ADVANCES IN MANAGEMENT

Volume 1(8) November, 2008

From Editor's Desk:

Optimization and Logistic

Farouk Yalaoui

Our editor from Institut Charles Delaunay, FRE CNRS 2848, Université de Technologie de Troyes, FRANCE
farouk.yalaoui@utt.fr

The first interest of this paper is to participate to this amazing adventure which represents the “Advances In Management” journal. This new expression field is an addi­ti­onal space to make valuable the works developed almost anywhere in the world and to make them a profit for a wide range of persons. The fields covered by our journal are as large as the importance that represents the concept of management. We accept easily that the management of any structure, regardless its finality, requires taking in account a number of parameters. This considers equally the human resources, mechanics, electronics, as well as the process or the applied methods and the environment. In this paper a presentation of a well particular field which is the research in the optimization of logistic systems is done. The link with the management is obvious. This type of activities reports in a main way to the intelligent and efficient management of products, process and resources. The optimization consists to propose the best solution to a given problem and the logistic concerns all the operations and decisions required for the realization of a given product or activity. We have mainly two types of logistics: internal and external. The first is focalized on the problems concerning the system inside its bounds and it is equally called production management with issues like scheduling, layout and lines design. For the second one, we consider the system in its environment including the external one with, for example, the management problem of a transpo­rtation system or the supply chain. The optimization might concern operational problems or tactical ones. This is due to the fact that problems have different time impact and thus different constraints and approaches.

 In a general manner, the problems are addressed regarding the following step: the identification or the choice of an issue or a problem to treat, looking for different works and realizations leading to the problem and finally modelling and proposing resolution and optimiz­ation methods. In the adopted approach for the production management problems, we have to face, in a majority of cases, to the NP-hard problems. This means that there is a small probability that we may get systematically, in the actual state of knowledge and computation methods, an optimal solution in a polynomial time. For large instances in terms of variables and decision parameters, it is not realistic to look for solving them in an exact way (with a guaranteed optimal regardless the instances size). We must then develop approximate methods, with solutions of a good quality in reasonable times. This complexity depends also on the one or the several criterion considered and on the set of constraints to be satisfied.

 There exists a methodology for the optimization of logistic problems. The different problems are covered in such a way that respects a given number of steps in order to lead to appropriate methods and approaches. Those latter may be exact or approximated. A use of operational research approach and simulation is adopted in function of the complexity and the objective of the study case. It is not enough to propose resolution and optimization methods but we need to be able to judge their efficiency and usefulness. This is a part of research objectives in this field. It remains that the methods are not evaluated within the same criterion. The quality of exact methods is judged in terms of the size importance of the treated instances. For approximate methods, we measure the deviation between the proposed solutions and the corresponding optimal solution. This deviation is obviously difficult to be establi­shed directly but it is rather estimated via minors (for criterion to be minimized for example). For the different developed methods, a continuous effort is supp­l­ied in order to establish properties and theoretical charac­t­eristics for the problems by using the methods of the operational research.

 Some criterion, called equally dominance prop­e­r­t­i­e­s (especially in the frame of developing exact tree met­h­o­ds) on the level of the sets of solutions are constantly sou­g­h­t in order to integrate them in the construction of exact methods reducing then the exploration times, or in the approximate methods, in order to increase the quality of the obtained solution. Bounds are the criterion to be opt­i­mized allowing avoiding the construction of non prom­ising solutions but give equally an idea, an increase (with lower bounds) in the minimization case, of the deviation value compared to the optimum. The different methods are tested with computer simulation in order to review their perfor­m­a­nces. Thus, a programming effort is equally done to test and validate the methods, but also to solve in a direct way some problems by simulation. The techniques validation dep­ends on the data generation protocol and that is no matter if they are random or real, applications issues or not. This scheme is valid with more or less of diffic­u­l­ties in the case of scalar (mono criteria) or vector optim­i­z­a­t­ion (multi objective).

 In what follows, some examples of classical pr­oblems on the logistic optimization are treated such as sc­h­e­­­duling, production, line design, layout and many oth­e­r­s. The main door is on the tactical (medium term) and op­­­e­­ra­t­i­­onal level (short term). The goal is to return a given num­b­e­r of thematic of a new or an old interest and always upd­ate that any manager would raise its structure at a given time. The presentation is not exhaustive but the idea is to see for each case the original interest, the proposed app­r­o­a­c­h and its impact when it is possible either on the scientific or on the practical term. The certainty is that all the ideas th­­at have been carried out have an impact and work on the lo­g­istic optimization and also on the manage­ment in ge­n­e­r­a­l.

