An interactive fuzzy goal programming approach for multi-period multi-product production planning problem

This study addresses an interactive multiple fuzzy goal programming (FGP) approach to the multi-period multi-product (MPMP) production planning problem in an imprecise environment. The proposed model attempts to simultaneously minimize total production costs, rates of changes in labor levels, and maximizing machine utilization, while considering individual production routes of parts, inventory levels, labor levels, machine capacity, warehouse space, and the time value of money. Piecewise linear membership functions are utilized to represent decision maker’s (DM’s) overall satisfaction levels. A numerical example demonstrates the feasibility of applying the proposed model to the MPMP problem. Furthermore, the proposed interactive approach facilitates the DM with a systematic framework of decision making process which enables DM to modify the search direction to reach the most satisfactory results during solving process.     

Multi-product production planning: A goal programming approach

Cost minimization multi-product production problems with static production resource usage and internal product flow requirements have been solved by linear programming (LP) with input/output analysis. If the problem is complicated by interval resource estimates, interval linear programming (ILP) can be used. The solution of realistic problems by the above method is cumbersome. This paper suggests that linear goal programming (LGP) can be used to model a multi-product production system. LGP's unique modeling capabilities are used to solve a production planning problem with variable resource parameters. Input/output analysis is used to determine the technological coefficients for the goal constraints and is also used to derive an information sub-model that is used to reduce the number of variable resource goal constraints. Preliminary findings suggest that the LGP approach is more cost-efficient (in terms of CPU time) and in addition provides valuable information for aggregate planning.     

Interactive fuzzy goal programming approach for bilevel programming problem

This paper presents an interactive fuzzy goal programming (FGP) approach for bilevel programming problems with the characteristics of dynamic programming (DP).     

A fuzzy goal programming approach for mid-term assortment planning in supermarkets

We develop a fuzzy mixed integer non-linear goal programming model for the mid-term assortment planning of supermarkets in which three conflicting objectives namely profitability, customer service, and space utilization are incorporated. The items and brands in a supermarket compete to obtain more space and better shelf level. This model offers different service levels to loyal and disloyal customers, applies joint replenishment policy, and accounts for the holding time limitation of perishable items. We propose a fuzzy approach due to the imprecise nature of the goals’ target levels and priorities as well as critical data. A heuristic method inspiring by the problem-specific rules is developed to solve this complex model approximately within a reasonable time. Finally, the proposed approach is validated through several numerical examples and results are reported.     

A method for solving fuzzy goal programming problems based on MINMAX approach

Narasimhan incorporated fuzzy set theory within goal programming formulation in 1980. Since then numerous research has been carried out in this field. One of the well-known models for solving fuzzy goal programming problems was proposed by Hannan in 1981. In this paper the conventional MINMAX approach in goal programming is applied to solve fuzzy goal programming problems. It is proved that the proposed model is an extension to Hannan model that deals with unbalanced triangular linear membership functions. In addition, it is shown that the new model is equivalent to a model proposed in 1991 by Yang et al. Moreover, a weighted model of the new approach is introduced and is compared with Kim and Whang’s model presented in 1998. A numerical example is given to demonstrate the validity and strengths of the new models.     

A chance constraints goal programming model for the advertising planning problem

This paper presents a model which has been designed to decide the number of advertisement in different advertising media and the optimal allocation of the budget assigned to the different media. The main objective of this problem is to maximize the reach to the desired section of people for different media within their maximum allowable budget without violating the max and min number of advertisement goals. The media have been considered as different newspapers and different channels in Televisions. Here in this article the model has been formulated in such a way that the advertisement should reach to those who are suitable for the product instead of going to those section who are not considered suitable for the product as well. A chance constrained goal programming model has been designed after considering the parameter corresponding to reach for different media as random variables. The random variables in this case has been considered as values which have known mean and standard deviations. A case for an upcoming institution who are interested to advertise for its two years Post Graduate Diploma in Management (PGDM) programme to the different newspapers and television channels has been designed to illustrate the solution methodology.     

Exact and heuristic procedures for solving the fuzzy portfolio selection problem

We propose a fuzzy model for the portfolio selection problem which takes into account the vagueness of the investor’s preferences regarding the assumed risk. We also describe an exact method for solving it as well as a hybrid meta-heuristic procedure which is more adequate for medium and large-sized problems or in cases in which a quick solution is needed. As an application, we solve several problems based on data from the IBEX35 index and the Spanish Stock Exchange Interconnection System.     

An approach for solving a fuzzy multiobjective programming problem

In this paper we present a new approach, based on the Nearest Interval Approximation Operator, for dealing with a multiobjective programming problem with fuzzy-valued objective functions.     

A fuzzy goal programming approach to multi-objective optimization problem with priorities

In goal programming problem, the general equilibrium and optimization are often two conflicting factors. This paper proposes a generalized varying-domain optimization method for fuzzy goal programming (FGP) incorporating multiple priorities. According to the three possible styles of the objective function, the varying-domain optimization method and its generalization are proposed. This method can generate the results consistent with the decision-maker (DM)’s expectation, that the goal with higher priority may have higher level of satisfaction. Using this new method, it is a simple process to balance between the equilibrium and optimization, and the result is the consequence of a synthetic decision between them. In contrast to the previous method, the proposed method can make that the higher priority achieving the higher satisfactory degree. To get the global solution of the nonlinear nonconvex programming problem resulting from the original problem and the varying-domain optimization method, the co-evolutionary genetic algorithms (GAs), called GENOCOPIII, is used instead of the SQP method. In this way the DM can get the optimum of the optimization problem. We demonstrate the power of this proposed method by illustrative examples.     

