基于前景理论的多阶段随机多准则决策方法

研究一种基于动态参考点的多阶段随机多准则决策方法。考虑多阶段决策过程中决策者的风险偏好,建立了基于前景理论的多阶段随机多准则决策分析框架,提出了一种基于阶段发展特征的动态参考点设置方法;构建准则权重的目标规划模型,结合阶段参考点动态变化的特征测算各阶段备选方案的综合前景值;设计方案综合前景值的范围估算模型,以反映决策风险对评价结果的影响;案例研究验证了上述方法的可行性和实际效果。     

Strategic supply network planning with vendor selection under consideration of risk and demand uncertainty

We present a stochastic version of a three-layer supply network planning problem that includes the selection of vendors that must be equipped with company-specific tools. The configuration of a supply network must be determined by using demand forecasts for a long planning horizon to meet a given service level. The risk induced by the uncertain demand is explicitly considered by incorporating the conditional value at risk. The objective is to maximize the weighted sum of the expected net present value of discounted cash flows and the conditional value at risk. This would lead to a non-linear model formulation that is approximated by a mixed-integer linear model. This approximation is realized by a piecewise linearization of the expected backlogs and physical inventory as non-linear functions of cumulative production quantities. A two-stage stochastic programming approach is proposed. Our numerical analysis of generic test instances indicates that solving the linearized model formulation yields a robust and stable supply network configuration when demand is uncertain.     

An integrated approach for water resources decision making under interactive and compound uncertainties

In recent years, the issue of water allocation among competing users has been of great concern for many countries due to increasing water demand from population growth and economic development. In water management systems, the inherent uncertainties and their potential interactions pose a significant challenge for water managers to identify optimal water-allocation schemes in a complex and uncertain environment. This paper thus proposes a methodology that incorporates optimization techniques and statistical experimental designs within a general framework to address the issues of uncertainty and risk as well as their correlations in a systematic manner. A water resources management problem is used to demonstrate the applicability of the proposed methodology. The results indicate that interval solutions can be generated for the objective function and decision variables, and a number of decision alternatives can be obtained under different policy scenarios. The solutions with different risk levels of constraint violation can help quantify the relationship between the economic objective and the system risk, which is meaningful for supporting risk management. The experimental data obtained from the Taguchi's orthogonal array design are useful for identifying the significant factors affecting the means of total net benefits. Then the findings from the mixed-level factorial experiment can help reveal the latent interactions between those significant factors at different levels and their effects on the modeling response.     

Application of interactive possibilistic linear programming to aggregate production planning with multiple imprecise objectives

Aggregate production planning (APP) addresses matching supply to forecast demand, with varying customer orders over the intermediate planning horizon. In real-world APP problems, input data and related parameters are commonly imprecise because information is incomplete or unavailable, and the decision maker (DM) must simultaneously consider conflicting objectives. This study develops an interactive possibilistic linear programming (i-PLP) approach to solve multi-product and multi-time period APP problems with multiple imprecise objectives and cost coefficients by triangular possibility distributions in uncertain environments. The imprecise multi-objective APP model designed here seeks to minimise total production costs and changes in work-force level with reference to imprecise demand, cost coefficients, available resources and capacity. Additionally, the proposed i-PLP approach provides a systematic framework that helps the decision-making process to solve fuzzy multi-objective APP problems, enabling a DM to interactively modify the imprecise data and parameters until a set of satisfactory solutions is derived. An industrial case demonstrates the feasibility of applying the proposed approach to a practical multi-objective APP problem.     

Sequential and Simultaneous Decision Making for Optimizing Health Care Resource Flexibilities