 For the short term decisions, scheduling is a per­f­e­ct example. Scheduling is a topic that is largely stu­d­i­e­d. It consists on determining at each moment to treat a task with resource while respecting a set of constraints and resp­e­c­ting one or several criterion. For some problems, such as the PSMP problems (Parallel Machine Scheduling Prob­lems), they have been carried out in the frame of my works under various criterion and different constraints such as the arrival dates different from tasks and setup times between tasks. This interest toward the PMSP is due to the practical reality and its scientific interest. There exists a mu­­ltitude of configurations in the current workshops which could be considered as parallel machines scheduling pro­b­l­e­ms.

 In the realized studies, various structures and many constraints were considered such as: tasks splitting, setup times, tasks and resources release dates, delivery due dates etc. Different criterion were carried out such as the makespan which aims at maximizing the productivity, the minimization of waiting time or the flow time in the system and the tardiness minimization. Those mono criteria cases were carried out with or without taking in consideration the weightings and the priorities of the tasks. The minimization of the makespan is among the most studied criteria in scheduling. This latter consists on minimizing the makespan with setup times depending on the sequence between two consecutive tasks and where splitting tasks is authorized and quite interesting. This problem is quite frequent in some industries, in particular the textile but no study has been ever devoted to it before 2000. From a practical viewpoint and for the textile industry for example, a task may be a batch of several pieces (100 shirts or 1000 socks). Each batch may be divided in sub batches letting then the hypothesis of splitting tasks realistic. Taking in consideration setup times is justified equally in the case of a painting unit or a step of coloration of a given product. The proposed method, heuristic, is very near from the optimum.

 Studying the problem due to the minimization of the total completion time of jobs in the system presents a proof to be of a practical interest. Indeed, a perfect quality service with a minimal waiting time is among the objectives that every contractor, in all disciplines, seeks to ensure. Faced with a communication and a work style in networks, the quick satisfaction of users requires a good organization and management of the different demands in function of resources. To reflect this situation, it is enough to stop a moment to note that with the internet boom and its related activities, the concept of time is the leitmotif of all these shops. In addition to that, the globalization of exchanges and markets has generate needs and conditions so that a distinction between suppliers may go through the achievement speed and systems reactions whether they are of production, transmission, communication or other. Rel­i­a­­ble and efficient algorithms and decision aid tools are available for tasks sequencing. The computer environment, for some applications such as network organizations and parallel programming of logic controllers, looks inevitably for a high performance for each process or user. Studying the minimization of tasks sojourn times (process, users) going at different instants into a system, composed for example by identical resources working in parallel, contributes to give answers to this issue.

 Addressing a problem of parallel machines is, in some cases, approaching a floor of hybrid structures. A hybrid structure is a succession of floors composed by machines with a given mode of disposal. We mean by disposal the type of operating sequence that tasks must follow. The most known are: the linear unidirectional where all sequences are identical, called flowshop, workshops with multiple paths (linear) where each product has a specific sequence, called jobshop, and finally the most general one, the openshop, where paths are free. This enumeration is incomplete because there are other types of workshops such as those with re-entrant resources and tasks. We have to note that, in the case where at each floor we only have a single machine, it is then up to classical problems of workshops scheduling (non hybrids).

The jobshop problem is NP-hard. The scheduling problem in flexible jobshop workshops has at least the same complexity as a jobshop problem. This latter is considered as one of the most difficult problems in scheduling optimization. Addressing a problem of such complexity always requires a modelling of precision. The most classical formulation is without any doubt under the form of a disjunctive graph, very often used in the development of resolution methods, but modelling with mathematical programming is the oldest one. However, those developed methods are dedicated to problems of a small size regarding the important number of variables which increase significantly depending on the number of constraints taken in consideration. The jobshop scheduling problem has inspired many authors and the proposition of resolution methods is extremely varied. The tactical and design problems are an exciting field of investigation. Those works focus on design proble­m­s and thus on decisions brought to a time horizon larger than a scheduling problem. This implies then to take in acc­ount some particular constraints and given ones. In ter­m­s of methodology and tools there is no difference betw­­e­en the tactical problems themselves and operational ones as scheduling problems. This observation is also valid as soon as model and an analogy are established, because ope­r­­at­ional research methods and simulation are fairly generics.

 In the study of this problem category we have noticed that actually, production systems design relies heavily on computer tools and methods. This situation is explained by a modification supported by the technical (technologies evolution), financial and social environment of industries: decrease in the products life, competitive situations between products and consequently between industries, fluctuation in markets. Thus design and re-design problems arise more frequently and they are increasingly complex. This confers then for computers to give powerful, efficient and responsive decision aid tools.

