Credibility-based chance-constrained integer programming models for capital budgeting with fuzzy parameters

In this paper, we discuss a problem of capital budgeting in a fuzzy environment. Two types of models are proposed using credibility to measure confidence level. Since the proposed optimization problems are difficult to solve by traditional methods, a fuzzy simulation-based genetic algorithm is applied. Two numerical experiments demonstrate the effectiveness of the proposed algorithm.     

A mixed-integer goal programming model for capital budgeting within a police department

A difficult problem for most police departments is allocating limited dollars for capital expenditures in the most efficient manner possible. Because of the varied objectives of police services as perceived by police administrators, government officials and citizens, traditional allocation criteria, such as cost-benefit analysis, are not viable. As such, this paper proposes the use of mixed-integer goal programming as a methodology for selecting police expenditure items given a limited budget and multiple, conflicting objectives. In order to demonstrate this technique, a case example involving 18 potential expenditure items for a moderately-sized police department will be employed. This example model will be solved using a predetermined priority structure, and the results interpreted. Several alternative priority structures that reflect the objectives of different interest groups will then be tested in order to demonstrate the flexibility of this approach.     

Genetic algorithm-based fuzzy goal programming for class of chance-constrained programming problems

This paper presents a procedure for solving a multiobjective chance-constrained programming problem. Random variables appearing on both sides of the chance constraint are considered as discrete random variables with a known probability distribution. The literature does not contain any deterministic equivalent for solving this type of problem. Therefore, classical multiobjective programming techniques are not directly applicable. In this paper, we use a stochastic simulation technique to handle randomness in chance constraints. A fuzzy goal programming formulation is developed by using a stochastic simulation-based genetic algorithm. The most satisfactory solution is obtained from the highest membership value of each of the membership goals. Two numerical examples demonstrate the feasibility of the proposed approach.     

A zero-one goal programming model for capital budgeting in a property and liability insurance company

This paper presents a zero-one goal programming model for capital budgeting in a property and liability insurance company. The model structure allows for the inclusion of multiple goals, indivisible projects and a multiple period planning horizon. The model offers an advantage of being closer to reality than many previous models and, at the same time, is easy for decision makers to understand and use. Model solutions and sensitivity analyses are presented.     

A zero-base budgeting process with goal programming feedback

This paper describes the decision process used to establish the annual budget for allocating general fund revenues to non-revenue generating service activities of a city. This process combines zero-base budgeting (ZBB) and goal programming. The goal programming model formalizes the relationship between the ZBB decision packages specified by city departmental needs and the planning issue goals identified by either the city council, the city administrative staff or a citizens' survey. A budget committee reviews input data, forms the model and uses its output to revise budget inputs. The goal programming model provides a format for (1) effectively evaluating budget assumptions, (2) consistently representing the relationships between the ZBB decision packages and the city planning issues, and (3) quantifying and evaluating the contribution made by the decision packages toward satisfying the planning issue goals.     

Equivalent mathematical programming models of the capital budgeting problem

This paper is concerned with a capital budgeting problem where both investment and borrowing decisions are considered in imperfect capital markets. The capital budgeting problem allows for project indivisibility and lets the borrowing interest rate vary from period to period in close relation to the size of debt. Generally, a formulated model in mixed integer non-linear programming is difficult to solve since the solution space is not convex. However, characterizing the dominance properties of solutions enables the model to be solved by enumeration by virtue of special structures inherent in the model. An equivalent model is employed in order to develop the implicit enumeration algorithm which requires much less computation. Computational results for a set of example problems are also provided.     

Abandonment value in capital budgeting: A mathematical programming approach

While some general algorithms for evaluating interrelated capital projects with abandonment values are illustrated in a separate study, this paper shows how an integer program may be used to resolve the project interaction problem when including abandonment value in capital budgeting. In addition, by employing the mathematical programming framework, the optimal capital budgeting decision is obtained for all the projects under consideration. Thus, the technique provided here gives an efficient and general algorithm for capital budgeting decisions.     

Fuzzy random chance-constrained programming

By fuzzy random programming, we mean the optimization theory dealing with fuzzy random decision problems. This paper presents a new concept of chance of fuzzy random events, and constructs a general framework of fuzzy random chance-constrained programming. We also design a spectrum of fuzzy random simulations for computing uncertain functions arising in the area of fuzzy random programming. To speed up the process of handling uncertain functions, we train a neural network to approximate uncertain functions based on the training data generated by fuzzy random simulation. Finally, we integrate the fuzzy random simulation, neural network, and genetic algorithm to produce a more powerful and effective hybrid intelligent algorithm for solving fuzzy random programming models and illustrate its effectiveness by some numerical examples     

Revised multi-segment goal programming: Percentage goal programming

The multi-segment goal programming (MSGP) model is an extension model of GP wherein the core thinking is inherited from the multi-choice goal programming (MCGP) model. In this paper, we recommend certain points of the MSGP model and offer a Revised MSGP Model as an aid to burdened decision makers who cannot expect an either-or selection of coefficients in practice. The proposed model takes into account a scenario in which the selection of all possible coefficients pertaining to each decision variable in the MSGP model can be an in-between selection instead of an exclusive-or selection. We hope this study can fill in a possible gap that might exist when applying the MSGP model, and can offer an extension model for practitioners when they use this model to solve related decision problems.     