Health care administrators commonly employ two types of resource flexibilities (demand upgrades and staffing flexibility) to efficiently coordinate two critical internal resources, nursing staff and beds, and an external resource (contract nurses) to satisfy stochastic patient demand. Under demand upgrades, when beds are unavailable for patients in a less acute unit, patients are upgraded to a more acute unit if space is available in that unit. Under staffing flexibility, nurses cross‐trained to work in more than one unit are used in addition to dedicated and contract nurses. Resource decisions (beds and staffing) can be made at a single point in time (simultaneous decision making) or at different points in time (sequential decision making). In this article, we address the following questions: for each flexibility configuration, under sequential and simultaneous decision making, what is the optimal resource level required to meet stochastic demand at minimum cost? Is one type of flexibility (e.g., demand upgrades) better than the other type of flexibility (e.g., staffing flexibility)? We use two‐stage stochastic programming to find optimal resource levels for two nonhomogeneous hospital units that face stochastic demand following a continuous, general distribution. We conduct a full‐factorial numerical experiment and find that the benefit of using staffing flexibility on average is greater than the benefit of using demand upgrades. However, the two types of flexibilities have a positive interaction effect and they complement each other. The type of flexibility and decision timing has an independent effect on system performance (capacity and staffing costs). The benefits of cross‐training can be largely realized even if beds and staffing levels have been determined prior to the establishment of a cross‐training initiative.     

Designing Distribution Systems to Support Vendor Strategies in Supply Chain Management*

The interactions among a firm's distribution strategy, market share, and distribution costs are an important consideration in the design of supply chain networks. However, these interactions are largely ignored by existing distribution system design methodologies, which assume demand is constant regardless of the firm's distribution strategy. This paper describes a multidisciplinary framework that considers these interactions in the design of “profit maximizing” distribution networks. The framework employs two major decision support methodologies: (1) binary logit models for estimating market share considering various demand-influencing parameters such as product price and distribution service, and (2) a mixed-integer programming (MIP) model for finding optimal distribution network designs. We applied the framework to an actual design problem facing a national distributor of industrial chemical products. The test results verify the framework's large-scale capability and the potential benefit of the integrated solution methodology.     

A stochastic programming model for production planning of perishable products with postponement

This study addresses the production planning problem for perishable products, in which the cost and shortage of products are minimised subject to a set of constraints such as warehouse space, labour working time and machine time. Using the concept of postponement, the production process for perishable products is differentiated into two phases to better utilise the resources. A two-stage stochastic programming with recourse model is developed to determine the production loading plan with uncertain demand and parameters. A set of data from a toy company shows the benefits of the postponement strategy: these include lower total cost and higher utilisation of resources. The impact of unit shortage cost under different probability distribution of economic scenarios on the total cost is analyzed. Comparative analysis of solutions with and without postponement strategies is also performed.     

A multi-stage stochastic supply network design problem with financial decisions and risk management

In this paper, a multi-period supply chain network design problem is addressed. Several aspects of practical relevance are considered such as those related with the financial decisions that must be accounted for by a company managing a supply chain. The decisions to be made comprise the location of the facilities, the flow of commodities and the investments to make in alternative activities to those directly related with the supply chain design. Uncertainty is assumed for demand and interest rates, which is described by a set of scenarios. Therefore, for the entire planning horizon, a tree of scenarios is built. A target is set for the return on investment and the risk of falling below it is measured and accounted for. The service level is also measured and included in the objective function. The problem is formulated as a multi-stage stochastic mixed-integer linear programming problem. The goal is to maximize the total financial benefit. An alternative formulation which is based upon the paths in the scenario tree is also proposed. A methodology for measuring the value of the stochastic solution in this problem is discussed. Computational tests using randomly generated data are presented showing that the stochastic approach is worth considering in these types of problems.     

震后应急医疗救援流程效率评价研究

为了最大程度减少地震灾害造成的人员伤亡，实施快速有效的应急医疗救援，在资源有限情景下，迫切需要提高应急医疗救援效率。通过案例分析方法提出了震后应急医疗救援的一般流程，构建了应急医疗救援流程的模糊随机Petri网模型，根据模糊随机Petri网与马尔科夫链的同构关系，得到系统状态的稳态概率表达式，据此分析震后应急医疗救援流程中的关键环节。在此基础上，考虑医疗资源投入的数量与救援工作效率之间的关系，引入时效性评估函数对关键环节的实施效率进行评价，通过理论推导证明同一资源配比存在最优值。以"汶川地震"为例，通过动态和静态分析，得到各状态下稳态概率变化情况，明确了震后应急医疗救援流程的关键环节。以救援过程中资源的投入量作为自变量，通过算例仿真得出医疗资源确定情况下关键环节的最优资源配比。由此对震后应急医疗救援过程提出相应对策与建议，可以为地震灾害应急医疗救援工作部署提供决策支持，促进灾后医疗救援工作的有序进行，实现应急医疗救援效率的提升。     

