A hybrid fuzzy goal programming approach with different goal priorities to aggregate production planning

In this study a hybrid (including qualitative and quantitative objectives) fuzzy multi objective nonlinear programming (H-FMONLP) model with different goal priorities will be developed for aggregate production planning (APP) problem in a fuzzy environment. Using an interactive decision making process the proposed model tries to minimize total production costs, carrying and back ordering costs and costs of changes in workforce level (quantitative objectives) and maximize total customer satisfaction (qualitative objective) with regarding the inventory level, demand, labor level, machines capacity and warehouse space. A real-world industrial case study demonstrates applicability of proposed model to practical APP decision problems. GENOCOP III (Genetic Algorithm for Numerical Optimization of Constrained Problems) has been used to solve final crisp nonlinear programming problem.     

A goal programming approach for fuzzy multiobjective fractional programming problems

Fuzzy multiple objective fractional programming (FMOFP) is an important technique for solving many real-world problems involving the nature of vagueness, imprecision and/or random. Following the idea of binary behaviour of fuzzy programming (Chang 2007 Chang, C-T. 2007. Binary Behavior of Fuzzy Programming with Piecewise Membership Functions. IEEE Transactions on Fuzzy Systems, 15: 342–349.  [Google Scholar]), there may exist a situation where a decision-maker would like to make a decision on FMOFP involving the achievement of fuzzy goals, in which some of them may meet the behaviour of fuzzy programming (i.e. level achieved) or the behaviour of binary programming (i.e. completely not achieved). This is turned into a fuzzy multiple objective mixed binary fractional programming (FMOMBFP) problem. However, to the best of our knowledge, this problem is not well formulated by mathematical programming. Therefore, this article proposes a linearisation strategy to formulate the FMOMBFP problem in which extra binary variable is not required. In addition, achieving the highest membership value of each fuzzy goal defined for the fractional objective function, the proposed method can alleviate the computational difficulties when solving the FMOMBFP problem. To demonstrate the usefulness of the proposed method, a real-world case is also included.     

Transmission planning for Indian power grid: a mixed integer programming approach

The paper presents a modeling framework to analyze some important issues associated with operation planning of a power system. Major activities involved in operations planning of large integrated power systems are considered simultaneously to ensure optimal utilization of generation and transmission capacity. The model also examines optimal transmission expansion plans vis-à-vis fuel supply issues. A mixed integer programming model is developed for this purpose and the Indian power system considered. Specific emphasis is on spatial transmission expansion plan for the existing Indian inter-state transmission grid and new transmission links, coordinated operation of the isolated regional grids and system benefits accruing from transmission expansion, enhanced fuel production and supply rescheduling to ensure efficient operation of various generating stations.     

Operation planning of district heating and cooling plants using genetic algorithms for mixed integer programming

In recent years, an operation planning of a district heating and cooling (DHC) plant has been arousing interest as a result of development of cooling load or heat demand prediction methods for district heating and cooling systems. In this paper, we formulate an operation planning of a district heating and cooling plant as a mixed integer linear programming problem. Since the formulated problem involves hundreds of variables, we anticipate that it is difficult to strictly solve it by enumeration-based methods. Thereby, we propose an approximate solution method based on genetic algorithms for mixed integer programming problems. Furthermore, we show the feasibility and effectiveness of the proposed method by comparison with the branch-and-bound method through numerical experiments using actual plant data.     

A multiple objective integer programming approach for planning franchise expansion

The number and configuration of franchise outlets in a market defines the distribution strategy of a franchise company. The introduction of new franchise outlets contributes to conflict between the franchisee and franchisor over the degree of market penetration. The selection of sites for new franchises is an important factor in the long-term profitability of many types of franchises. This selection process requires consideration of objectives of the franchisee and franchisor which are often conflicting in nature. This paper deals with the problem of locating new franchises in an existing franchise network using multiple objective integer programming models and methods.     

A sequential linear programming approach to solve mixed integer programming problems

The optimal operation of pumps in a large water supply system under time-of-use electricity rates is formulated as a mixed integer programming (MIP) problem. The problem is solved using an iterative linear programming (LP) scheme. The scheme is applied to an actual world problem, the City of Inglewood Water Supply System. Computational results are presented and termination criteria for the solution scheme are discussed.     