 Preliminary of a production line consists of the following steps: the resources choice and the dimens­i­o­n­ing, it means the selection of equipments and the means of transportation, the layout, the management system select­ion, the evaluation of the dynamic behaviour. Depending on the type of the system and the importance of changes, the previous steps can be completed. This can be done by the choice: products to be manufactured, production seque­nces, in upstream, and/or by the choice of the pilot algori­t­hm in real time of the transportation means, in do­wns­tream. The preliminary design starts then by the chara­c­­­t­er­iz­a­tion of the products to be manufactured (number of operations, production volume, production sequence, etc.), then by the selection of equipment and resources, then by a layout of resources on a given surface in order to minimize the operations costs. The difference between the prelimi­nary design and the detailed design is that the second one is based on the results of the first one. This allows detailing them, to give precisions and to determine if the decisions taken at the step of the preliminary design will be imple­m­e­nted or whether we should go back to that step to modify, correct or satisfy some constraints. The prelimi­nary design is very important in the life cycle of such a line, because a mistake in this step, regarding the scales effect, may be very expensive.

 The other problem of tactical level that we will address concerns the facility layout problem (FLP). It consists of finding a good disposal of machines, equipments or departments in a given space in order to achieve a time or space saving and to simplify the production system and thus enhance the performance and the productivity of an industry. It is implemented either at a new organization in a workshop or during the establish­ment of a new production structure. In a facility layout, we have to take a given number of constraints in consider­ation. Generally, they are related to the geometry of the stations, cells and the machines to be placed in the entrance space, to the process of products as well as to the quality and industrial security requirements. For the implement­ation of a rational occupation of the workshop spaces, we have to take in account the use of these spaces, the travelled distances by workers and products, as well as the flexibility of fabrication process which allows the adap­t­a­t­ion to future changes in the demand. The different studies realized on layout deal with standard simple problems. Many methods have been used to solve the different classes of layout problems. They are mainly based on metaheuristics such as genetic algorithms, the tabu search, the simulated annealing, the ant colonies or also combining two of them. We cite as an example the software (FACO­PT) which includes a simulated annealing and a genetic algorithm. This one was compared successfully to CRAFT which was developed earlier.

 The integration of the optimization with the simulation becomes increasingly pervasive. Until the end of the last millennium, the optimization and the simulation were completely separated in practice despite many rese­a­rch works aiming to couple them. However, in the last decade, the optimization techniques have found their way so that they can be integrated with simulation tools. That is why all actual optimization tools such as Autostat, Opt­quest, did not exist at the simulation software’s first vers­ions release times. At present, most of the softwares are equipped with an optimization tool which was not the case at the beginning of the last decade. The goal is to guide a series of simulations in the most efficient way instead of testing scenarios blindly. The principle of sim­ulation based optimization is based on the fact of coupling a simulation model with one or many optimizat­ion mod­ules through opti­m­ization tools already existing in the markets or by developing new ones in the case of specific needs and thus with programming languages while being based on ded­i­c­a­t­ed methods. The two tools will be coupled in a manner that the output data of a one become the input data of the other one and vice versa. Thus, at the end of each sim­ulation, the optimization module will man­age the new data in its disposal in order to optimize in crea­ting new solu­t­ions. Those latter will be then sent to be si­mulated in order to see the corresponding results and so on.

 The final goal of these works is to propose solutions and help to the decision maker. This goes through assistance and equally by developing of a computer tool with a suitable interface by including all the programs and algorithms on the different issues that could arise on the field. It exists, for example, on the market many software’s and decision aid tools to optimize the production lines design: DELMIA (Digital Enterprise Lean Manufacturing Interactive Applications) and its product PLM Process Planning, LG Electronics and its product FLB 3.0 (Flexible Line Balancing version 3.0), ARENA with Siman. In fact, a lot of problems need a thorough scientific analysis to develop efficient methods in terms of solutions quality and computation time. Academic studies are dedicated to it and a lot of efforts are made. Results are often very relevant but still achieved without any impact or significance for users that are either industrials or researchers. In the research field, the expectations are multiple and complementary with answers for either scientific or practical questions.

 We had an overview about logistics and optimi­zation and I hope that our journal will become a ref­er­­ence in the field.

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ó If you want to give a man credit, put it in writing. If you want to give him hell, do it on the phone.

ó Don't be a time manager, be a priority manager. Cut major goals into bite-sized pieces. Each small priority or requirement on the way to ultimate goal become a mini goal in itself.

Portuguese Proverb

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