the incoming user requests into an effective way. For this reason Bin-Packing algorithms were considered and evaluated. Therefore, we have analyzed using software engineering methodologies; designed while presenting the algorithm’s workflows; implemented with Java programming language; and tested  through NetBeans IDE; a working version of a program while incorporating five algorithms of Bin-Packing family.

Partitioning a permutation into a minimum number of monotone subsequences is N Phard. We extend this complexity result to minimum partitioning into k-modal subsequences; here unimodal is the special case k = 1. Based on a network flow interpretation we formulate both, the monotone and the k-modal version, as mixed integer programs. This is the first proposal to obtain provably optimal partitions of permutations. LP rounding gives a 2-approximation for minimum monotone partitions and a (k+1)-approximation for minimum (upper) k-modal partitions. For the online problem, in which the permutation becomes known to an algorithm sequentially, we derive a logarithmic lower bound on the competitive ratio for minimum monotone partitions, and we analyze two (bin packing) online algorithms. These immediately apply to online cocoloring of permutation graphs.

In this article, a multi-objective evolutionary framework to build selection hyper-heuristics for solving instances of the 2D bin packing problem is presented. The approach consists of a multi-objective evolutionary learning process, using specific tailored genetic operators, to produce sets of variable length rules representing hyper-heuristics. Each hyper-heuristic builds a solution to a given problem instance by sensing the state of the instance , and deciding which single heuristic to apply at each decision point. The hyper-heuristics consider the minimization of two conflicting objectives when building a solution: the number of bins used to accommodate the pieces and the total time required to do the job. The proposed framework integrates three well-studied multi-objective evolutionary algorithms to produce sets of Pareto-approximated hyper-heuristics: the Non-dominated Sorting Genetic Algorithm-II, the Strength Pareto Evolutionary Algorithm 2, and the Generalized Differential Evolution Algorithm 3. We conduct an extensive experimental analysis using a large set of 2D bin packing problem instances containing convex and non-convex irregular pieces, under many conditions, settings and using several performance metrics. The analysis assesses the ro-bustness and flexibility of the proposed approach, providing encouraging results when compared against a set of well-known baseline single heuristics.