A mixed integer programming approach to multi-spectral image classification

A supervised discriminant mixed integer programming algorithm (DISMIP) is described which achieves either linear or non-linear separation, without assuming any specific probability distribution. This system offers greater flexibility in dealing with problems of multi-spectral classification. If the training sets are disjoint, a strictly separating surface is generated that maximizes a “dead zone” between the sets. If the sets intersect, a surface is generated that minimizes a specified misclassification error. The system has been experimentally tested in three practical applications and the results are given in comparison with a supervised classification using the LARSIS classifier.⁽¹⁾     

A mixed integer programming approach to multi-skilled workforce scheduling

The potential benefits of using human resources efficiently in the service sector constitute an incentive for decision makers in this industry to intelligently manage the work shifts of their employees, especially those dealing directly with customers. In the long term, they should attempt to find the right balance between employing as few labor resources as possible and keeping a high level of service. In the short run (e.g., 1 week), however, contracted staff levels cannot be adjusted, and management efforts thus focus on the efficient assignment of shifts and activities to each employee. This article proposes a mixed integer program model that solves the short-term multi-skilled workforce tour scheduling problem, enabling decision makers to simultaneously design workers’ shifts and days off, assign activities to shifts and assign those to employees so as to maximize and balance coverage of a firm’s demand for on-duty staff across multiple activities. Our model is simple enough to be solved with a commercial MIP solver calibrated by default without recurring to complex methodologies, such as extended reformulations and exact and/or heuristic column generation subroutines. A wide computational testing over 1000 randomly generated instances suggests that the model’s solution times are compatible with daily use and that multi-skilling is a significant source of labor flexibility to improve coverage of labor requirements, in particular when such requirements are negatively correlated and part-time workers are a scarce resource.     

一种求解整数规划与混合整数规划非线性罚函数方法

证明了任何一个变量有界的整数规划问题（IP）和混合整数规划问题（MIP）都可以转化为一个等价的非整数（或连续化）规划问题（NIP），并给出一个用非线性精确罚函数法来求解该等价NIP的方法，从而达到求解IP或MIP的目的，数值实验表明了算法的可行性。该方法可广泛用于各应用领域里IP和MIP的求解，特别是为非线性IP和MIP问题提供了一条通用 的求解途径，对解决许多实际优化问题具有重要意义。     

A linearized polynomial mixed integer programming model for the integration of process planning and scheduling

This paper presents a linearized polynomial mixed-integer programming model (PMIPM) for the integration of process planning and scheduling problem. First, the integration problem is modeled as a PMIPM in which some of the terms are of products of up to three variables, of both binary and continuous in nature. Then, an equivalent linearized model is derived from the polynomial model by applying certain linearization techniques. Although the linearized models have more variables and constraints than their polynomial counterparts, they are potentially solvable to the optimum in comparison to their equivalent polynomial models. Experiments show that the linearized model possesses certain characteristics that are absent from other models in the literature, and provides a fundamental framework for further research in this area.     

Activity-based divergent supply chain planning for competitive advantage in the risky global environment: A DEMATEL-ANP fuzzy goal programming approach

Supply chain management allows modern enterprises to relax their own capacities and produce in a more flexible manner for diversified consumer demands. However, for an enterprise with divergent supply chain (DSC) and multiple product lines, to plan the production allocation for higher competitive advantage in the risky global market is a challenging problem. The existing literature still has not address this problem very well. This paper is aimed to treat this problem by using an integrated approach of activity based costing (ABC) and management, five forces analysis, risk and value-at-risk analysis, decision making trial and evaluation laboratory (DEMATEL), analytic network process (ANP), and fuzzy goal programming (FGP). The proposed model can effectively incorporate the key factors of precise costing, managerial constraints, competitive advantage analysis, and risk management into DSC forecasting and multi-objective production planning. A case study of a consumer-oriented cell phone DSC is also presented. The sensitivity analysis shows that identifying and relaxing crucial constraints can play an important role in DSC planning for higher competitive advantage and lower risk.     

Nonlinear integer goal programming models for acceptance sampling

Two lexicographic goal programming models are developed for determining the optimal sample size and acceptance number for acceptance sampling plans in quality control. Both models address the conflicting criteria inherent in such sampling problems, namely the average lot inspection cost and the average outgoing quality. The first model assumes a known constant lot fraction defective, while the second relaxes this assumption and instead assumes knowledge of a prior distribution on the fraction of defectives. A three-phase algorithm is developed which exploits the problem structure in order to find optimal solutions after examining a small percentage of the feasible sampling plans. On a set of 64 test problems the algorithm always found the optimal solution, typically after evaluating only 3–5% (and never more than 9%) of the feasible points.     

