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.     

Multi-objective stochastic programming for portfolio selection

Generally, in the portfolio selection problem the Decision Maker (DM) considers simultaneously conflicting objectives such as rate of return, liquidity and risk. Multi-objective programming techniques such as goal programming (GP) and compromise programming (CP) are used to choose the portfolio best satisfying the DM’s aspirations and preferences. In this article, we assume that the parameters associated with the objectives are random and normally distributed. We propose a chance constrained compromise programming model (CCCP) as a deterministic transformation to multi-objective stochastic programming portfolio model. CCCP is based on CP and chance constrained programming (CCP) models. The proposed program is illustrated by means of a portfolio selection problem from the Tunisian stock exchange market.     

A multi-objective joint replenishment inventory model of deteriorated items in a fuzzy environment

In this study, a fuzzy multi-objective joint replenishment inventory model of deteriorating items is developed. The model maximizes the profit and return on inventory investment (ROII) under fuzzy demand and shortage cost constraint. We propose a novel inverse weight fuzzy non-linear programming (IWFNLP) to formulate the fuzzy model. A soft computing, differential evolution (DE) with/without migration operation, is proposed to solve the problem. The performances of the proposed fuzzy method and the conventional fuzzy additive goal programming (FAGP) are compared. We show that the solution derived from the IWFNLP method satisfies the decision maker’s desirable achievement level of the profit objective, ROII objective and shortage cost constraint goal under the desirable possible level of fuzzy demand. It is an effective decision tool since it can really reflect the relative importance of each fuzzy component.     

Fractional Goal Programming for Fuzzy Solid Transportation Problem with Interval Cost

In this paper, we study a solid transportation problem with interval cost using fractional goal programming approach (FGP). In real life applications of the FGP problem with multiple objectives, it is difficult for the decision-maker(s) to determine the goal value of each objective precisely as the goal values are imprecise, vague, or uncertain. Therefore, a fuzzy goal programming model is developed for this purpose. The proposed model presents an application of fuzzy goal programming to the solid transportation problem. Also, we use a special type of non-linear (hyperbolic) membership functions to solve multi-objective transportation problem. It gives an optimal compromise solution. The proposed model is illustrated by using an example.     

Chance constrained programming models for refinery short-term crude oil scheduling problem

The main objective of this work is to put forward chance constrained mixed-integer nonlinear stochastic and fuzzy programming models for refinery short-term crude oil scheduling problem under demands uncertainty of distillation units. The scheduling problem studied has characteristics of discrete events and continuous events coexistence, multistage, multiproduct, nonlinear, uncertainty and large scale. At first, the two models are transformed into their equivalent stochastic and fuzzy mixed-integer linear programming (MILP) models by using the method of Quesada and Grossmann [I. Quesada, I E. Grossmann, Global optimization of bilinear process networks with multicomponent flows, Comput. Chem. Eng. 19 (12) (1995) 1219–1242], respectively. After that, the stochastic equivalent model is converted into its deterministic MILP model through probabilistic theory. The fuzzy equivalent model is transformed into its crisp MILP model relies on the fuzzy theory presented by Liu and Iwamura [B.D. Liu, K. Iwamura, Chance constrained programming with fuzzy parameters, Fuzzy Sets Syst. 94 (2) (1998) 227–237] for the first time in this area. Finally, the two crisp MILP models are solved in LINGO 8.0 based on scheduling time discretization. A case study which has 267 continuous variables, 68 binary variables and 320 constraints is effectively solved with the solution approaches proposed.     

A compromised multi-objective solution using fuzzy mixed integer goal programming for market-based short-term unit commitment problem

When implementing, the solution of single-objective unit commitment models may be dissatisfactory or inapplicable. This might mainly be due to not considering the secondary conflicting objectives from the policy-making in internal/external environment of generation companies in the developed models. To attain a practical compromised multi-objective solution for the short-term unit commitment in the deregulated hybrid markets, a novel fuzzy mixed integer linear goal programme is developed in which several complementary objectives with lower relative importances are also incorporated. Non-linear characteristic curves of the generating units are approximated through the piece-wise linear functions. The fuzzy approach is proposed to handle the imprecise nature of the goals’ target levels and priorities as well as some critical data. The critical aspects of power systems are considered in the model. The efficiency of the proposed approach is demonstrated using the experimental results inspired by a real case. The applicable nice feature of our model is that it can easily and efficiently be matched with a various line of unit commitment problems.     