Multi-coefficients goal programming

In today’s increasingly competitive business environment, maintaining profit margins or quantities of goods sold is an important issue for businesses. Accordingly, more and more industries use group pricing discrimination strategy to attract potential customers in order to increase competitive advantage. Hence, to find ways maximize profit and to minimize total cost, group pricing discrimination strategy has become an important issue for decision makers. Unfortunately, these types of problems cannot be solved by any current goal programming models. The objective of this study is to deduce a new method, which we call the multi-coefficients goal programming, for group pricing discrimination problems. In addition, an example is given to illustrate the correctness and usefulness of the proposed model.     

Optimal multinational capital budgeting under uncertainty

This paper discusses the multinational capital budgeting problem — when there are some candidate foreign projects, which project(s) should the investor choose? In the paper, special cash flows and value sources of foreign projects are introduced. Regarding project parameters such as construction costs, annual net operating cash flows, terminal values of the projects as well as the foreign exchange rates as uncertain variables, the paper proposes one new uncertain zero-one integer model for optimal multinational project selection. To solve the problem, a hybrid intelligent algorithm integrating the 99 Methods and genetic algorithm is provided. As an illustration, an application example is also presented.     

Mean-variance model for fuzzy capital budgeting

In an uncertain economic environment, it is usually difficult to predict accurately the investment outlays and annual net cash flows of a project. In addition, available investment capital sometimes cannot be accurately given either. Fuzzy variables can reflect vagueness of these parameters. In this paper, capital budgeting problem with fuzzy investment outlays, fuzzy annual net cash flows and fuzzy available investment capital is studied based on credibility measure. One new mean-variance model is proposed for optimal capital allocation. A fuzzy simulation-based genetic algorithm is provided for solving the proposed optimization problem. One numerical example and an experiment are also presented to show the optimization idea and the effectiveness of the algorithm.     

Multiple objective capital budgeting within the university

The problem of selecting capital projects in universities is compounded by the existence of conflicting multiple objectives on the part of different groups within the university community. Administrators, faculty members, students and politicians all have different goals and projects which they feel are important to the university and themselves. Because of the multiple objective dimension of the capital budgeting process goal programming becomes an appropriate solution approach. However, because of the indivisibility of some capital projects, mixed integer goal programming, a variation of the traditional GP model, must be employed. The solution approach is demonstrated via an illustrative case example. Model goals in the example (which are prioritized by the top administrative officers of the university) exist for capital budget and operating expenses, building and laboratory construction, accreditation, political interest and area performance.     

Fuzzy multi-objective chance-constrained programming model for hazardous materials transportation

Hazardous materials transportation is an important and hot issue of public safety. Based on the shortest path model, this paper presents a fuzzy multi-objective programming model that minimizes the transportation risk to life, travel time and fuel consumption. First, we present the risk model, travel time model and fuel consumption model. Furthermore, we formulate a chance-constrained programming model within the framework of credibility theory, in which the lengths of arcs in the transportation network are assumed to be fuzzy variables. A hybrid intelligent algorithm integrating fuzzy simulation and genetic algorithm is designed for finding a satisfactory solution. Finally, some numerical examples are given to demonstrate the efficiency of the proposed model and algorithm.     

Generalized goal programming An overview

Generalized goal programming is a practical and robust tool for use in multiobjective mathematical programming. In this paper we introduce this approach, describe its underlying philosophy, and indicate the specific subclass of models and methods which serve to comprise the overall approach.     

Formulating the multi-segment goal programming

Goal programming (GP) is an important analytical approach devised to solve many real-word problems. However, the condition of multi-segment aspiration levels (MSAL) may exist in many marketing or decision management problems. The problem cannot be solved by current GP techniques. In order to improve the effective of GP and solve the multi-segment goal programming (MSGP) problem, this paper provides a new idea for programming the MSAL problem from multi-aspiration contribution levels viewpoint. This significantly improved the utility of GP in real application; in addition, two illustrative examples are included to demonstrate the solution procedure of the proposed model.     

Solve least absolute value regression problems using modified goal programming techniques

Least absolute value (LAV) regression methods have been widely applied in estimating regression equations. However, most of the current LAV methods are based on the original goal program developed over four decades. On the basis of a modified goal program, this study reformulates the LAV problem using a markedly lower number of deviational variables than used in the current LAV methods. Numerical results indicate that for the regression problems with hundreds of observations, this novel method can save more than 1/3 of the CPU time compared to current LAV methods.     

Method for solving nonlinear goal programming with interval coefficients using genetic algorithm

Traditional formulations on reliability optimization problems have assumed that the coefficients of models are known as fixed quantities and reliability design problem is treated as deterministic optimization problems. Because that the optimal design of system reliability is resolved in the same stage of overall system design, model coefficients are highly uncertainty and imprecision during design phase and it is usually very difficult to determine the precise values for them. However, these coefficients can be roughly given as the intervals of confidence.

In this paper, we formulated reliability optimization problem as nonlinear goal programming with interval coefficients and develop a genetic algorithm to solve it. The key point is how to evaluate each solution with interval data. We give a new definition on deviation variables which take interval relation into account. Numerical example is given to demonstrate the efficiency of the proposed approach.     

Bank funds management by goal programming

A goal programming model was developed which attempts to achieve a number of objectives normally desired in the banking industry. The model incorporates objectives relative to providing sufficient liquidity, minimizing risk, maintaining adequate levels of capital, minimizing the cost of capital, maximizing profit and providing reasonable dividends. The constraints on the model relate to pledged assets required by the government, required reserves and limits on certain balance sheet items.

Model validation is accomplished by utilizing data obtained from a commercial bank. The data includes financial information for 1982–1984. The 1982 actual data is utilized by the model to project 1983 and 1984 conditions. These projected numbers are then compared with actual financial data to compare the model's performance with results achieved by management without the use of the model.

Total underachievement of several goals in banking is minimized within the limits of the actual decision environment.