Goal programming

About: Goal programming is a research topic. Over the lifetime, 4330 publications have been published within this topic receiving 117758 citations.

The falling tide algorithm: A new multi-objective approach for complex workforce scheduling

Abstract: We present a hybrid approach of goal programming and meta-heuristic search to find compromise solutions for a difficult employee scheduling problem, i.e. nurse rostering with many hard and soft constraints. By employing a goal programming model with different parameter settings in its objective function, we can easily obtain a coarse solution where only the system constraints (i.e. hard constraints) are satisfied and an ideal objective-value vector where each single goal (i.e. each soft constraint) reaches its optimal value. The coarse solution is generally unusable in practise, but it can act as an initial point for the subsequent meta-heuristic search to speed up the convergence. Also, the ideal objective-value vector is, of course, usually unachievable, but it can help a multi-criteria search method (i.e. compromise programming) to evaluate the fitness of obtained solutions more efficiently. By incorporating three distance metrics with changing weight vectors, we propose a new time-predefined meta-heuristic approach, which we call the falling tide algorithm, and apply it under a multi-objective framework to find various compromise solutions. By this approach, not only can we achieve a trade off between the computational time and the solution quality, but also we can achieve a trade off between the conflicting objectives to enable better decision-making.

Applying fuzzy goal programming to project management decisions with multiple goals in uncertain environments

Abstract: In real-life situations, the project manager must handle multiple conflicting goals and these conflicting goals are normally fuzzy owing to information is incomplete and unavailable. This study develops a two-phase fuzzy goal programming (FGP) method for solving the project management (PM) decision problems with multiple goals in uncertain environments. The original multi-objective linear programming (MOLP) model designed here attempts to simultaneously minimize total project costs, total completion time and total crashing costs with reference to direct costs, indirect and contractual penalty costs, duration of activities and the constraint of available budget. An industrial case is implemented to demonstrate the feasibility of applying the proposed two-phase FGP method to practical PM decisions. The contribution of this study lies in presenting a fuzzy mathematical programming methodology to fuzzy multi-objective PM decisions, and provides a systematic decision-making framework that facilitates the decision maker to interactively adjust the search direction until the preferred efficient solution is obtained.

Multicriteria Decision Making Methods

Abstract: Multi-criteria decision making (MCDM) deals with decisions involving the choice of the best alternative among several potential candidates in a decision. Every decision requires the balancing of multiple factors, the criteria, which is done sometimes explicitly, sometimes without conscious consideration. Decision might be a simple choice between two or more well-defined alternatives; however, often, decision problems are rather complex problems covering information of complex and conflicting nature reflecting differing perspectives. It is under these conditions that the tools and methods presented in this chapter come into play. We reviewed a number of methods that have been widely used to facilitate the structuring and understanding of the perceived decision problem. We started with the simplest approaches, such as the Pareto optimality and the simple additive ranking approach followed by the approaches belonging to the so-called multiattribute value theory, that is, utility, desirability, and dominance functions. In these models, numerical scores are constructed to represent the degree to which an alternative may be preferred to another. These scores are developed initially for each criterion and are aggregated into a higher level of preference models. The outranking model category, which includes PROMETHEE, ELECTRE, and ORESTE (Organisation, Rangement Et Synthese de donnees relaTionElles) methods, is then presented. In these methods, alternatives are compared pairwise, initially in terms of each criterion and then the preference information is aggregated across all the criteria. These methods attempt to set up the strength of evidence in favor of one alternative over the others. A fairly detailed description of the methods ELECTRE I, II, and III is provided to illustrate its evolution from a simple method to a quite sophisticated method. The Hasse diagram technique is illustrated as an example of partial order ranking (POR) methods, which are vectorial approaches that recognize that different criteria are not always in agreement, but can be conflicting, which means that not all the alternatives can be directly compared with others. This approach not only ranks alternatives but also identifies contradictions in the criteria used for ranking, allowing the so-called incomparable condition where some residual order remains. The chapter also provides a short overview of the goal programming approach. The theoretical background of each of these models is presented together with the practical implementation of some of these methods provided as an illustrative example.

Robust and fuzzy goal programming optimization approaches for a novel multi-objective hub location-allocation problem

Abstract: Developing a novel multi-objective p-hub covering mathematical model (supply chain overview).Considering new features namely, production facilities, opening and reopening modes, greenhouse gas and transportation modes.Using a recent fuzzy-robust tool to solve the resulting multi-objective model. In this paper, a novel multi-objective mathematical model is developed to solve a capacitated single-allocation hub location problem with a supply chain overview. Three mathematical models with various objective functions are developed. The objective functions are to minimize: (a) total transportation and installation costs, (b) weighted sum of service times in the hubs to produce and transfer commodities and the tardiness and earliness times of the flows including raw materials and finished goods, and (c) total greenhouse gas emitted by transportation modes and plants located in the hubs. To come closer to reality, some of the parameters of the proposed mathematical model are regarded as uncertain parameters, and a robust approach is used to solve the given problem. Furthermore, two methods, namely fuzzy multi-objective goal programming (FMOGP) and the Torabi and Hassini's (TH) method are used to solve the multi-objective mathematical model. Finally, the concluding part presents the comparison of the obtained results.

An Intuitionistic Fuzzy Multi-Objective Goal Programming Approach to Portfolio Selection

Abstract: Portfolio selection can be regarded as a type of multi-objective decision problem. However, traditional solution methods rarely discussed the decision maker’s nonsatisfaction and hesitation degrees...