A new heuristic and an exact approach for a production planning problem

Central European Journal of Operations Research - We deal with a very complex and hard scheduling problem. Two types of products are processed by a heterogeneous resource set, where resources have...     

Interactive fuzzy decision making method for solving bilevel programming problem

In this paper, an interactive fuzzy decision making method is proposed for solving bilevel programming problem. Introducing a new balance function, we consider the overall satisfactory balance between the leader and the follower. Then, a satisfactory solution can be obtained by the proposed method. Finally, numerical examples are reported to illustrate the feasibility of the proposed method.     

A fuzzy goal programming method with imprecise goal hierarchy

Two most widely used approaches to treating goals of different importance in goal programming (GP) are: (1) weighted GP, where importance of goals is modelled using weights, and (2) preemptive priority GP, where a goal hierarchy is specified implying infinite trade-offs among goals placed in different levels of importance. These approaches may be too restrictive in modelling of real life decision making problems. In this paper, a novel fuzzy goal programming method is proposed, where the hierarchical levels of the goals are imprecisely defined. The imprecise importance relations among the goals are modelled using fuzzy relations. An additive achievement function is defined, which takes into consideration both achievement degrees of the goals and degrees of satisfaction of the fuzzy importance relations. Examples are given to illustrate the proposed method.     

Earliness–tardiness production planning for just-in-time manufacturing: A unifying approach by goal programming

With popularity of the just-in-time (JIT) philosophy, researchers have started to seek the integration of Manufacturing Resource Planning (MRP-II) and JIT methodologies. This paper deals with the master production planning problem for a mass manufacturing system in the JIT environment, an earliness–tardiness production planning (ETPP) problem. The objective is to determine the optimum production rate for each product so that the total penalties imposed on the early and tardy production for all production periods be minimized. A goal programming (GP) approach is proposed to formulate the ETPP problem in a more generalized form, which includes several existing models in one unifying model. Moreover, the proposed GP algorithm ensures a global optimum solution, while the existing ones did not. In addition, it also possesses the advantages over others, such as easier to comprehend, easier to solve, and easier to extend it to the problem of multiple goals.     

A heuristic algorithm for a production planning problem in an assembly system

This paper focuses on a production planning problem in an assembly system operating on a make-to-order basis. Due dates are considered as constraints in the problem, that is, tardiness is not allowed. The objective of the problem is to minimise holding costs for final product inventory as well as work-in-process inventory. A non-linear mathematical model is presented and a heuristic algorithm is developed using a solution property and a network model for defining solutions of the problem. A series of computational tests were done to compare the algorithm with a commercial planning/scheduling software and backward finite-loading methods that employ various priority rules. The results showed that the suggested algorithm outperformed the others.     

A dynamic programming heuristic for the P-median problem

A new heuristic algorithm is proposed for the P-median problem. The heuristic restricts the size of the state space of a dynamic programming algorithm. The approach may be viewed as an extension of the myopic or greedy adding algorithm for the P-median model. The approach allows planners to identify a large number of solutions all of which perform well with respect to the P-median objective of minimizing the demand weighted average distance between customer locations and the nearest of the P selected facilities. In addition, the results indicate regions in which it is desirable to locate facilities. Computational results from three test problems are discussed.     

A method for solving a fuzzy linear programming

In this paper a fuzzy linear programming problem is presented. Then using the concept of comparison of fuzzy numbers, by the aid of the Mellin transform, we introduce a method for solving this problem.     

A fuzzy goal programming approach to integrated loading and scheduling of a batch processing machine

This paper concerns a real-life problem of loading and scheduling a batch-processing machine. The integrated loading and scheduling problem is stated as a multicriteria optimization problem where different types of objectives are included: (1) short-term objectives of relevance to the shop floor, such as throughput maximization and work-in-process inventory minimization, and (2) long-term objectives such as balancing of end product inventory levels and meeting financial targets imposed by the higher production planning level. Two types of uncertainty are considered: (1) uncertainty inherent in loading and scheduling objective targets (goals) such as the allocated budget and end product demand, and (2) uncertainty in importance relations among the objectives. These two types of uncertainty are modelled using fuzzy sets and fuzzy relations, respectively. A fuzzy goal programming model and the corresponding method are developed which handle both fuzzy and crisp goals and fuzzy importance relations among the goals. Numerical examples are given to illustrate the effectiveness of the developed model.     

A heuristic procedure for solving the quadratic assignment problem

An heuristic approach to the solution of the quadratic assignment problem is presented. A simple procedure is used to get a good feasible starting point, then the problem is solved as a nonlinear program (ignoring the integrality conditions) using MINOS, and lastly the near integer solution is converted into an integer feasible solution using an heuristic procedure. The results compare favourably with other procedures in the literature. A superior solution to the 19 × 19 hospital layout problem is found.     

Satisfying optimization method based on goal programming for fuzzy multiple objective optimization problem

This paper proposes a satisfying optimization method based on goal programming for fuzzy multiple objective optimization problem. The aim of this presented approach is to make the more important objective achieving the higher desirable satisfying degree. For different fuzzy relations and fuzzy importance, the reformulated optimization models based on goal programming is proposed. Not only the satisfying results of all the objectives can be acquired, but also the fuzzy importance requirement can be simultaneously actualized. The balance between optimization and relative importance is realized. We demonstrate the efficiency, flexibility and sensitivity of the proposed method by numerical examples.     

A class of heuristic algorithms for the routing problem

Transiated fromIssledovaniya po Prikladnoi Matematike, No. 18, 1992, pp. 38–48.