垃圾填埋场选址问题的模糊数学模型研究

为有助于在环境和经济框架内评价垃圾填埋场选址决策,本文建立了关于该问题的多目标模型,模型中既考虑了安置和运营设施需要的固定成本和可变成本,也考虑了居民区承受的风险,以及各居民区承担风险的公平性。并进一步讨论了用模糊方法处理的一般多目标规划模型的模糊最优解与有效解及弱有效解之间的关系。最后使用两种模糊目标规划方法求解数值例子以分析所建模型的适用性,结果表明,加权模糊方法可以为决策者提供更接近期望值的满意方案。     

Solving multi-criteria scheduling flow shop problem through compromise programming and satisfaction functions

The multi-criteria scheduling problem is one of the main research subjects in the field of multiple objectives programming. Several procedures have been developed to deal with this type of problem where some conflicting criteria have to be optimized simultaneously. The aim of our paper is to propose an aggregation procedure that integrates three different criteria to find the best sequence in a flow shop production environment. The compromise programming model and the concept of satisfaction functions will be utilized to integrate explicitly the manager’s preferences according to the deviations between the achievement and the aspiration levels of the following criteria: Makespan, total flow time and total tardiness.     

A Comparative Study of Multiple-Objective Metaheuristics on the Bi-Objective Set Covering Problem and the Pareto Memetic Algorithm

Many organizations face employee scheduling problems under conditions of variable demand for service over the course of an operating day and across a planning horizon. These organizations are concerned with the tour scheduling problem that involves assigning shifts and break times to the work days of employees and allocating days off to individual work schedules. Nowadays, organizations try to adopt various scheduling flexibility alternatives to meet the fluctuating service demand. On the other hand, they have also realized that providing employee productivity and satisfaction is as much important as meeting the service demand. Up to date, tour scheduling solution approaches have neglected considering employee preferences and tried to develop work schedules for employees in a subsequent step. This paper presents a goal programming model that implicitly represents scheduling flexibility and also incorporates information about the preferred working patterns of employees. After solving the proposed model, a work schedule will be generated for each employee without requiring a further step for the assignment of shifts, break times, and work days to employees. The model is capable of handling multiple scheduling objectives, and it can produce optimal solutions in very short computing times.     

A Goal Programming Model for Staff Scheduling at a Telecommunications Center

In this paper, a mathematical model is developed to solve a staff scheduling problem for a telecommunications center. Currently, weekly schedules are manually produced. The manual nature of the process and the large number of constraints and goals lead to a situation where the used schedules are both inefficient and unfair. A zero-one linear goal programming model is suggested to find an optimized cyclical schedule. The center objectives as well as the engineers’ preferences are taken into account. The developed model had to produce balanced schedules that provide the required coverage while satisfying fairness considerations, in terms of weekends off, working night shifts, isolated days on, and isolated days off. A staffing analysis and mathematical properties have been developed to find the optimal parameters of the staff scheduling model. A 6-week scheduling period has been suggested instead of the current weekly period. Work patterns have been suggested to improve schedules quality. These work patterns have been mathematically formulated as a set of soft constraints. The suggested mathematical model has been implemented using Lingo software. The optimal cyclical schedule has been found. It significantly increases both efficiency and staff satisfaction. The suggested approach can be used for any similar staff scheduling problem.     