An integrated system for capacity planning and facility layout

In order to achieve efficient facility design for service type activities, operating under dynamic conditions and a large number of constraints, the use of a traditional approach has proved to be tedious and time consuming. Development of an efficient decision support system for such a situation calls for the consideration of the complex nature of interaction between the system parameters and the relationship between the working environment and the resources within the system. Mathematical programming techniques, e.g. linear and integer programming as well as queuing models, though useful in handling combinatorial optimization problems, are incapable of dealing with stochastic utilization problems normally encountered in the design of facilities of a fast changing environment. This paper makes use of a pattern search algorithm for the optimal allocation of service facility resources. The layout of the facilities has then been optimized by the use of the CLASS algorithm. The two separate algorithms have suitably been integrated together into a single simulation-based system. The effectiveness of the proposed methodology has been demonstrated by means of a real case study pertaining to design and layout optimization of a multi-functional gasoline service station in Bangkok.     

A strategic and global manufacturing capacity management optimisation model: A Scenario-based multi-stage stochastic programming approach

Large-scale multinational manufacturing firms often require a significant investment in production capacity and extensive management efforts in strategic planning in an uncertain business environment. In this research we first discuss what decision terms and boundary conditions a holistic capacity management model for the manufacturing industry must contain. To better understand how these decision terms and constraints have been employed by the recent model developers in the area of capacity and resource management modelling for manufacturing, 69 optimisation-based (deterministic and stochastic) models have been carefully selected from 2000 to 2018 for a brief comparative analysis. The results of this comparison shows although applying uncertainty into capacity modelling (in stochastic form) has received a greater deal of attention most recently (since 2010), the existing stochastic models are yet very simplistic, and not all the strategic terms have been employed in the current model developments in the field. This lack of a holistic approach although is evident in deterministic models too, the existing stochastic counterparts proved to include much less decision terms and inclusive constraints, which limits them to a limited applications and may cause sub-optimal solutions. Employing this set of holistic decision terms and boundary conditions, this work develops a scenario-based multi-stage stochastic capacity management model, which is capable of modelling different strategic terms such as capacity level management (slight, medium and large capacity volume adjustment to increase/decrease capacity), location/relocation decisions, merge/decomposition options, and product management (R&D, new product launch, product-to-plant and product-to-market allocation, and product phase-out management). Possibility matrix, production rates, different financial terms and international taxes, inflation rates, machinery depreciation, investment lead-time and product cycle-time are also embedded in the model in order to make it more practical, realistic and sensitive to strategic decisions and scenarios. A step-by-step open-box validation has been followed while designing the model and a holistic black-box validation plan has been designed and employed to widely validate the model. The model then has been verified by deploying a real-scaled case of Toyota Motors UK (TMUK) decision of mothballing one of their production lines in the UK after the global recession in 2010.     

Assessing the impact of uncertainty and the level of aggregation in case mix planning

In this article, we present a framework for evaluating the impact of uncertainty and the use of different aggregation levels in case mix planning on the quality of strategic decisions regarding the case mix of a hospital. In particular, we analyze the effect of modeling (i) demand, (ii) resource use, and (iii) resource availability as stochastic input parameters on the performance of case mix planning models. In addition, the consequences of taking the weekly structure with inactive days without surgeries into account are assessed (iv). The purpose of this paper is to provide a guideline for the decision-maker planning the case mix on the consideration of stochastic aspects and different aggregation levels. We formulate a mixed integer programming model for case mix planning along with different stochastic and deterministic extensions. The value of the different extensions is analyzed using a factorial design. The resulting stochastic models are solved using sample average approximation. Simulation is used to evaluate the strategies derived by the different models using real-world data from a large German hospital. We find that highly aggregated basic case mix planning models can overestimate the objective value by up to 10% and potentially lead to biased results. Refining the problem decreased the gap between projected case mix planning results and simulated results considerably and led to improved solutions.     

