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     

Information technology capital budgeting using a knapsack problem

In this paper, we describe an information technology capital budgeting (ITCB) problem, show that the ITCB problem can be modeled as a 0–1 knapsack optimization problem, and propose two different simulated annealing (SA) heuristic solution procedures to solve the ITCB problem. Using several simulations, we empirically compare the performance of two SA heuristic procedures with the performance of two well‐known ranking methods for capital budgeting. Our results indicate that the information technology (IT) investments selected using the SA heuristics have higher after‐tax profits than the IT investments selected using the two ranking methods.     

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.     

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.     

An integer goal programming model for determining capital expenditures for correctional facilities

The selection of capital expenditure projects for the construction of state correctional facilities is often complicated by the existence of multiple and conflicting objectives on the part of the various interest groups involved in the decision-making process. While some groups view the limited availability of state funds to construct such facilities as the paramount consideration, others might consider having adequate capacity to house prisoners in a satisfactory manner, and the effect of prison overcrowding on prisoner sentencing as the primary factors in the decision to construct new facilities. As such. it is imperative that the limited funds available for constructing correctional facilities be allocated in the most efficient and satisfactory manner possible. In this paper, integer goal programming is demonstrated via a case example as a means for allocating funds for capital expenditures for new and renovated correctional facilities. Sensitivity analysis is performed using the model in order to demonstrate its capability for testing various planning scenarios including alternative priority structures, goal constraints and goal levels.     

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.     

Adaptive sampling immune algorithm solving joint chance-constrained programming

This work investigates one immune optimization algorithm in uncertain environments, solving linear or nonlinear joint chance-constrained programming with a general distribution of the random vector. In this algorithm, an a priori lower bound estimate is developed to deal with one joint chance constraint, while the scheme of adaptive sampling is designed to make empirically better antibodies in the current population acquire larger sample sizes in terms of our sample-allocation rule. Relying upon several simplified immune metaphors in the immune system, we design two immune operators of dynamic proliferation and adaptive mutation. The first picks up those diverse antibodies to achieve proliferation according to a dynamical suppression radius index, which can ensure empirically potential antibodies more clones, and reduce noisy influence to the optimized quality, and the second is a module of genetic diversity, which exploits those valuable regions and finds those diverse and excellent antibodies. Theoretically, the proposed approach is demonstrated to be convergent. Experimentally, the statistical results show that the approach can obtain satisfactory performances including the optimized quality, noisy suppression and efficiency.     

Entropy-based multiple criteria for capital budgeting

The information obtained by applying different criteria for ranking independent investment proposals is used to find a set of numbers, one for each of the investment proposals. The criteria can be quantitative and qualitative. The concept of entropy is used in obtaining these numbers, which can be used as the coefficients of the objective function of zero-one linear programming models for capital budgeting.     

产品设计方案费效权衡的随机机会约束规划模型

针对产品设计方案费效权衡中由于未考虑生产过程中不确定性因素影响而导致的权衡结果易产生偏差的问题, 提出将不确定优化理论引入产品设计方案费效权衡模型中。在对关键设计参数敏感性分析的基础上,将敏感性变量以及费用估算的偏差描述为随机变量,构建基于以产品设计方案费效权衡的随机机会约束规划模型,并采用嵌入蒙特卡洛模拟的遗传算法求解,得到考虑不确定因素影响的最优产品设计方案。最后以混凝土泵车为实例,验证了模型的有效性。研究表明,采用费效权衡随机机会约束规划模型得到的产品设计方案,更能反映生产实际,可以最大程度保证不确定条件下产品设计决策目标的实现。     

求解随机机会约束规划的混合智能算法

随机机会约束规划是一类有着广泛应用背景的随机规划问题,采用随机仿真产生样本训练BP网络以逼近随机函数,然后在微粒群算法中利用神经网络计算适应值和实现检验解的可行性,从而提出了一种求解随机机会约束规划的混合智能算法。最后通过两个实例的仿真结果说明了算法的正确性和有效性。