Solving a multiobjective possibilistic problem through compromise programming

Real decision problems usually consider several objectives that have parameters which are often given by the decision maker in an imprecise way. It is possible to handle these kinds of problems through multiple criteria models in terms of possibility theory.Here we propose a method for solving these kinds of models through a fuzzy compromise programming approach.To formulate a fuzzy compromise programming problem from a possibilistic multiobjective linear programming problem the fuzzy ideal solution concept is introduced. This concept is based on soft preference and indifference relationships and on canonical representation of fuzzy numbers by means of their α-cuts. The accuracy between the ideal solution and the objective values is evaluated handling the fuzzy parameters through their expected intervals and a definition of discrepancy between intervals is introduced in our analysis.     

A mathematical immunochemoradiotherapy model: A multiobjective approach

This study developed a near optimization immunochemoradiotherapy model, which has three objectives; maximizing total weighted damage of cancer cells, minimizing total weighted side effect and minimizing total dose related therapy costs, originated from the Weapon–Target Assignment problem (WTA) of military operations research. The multi-objective structure is transformed into a single-objective format via goal programming. The presented model is a mixed-integer nonlinear goal programming model. A non-clinical hypothetical illustrative example is solved using MS Excel's Solver tool as a powerful spreadsheet tool. The theoretical result is extremely impressive especially compared with result of the single-objective program. The model facilitates cancer therapists to act in a multi-objective frame. However, the model is extremely needed to have clinical experiments to validate its theoretical power. This theoretical model is a virtuous synthesis of military and medical operations research.     

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.     

Reliability and cost analysis of series system models using fuzzy parametric geometric programming

In this paper, we have discussed series system models with system reliability and cost. We have considered two types of the model; the former focuses on a problem of optimal reliability for series system with cost constraint and the latter is a center system cost model with reliability goal. It is necessary to improve the reliability of the system under limited available cost of system and also to minimize the systems cost subject to target goal of the reliability. Practically, cost of components has always been imprecise with vague in nature. So they are taken as fuzzy in nature and the reliability models are formulated as a fuzzy parametric geometric programming problem. Numerical examples are given to illustrate the model through fuzzy parametric geometric programming technique.     

A single machine scheduling problem with availability constraints and sequence-dependent setup costs

We study a single machine scheduling problem with availability constraints and sequence-dependent setup costs, with the aim of minimizing the makespan. To the authors’ knowledge, this problem has not been treated as such in the operations research literature. We derive in this paper a mixed integer programming model to deal with such scheduling problem. Computational tests showed that commercial solvers are capable of solving only small instances of the problem. Therefore, we propose two ways for reducing the execution time, namely a valid inequality that strengthen the linear relaxation and an efficient heuristic procedure that provides a starting feasible solution to the solver. A substantial gain is achieved both in terms of the linear programming relaxation bound and in terms of the time to obtain an integer optimum when we use the enhanced model in conjunction with providing to the solver the solution obtained by the proposed heuristic.     

Nonlinear goal programming using multi-objective genetic algorithms

Goal programming is a technique often used in engineering design activities primarily to find a compromised solution which will simultaneously satisfy a number of design goals. In solving goal programming problems, classical methods reduce the multiple goal-attainment problem into a single objective of minimizing a weighted sum of deviations from goals. This procedure has a number of known difficulties. First, the obtained solution to the goal programming problem is sensitive to the chosen weight vector. Second, the conversion to a single-objective optimization problem involves additional constraints. Third, since most real-world goal programming problems involve nonlinear criterion functions, the resulting single-objective optimization problem becomes a nonlinear programming problem, which is difficult to solve using classical optimization methods. In tackling nonlinear goal programming problems, although successive linearization techniques have been suggested, they are found to be sensitive to the chosen starting solution. In this paper, we pose the goal programming problem as a multi-objective optimization problem of minimizing deviations from individual goals and then suggest an evolutionary optimization algorithm to find multiple Pareto-optimal solutions of the resulting multi-objective optimization problem. The proposed approach alleviates all the above difficulties. It does not need any weight vector. It eliminates the need of having extra constraints needed with the classical formulations. The proposed approach is also suitable for solving goal programming problems having nonlinear criterion functions and having a non-convex trade-off region. The efficacy of the proposed approach is demonstrated by solving a number of nonlinear goal programming test problems and an engineering design problem. In all problems, multiple solutions (each corresponding to a different weight vector) to the goal programming problem are found in one single simulation run. The results suggest that the proposed approach is an effective and practical tool for solving real-world goal programming problems.     

