Manual Advances in Multicriteria Analysis

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The primary goal of the book is to present the most recent developments in the field of multicriteria analysis and in some of its principal areas of application.
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View all copies of this ISBN edition:. Synopsis About this title As its title implies, Advances in Multicriteria Analysis presents the most recent developments in multicriteria analysis and in some of its principal areas of application, including marketing, research and development evaluation, financial planning, and medicine.

From the Back Cover : The primary goal of the book is to present the most recent developments in the field of multicriteria analysis and in some of its principal areas of application including marketing, research and development evaluation, financial planning and medicine. The difficulty is not only due to the combinatorial complexity as in single-objective case, but also due to the research of all elements of the efficient set, whose cardinality grows with the number of objectives.

In the literature, some authors have proposed exact methods for solving specific MOCO problems, which are generally valid to bi-objective problems but cannot be adapted easily to a higher number of objectives. Genetic algorithms are the most commonly used metaheuristic in the literature to solve these problems [ 8 ].


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This is done in order to: reduce the total production time; prioritize the use of internal production centers of the company rather than the use of external production centers; and reduce the downtime of the internal production centers. With this purpose, initially a mixed integer programming model was developed for the problem. The mixed integer programming model, the MGA developed and its automatic combination with the multicriteria method WSM are original contributions of this work.

The production planning process of the Brazilian garment industry may be split into many phases from demand provision to tasks scheduling at each machine. Then it becomes available to the Issuance of Production Orders and Sequencing. These steps are depicted at Figure 1. This work approaches the scheduling phase where a set of tasks has to be distributed among production centers.

Multiple-criteria decision analysis - Wikipedia

As said before, production center is an internal or external production cell composed by a set of specialized individuals. Each task may be done by a set of production centers and each production center is able to execute many tasks. The objectives of this work are: i to minimize the total production time makespan — time from the beginning of the first task to the end of the last task ; ii to maximize the use of internal production centers — the use of internal production centers does not imply cost overhead [1] - since employees' salary are already at the payroll of the company; iii to minimize the internal production centers downtime.

These three objectives have been chosen in order to meet the needs of the analyzed company. Some couple of them are conflicting, i. Others objectives are not conflicting, but the optimization of one does not guarantee the optimization of the other. However, if tasks are allocated to an internal production center, which together have an execution time shorter than the total production time, it is possible to arrange them in different ways without changing the total production time.

In order to better describe the addressed problem, Figure 2 depicts the steps toward the production of a short. The production process is composed by a set of production stages. Each stage has a set of operations to be performed. In this work, this set is called task. In this example, there are 6 production stages scratch, cut, sewing, embroidery, laundry and finishing.

The sewing task lasts There are h production centers qualified to perform the sewing task. The execution time of a task is the sum of the execution time of its operations. This time is used during the scheduling, which hides the complexity of the operation distribution inside a stage. So it can be seen as a classical task scheduling where each production center is a machine and the operations set of each production stage is a task.

During the scheduling process the following constraints must be respected: i for each product exists an execution order of tasks, i. The addressed problem is similar to the flexible job shop problem, in which there is a set of work centers that groups identical machines operating concurrently; inside a work center, a task may be executed by any of the machines available [ 10 ]. Figure 3 depicts an example of adapting the flexible job shop to the addressed problem.

In Figure 3 the problem is divided into 2 subproblems: A and B. At subproblem A the tasks are distributed among the production centers that can execute them. At this step is important to prioritize internal production centers in order to take profit of the company processing power that is already available. At subproblem B the tasks must be scheduled respecting the precedence order of tasks. Figure 4 1 depicts an example of scheduling for the tasks listed in Figure 3. The Figure 4 2 shows the downtime gray arrows in the production centers.