An intuitionistic fuzzy goal programming approach for finding pareto-optimal solutions to multi-objective programming problems

Multi-objective optimization in the intuitionistic fuzzy environment is the process of finding a Pareto-optimal solution that simultaneously maximizes the degree of satisfaction and minimizes the degree of dissatisfaction of an intuitionistic fuzzy decision. In this paper, a new method for solving multi-objective programming problems is developed that unlike other methods in the literature, provides compromise solutions satisfying both the conditions of intuitionistic fuzzy efficiency and Pareto-optimality. This method combines the advantages of the intuitionistic fuzzy sets concept, goal programming, and interactive procedures, and supports the decision maker in the process of solving programming problems with crisp, fuzzy, or intuitionistic fuzzy objectives and constraints. A characteristic of the proposed method is that it provides a well-structured approach for determining satisfaction and the dissatisfaction degrees that efficiently uses the concepts of violation for both objective functions and constraints. Another feature of the proposed method comes from its continuous interaction with the decision maker. In this situation, through adjusting the problem's parameters, the decision maker would have the ability of revisiting the membership and non-membership functions. Therefore, despite the lack of information at the beginning of the solving process, a compromise solution that satisfies the decision maker's preferences can be obtained. A further feature of the proposed method is the introduction of a new two-step goal programming approach for determining the compromise solutions to multi-objective problems. This approach ensures that the compromise solution obtained during each iterative step satisfies both the conditions of intuitionistic fuzzy efficiency and Pareto-optimality. The application of the proposed model is also discussed in this paper.     

Standard goal programming with fuzzy hierarchies: a sequential approach

This paper proposes a pragmatic model for multi-objective decision-making processes involving clusters of objectives which have a decisional meaning for the decision maker (DM). We provide the DMs with a comfortable tool that allows them to express their preferences both by comparing criteria of the same cluster and via the comparison between the different clusters. In standard goal programming the importance of the goals is modeled by the introduction of preferential weights or/and the incorporation of pre-emptive priorities. However, in many cases the DM is not able to establish a precise preference structure. Even in the case of precise weights the solution does not match necessarily the relative weights or, in the case of precise pre-emptive priority, the result could be very restrictive. In order to overcome these drawbacks, in this paper the normalized unwanted deviations are interpreted in terms of achievement degrees of the goals and fuzzy relations are used to model the relative importance of the goals. Thus, we show how several methodologies from the fuzzy goal programming literature can be tailored for solving standard GP problems. We apply this new modeling to problems where there is a “natural” clustering between goals of the same class. We address this situation by solving two phases; in the first one each class is handled separately taking into account the hierarchy of their goals and, in the second phase, we integrate the results of the first phase and the imprecise hierarchy of the different classes. We formulate a new goal programming model called as sequential goal programming with fuzzy hierarchy model. Because many real situations involve decision making in this environment, our proposal can be a useful tool of broad application. A numerical example illustrates the methodology.     

Multi-stage multi-objective production planning using linguistic and numeric data-a fuzzy integer programming model

This paper introduces a methodology to solve a multi-stage production planning problem having multiple objectives, which are conflicting, non-commensurable and fuzzy in nature. The production process consists of multiple stages having one or more machines in each stage. Every processing stage produces work-in-process, semi-finished items as an output, which becomes an input to the subsequent stage either fully or partially depending on the cycle times of the machines. Events of machine breakdowns and imbalances in input–output relations in one or more stages may affect both work-in-process (WIP) and final production targets. Our paper provides a methodology based on fuzzy logic to maintain the desired balanced input–output relation at each stage and the targeted production output at the final stage. This is done by procurement of work-in-process inventory (WIP) and installation of new machines at appropriate stages. The objectives or goals expressed in linguistic terms are represented as fuzzy sets. The Induced Ordered Weighted Averaging (IOWA) operator is used to aggregate the objectives as per their priorities and finally to formulate the production process as a Mixed Integer Programming (MIP) problem. The solution to MIP shows the degrees of achievements of the production process objectives. The methodology is illustrated with a real life application of crankshaft productions in an automobile industry.     

Many-valued logic and mixed integer programming

We generalize prepositional semantic tableaux for classical and many-valued logics toconstraint tableaux. We show that this technique is a generalization of the standard translation from CNF formulas into integer programming. The main advantages are (i) a relatively efficient satisfiability checking procedure for classical, finitely-valued and, for the first time, for a wide range of infinitely-valued propositional logics; (ii) easy NP-containment proofs for many-valued logics. The standard translation of two-valued CNF formulas into integer programs and Tseitin's structure preserving clause form translation are obtained as a special case of our approach.Part of the research reported here was carried out while the author was supported by a grant within the DFG Schwerpunktprogramm Deduktion. Preliminary and partial versions of this paper were published as [15, 16].     

A dynamic convexized method for nonconvex mixed integer nonlinear programming

We consider in this paper the nonconvex mixed-integer nonlinear programming problem. We present a mixed local search method to find a local minimizer of an unconstrained nonconvex mixed-integer nonlinear programming problem. Then an auxiliary function which has the same global minimizers and the same global minimal value as the original problem is constructed. Minimization of the auxiliary function using our local search method can escape successfully from previously converged local minimizers by taking increasing values of parameters. For the constrained nonconvex mixed-integer nonlinear programming problem, we develop a penalty based method to convert the problem into an unconstrained one, and then use the above method to solve the later problem. Numerical experiments and comparisons on a set of MINLP benchmark problems show the effectiveness of the proposed algorithm.