Coping with Group Behaviors in Uncertain Quality Function Deployment

Quality function deployment (QFD) is a planning and problem‐solving tool gaining wide acceptance for translating customer needs (CNs) into technical attributes (TAs) of a product. It is a crucial step to derive the prioritization of TAs from CNs in QFD. However, it is not so straightforward to prioritize TAs due to two types of uncertainties: human subjective perception and user variability. The main focus of this article is to propose a group decision‐making approach to uncertain QFD with an application to a flexible manufacturing system design. The proposed approach performs computations solely based on the order‐based semantics of linguistic labels to eliminate the burden of quantifying qualitative concepts in QFD. Moreover, it incorporates the importance weights of users and the concept of fuzzy majority into aggregations of individual fuzzy preference relations of different TAs in order to model the group behaviors in QFD. Finally, based on a quantifier‐guided net flow score procedure, the proposed approach derives a priority ranking with a classification of TAs into important and unimportant ones so as to provide a better decision‐support to the decision‐maker. Due to the easiness in articulating preferential information, our approach can reduce the cognitive burden of QFD planning team and give a practical convenience in the process of QFD planning.     

Zero-base budgeting—Dealing with conflicting objectives

While Zero-Base Budgeting (ZBB) has received considerable attention in the public sector, virtually all the studies dealing with the system have neglected or given cursory attention to the problem of multiple conflicting objectives. This paper presents a goal programming approach as a systematic means to develop the ZBB process for multiple objectives. This approach allows the administrators to more realistically portray the decision environment as well as their judgment in their budgetary planning models, thus making the budgeting an effective and pragmatic way to implement the planning and decision making process. This study demonstrates a goal programming based ZBB system in the public sector based on real-world data.     

An approach to stochastic programming for medium term planning

A number of methods of obtaining the distribution of the optimum of the ‘wait and see’ stochastic programming model have been proposed, but computational experience for these is currently limited to the solution of small problems. The purpose of this paper is to discuss the role of the ‘wait and see’ model in planning, and to propose a method of analysis based on the minimax and maximax decision criteria. The approach requires the solution of a special class of non-linear programming problems. Computational results to date suggest that it will be possible to analyse practically sized problems in this way.     

Managing stochastic demand in an Inventory Routing Problem with transportation procurement

We study an Inventory Routing Problem in which the supplier has a limited production capacity and the stochastic demand of the retailers is satisfied with procurement of transportation services. The aim is to minimize the total expected cost over a planning horizon, given by the sum of the inventory cost at the supplier, the inventory cost at the retailers, the penalty cost for stock-out at the retailers and the transportation cost. First, we show that a policy based just on the average demand can have a total expected cost infinitely worse than the one obtained by taking into account the overall probability distribution of the demand in the decision process. Therefore, we introduce a stochastic dynamic programming formulation of the problem that allows us to find an optimal policy in small size instances. Finally, we design and implement a matheuristic approach, integrating a rollout algorithm and an optimal solution of mixed-integer linear programming models, which is able to solve realistic size problem instances. Computational results allow us to provide managerial insights concerning the management of stochastic demand.     

LINEAR PROGRAMMING WITH DISCRETE STOCHASTIC RESOURCES: AN ALTERNATIVE APPROACH ACCOUNTING FOR INFEASIBILITY*

In this paper an alternative to, or extension of, the chance-constrained method of stochastic programming is presented whereby an expected cost of infeasibility is included in the objective function. The problem is to select a solution to implement before the available resources are known where the adaption of a non-feasible solution to the resources available involves a system cost. While increasing the amount of computation required, the model enables the decision maker to more effectively trade off increased payoff for decreased likelihood of feasibility.     

A chance-constraints linear programming model on the economic evaluation of flexible manufacturing systems

The implementation of flexible manufacturing systems (FMSs) normally entails a large initial investment under a long-term, uncertain environment. Many effects of installing a FMS will be due to improvement in throughput efficiency, quality, flexibility and the opportunity costs. However, most economic evaluations of FMSs assume the problem is deterministic, such that they fail to model accurately and capture the nature of FMSs. This paper uses stochastic variables to capture the.nature of a FMS under given resource limitations and leads to a multistage chance-constraints linear programming (LP) formulation. Finally, in order to incorporate the uncertainty of capital investment, the interest rate as a function of time is considered over the whole planning horizon and the decision model is extended under continuous and variable discounting.