For instance, task T 13 at production center C 5 waits for the task T 12 at C 3 before starts executing. Figure 4 3 shows that the tasks T 25 and T 31 at production center C 1 and T 38 at C 5 black boxes were ready but had to be frozen because of the unavailability of the production centers C 1 and C 5. The addressed problem is similar to some works found in the literature, like Senthilkumar and Narayanan [ 11 ], Santosa, Budiman and Wiratino [ 12 ], Abdelmaguid [ 13 ], Dayou, Pu and Ji [ 14 ], Chang and Chyu [ 15 ] and Franco [ 16 ]. However, these works do not consider real-time tasks sequencing or are not applied to real problems.

It is important to note that the chronoanalysis method used here is not the focus of this work. However, in this work, the production time includes tolerance, rhythm and others variables from the chronoanalysis. For this modeling was created a sequencing unit SU which defines a time-slice of work. Each production center has distinct sequencing units, in which tasks are scheduled all day long. Figure 5 depicts a set of sequencing units that describes the behavior of a particular production center. The overtime work is treated as a distinct sequencing unit, since they have particular features like cost.

This model defines a variable N that indicates the total number of tasks, including an additional task that is required for the initialization of the sequencing units. Below is presented the mixed integer programming model for the addressed problem. The parameters of the problem are presented, followed by the interval indexes, the decision variables and finally by the equations for the three objective functions together with their constraints. The last one is the fictitious task that was added to the model as the initial task of every sequencing unit. CP s — Production center of the sequencing unit s.

Minimum s — Starting time of the sequencing unit s. Time s — Amount of time available at sequencing unit s. CPJ i — Set of production centers that can execute the task i. PRE i — Set of tasks that are a precondition for the execution of task i. O f f S e t c k c l — Time for going from production center c k to c l. Start i — Non-negative linear variable that represents the starting time of task i. End i — Non-negative linear variable that represents the ending time of task i. WLS si — Non-negative linear variable that represents the workload of task i at the sequencing unit s.

StartS si — Non-negative linear variable that represents the starting time of task i at sequencing unit s. DT sij — Non-negative linear variable that represents the downtime between tasks i and j in the sequencing unit s.


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Y sij — Non-negative linear variable that represents the flow i , j of the sequencing unit s. MkSpan — Non-negative linear variable that represents the time between the end of the last finished task and the start of the first task. IntTime — Non-negative linear variable that represents the amount of execution time of tasks in the internal production centers. DownTime — Non-negative linear variable that represents the amount of internal production centers downtime. Objective function that aims to minimize the amount of downtime at the internal production centers.

The amount of downtime between tasks i and j in the sequencing unit s. Asserts that a task i can only be executed on a sequencing unit s if the task i is scheduled to the production center of the sequencing unit s. If the task j is performed in sequencing unit s then there is just one task that immediately precedes j in s. If the task j is performed in sequencing unit s then there is at most one task that is immediately preceded by j in s.

1. Introduction

Asserts that each task i must be started only after the start of the sequencing unit s where task i is allocated. Asserts that the workload of task i at the sequencing unit s is 0 zero if task i is not scheduled to the sequencing unit s. Asserts that the beginning time of task i , Start i , must be lower or equal to the beginning time of task i at any sequencing unit where it is allocated.

Asserts that the ending time of task i , End i , must be greater or equal to the ending time of task i at any sequencing unit where it is allocated. Asserts that the ending time of task i must be at least equal to its beginning. Asserts that the task i starts only after the ending time of the task j that immediately precedes i in the sequencing unit s. Asserts that task j only can starts after the ending time of its predecessor tasks.

Multi-Criteria Reverse Engineering for Food: Genesis and Ongoing Advances

This restriction takes into account the travel time between the production centers. We propose in this work a method that combines multiobjective genetic algorithm and multicriteria decision analysis for solving the addressed problem. The multiobjective genetic algorithm MGA aims to find a good approximation of the efficient solution set, considering the three objectives of the problem.

A multicriteria decision analysis method is applied on the solution set obtained by the MGA in order to choose one solution, which will be used by the analyzed garment company. Samson, with nice words on this early text download. Conferences Proceedings. Other published papers.

Dedication to the memory of Jean-Yves Jaffray , table of contents and preface. Roy ", Kluwer , , pages, Order Form of the book.