A group decision making model based on goal programming with fuzzy hierarchy: an application to regional forest planning

In this paper a multi-criteria group decision making model is presented in which there is a heterogeneity among the decision makers due to their different expertise and/or their different level of political control. The relative importance of the decision makers in the group is handled in a soft manner using fuzzy relations. We suppose that each decision maker has his/her preferred solution, obtained by applying any of the techniques of distance-based multi-objective programming [compromise, goal programming (GP), goal programming with fuzzy hierarchy, etc.]. These solutions are used as aspiration levels in a group GP model in which the differences between the unwanted deviations are interpreted in terms of the degree of achievement of the relative importance amongst the group members. In this way, a group GP model with fuzzy hierarchy (Group-GPFH) is constructed. The solution for this model is proposed as a collective decision. To show the applicability of our proposal, a regional forest planning problem is addressed. The objective is to determine tree species composition in order to improve the values achieved by Pan-European indicators for sustainable forest management. This problem involves stakeholders with competing interests and different preference schemes for the aforementioned indicators. The application of our proposal to this problem allows us to be able to comfortably address all these issues. The results obtained are consistent with the preferences of each stakeholder and their hierarchy within the group.     

A heuristic algorithm for the hospital health examination scheduling problem

This study considers the problem of health examination scheduling. Depending on their gender, age, and special requirements, health examinees select one of the health examination packages offered by a health examination center. The health examination center must schedule all the examinees, working to minimize examinee/doctor waiting time and respect time and resource constraints, while also taking other limitations, such as the sequence and continuity of the examination procedures, into consideration. The Binary integer programming (BIP) model is one popular way to solve this health examination scheduling problem. However, as the number of examinees and health examination procedures increase, solving BIP models becomes more and more difficult, if not impossible. This study proposes health examination scheduling algorithm (HESA), a heuristic algorithm designed to solve the health examination scheduling problem efficiently and effectively. HESA has two primary objectives: minimizing examinee waiting time and minimizing doctor waiting time. To minimize examinee waiting time, HESA schedules the various parts of each examinee’s checkup for times when the examinee is available, taking the sequence of the examination procedures and the availability of the resources required into account. To minimize doctor waiting time, HESA focuses on doctors instead of examinees, assigning waiting examinees to a doctor as soon as one becomes available. Both complexity analysis and computational analyses have shown that HESA is very efficient in solving the health examination scheduling problem. In addition to the theoretical results, the results of HESA’s application to the concrete health examination scheduling problems of two large hospitals in Taiwan are also reported.     

Project scheduling with finite or infinite number of activity processing modes – A survey

This paper surveys single-project, single-objective, deterministic project scheduling problems in which activities can be processed using a finite or infinite (and uncountable) number of modes concerning resources of various categories and types. The survey is based on a unified framework of a project scheduling model including resources, activities, objectives, and schedules. Most important models and solution approaches across the class of problems are characterized, and directions for future research are pointed out.     

Optimal compromise solution of multi-objective minimal cost flow problems in fuzzy environment

Ghatee and Hashemi [M. Ghatee, S.M. Hashemi, Ranking function-based solutions of fully fuzzified minimal cost flow problem, Inform. Sci. 177 (2007) 4271–4294] transformed the fuzzy linear programming formulation of fully fuzzy minimal cost flow (FFMCF) problems into crisp linear programming formulation and used it to find the fuzzy optimal solution of balanced FFMCF problems. In this paper, it is pointed out that the method for transforming the fuzzy linear programming formulation into crisp linear programming formulation, used by Ghatee and Hashemi, is not appropriate and a new method is proposed to find the fuzzy optimal solution of multi-objective FFMCF problems. The proposed method can also be used to find the fuzzy optimal solution of single-objective FFMCF problems. To show the application of proposed method in real life problems an existing real life FFMCF problem is solved.