Allocating fixed costs or resources and setting targets via data envelopment analysis

In many applications of data envelopment analysis (DEA), there is often a fixed cost or input resource which should be imposed on all decision making units (DMUs). Cook and Zhu [W.D. Cook, J. Zhu, Allocation of shared costs among decision making units: A DEA approach, Computers and Operations Research 32 (2005) 2171-2178] propose a practical DEA approach for such allocation problems. In this paper, we prove that when some special constraints are added, Cook and Zhu’s approach probably has no feasible solution. The research of this paper focuses on two main aspects: to obtain a new fixed costs or resources allocation approach by improving Cook and Zhu’s approach, and to set fixed targets according to the amount of fixed resources shared by individual DMUs. When such special constraints are attached, our model is proved to be able to achieve a feasible costs or resources allocation. Numerical results for an example from the literature are presented to illustrate our approach.     

Resource allocation for performance improvement

In this paper the problem of allocating resources among Decision Making Units is considered. This study covers the case in which several homogeneous units are operating under the supervision of a central unit. The resource allocation is carried out by the DM (central unit) in such a way that the overall performance of the system is improved. Performance is defined by means of a convex combination of the ratio of the efficiencies before and after the resource allocation. It is assumed that each unit is allowed to modify its resources within the current production possibility set. A novel model is proposed which aims at achieving the best performance of the system. The method is capable of dealing with some additional constraints, imposed by the DM. The model is illustrated by a simple numerical example and a real application.     

An optimization problem in the electricity market

New types of optimization problems are faced by the generating companies that operate on deregulated electricity markets. The characteristics of these problems depend on the various market structures. In the framework of the recently settled Italian electricity market, one of these new problems is the transition from hourly energy programs, defined by the market, to more detailed power generation dispatches, defined for intervals of 15 min. Such a more detailed plan is needed on the one hand by the national system operator (Terna, Rete Elettrica Nazionale) for the assessment of power system stability and security, and on the other hand by the power plant operators for its implementation. The transition procedure should respect the hourly energy constraints and take the main operating constraints of the generating units into account. The paper presents possible solutions of the problem through linear optimization models and reports computational results on real-world instances.      

A truck scheduling problem arising in intermodal container transportation

We address a truck scheduling problem that arises in intermodal container transportation, where containers need to be transported between customers (shippers or receivers) and container terminals (rail or maritime) and vice versa. The transportation requests are handled by a trucking company which operates several depots and a fleet of homogeneous trucks that must be routed and scheduled to minimize the total truck operating time under hard time window constraints imposed by the customers and terminals. Empty containers are considered as transportation resources and are provided by the trucking company for freight transportation. The truck scheduling problem at hand is formulated as Full-Truckload Pickup and Delivery Problem with Time Windows (FTPDPTW) and is solved by a 2-stage heuristic solution approach. This solution method was specially designed for the truck scheduling problem but can be applied to other problems as well. We assess the quality of our solution approach on several computational experiments.     

The multi-mode resource-constrained project scheduling problem with generalized precedence relations

In this paper, we tackle the challenging problem of scheduling activities to minimize the project duration, in which the activities (a) are subject to generalized precedence relations, (b) require units of multiple renewable, non-renewable and doubly constrained resources for which a limited availability is imposed, and (c) can be performed in one of several different ways, reflected in multiple activity scenarios or modes. These multiple modes give rise to several kinds of trade-offs (time/resource, time/cost and resource/resource trade-offs) which allow for a more efficient allocation and use of resources. We present a local search-based solution methodology which is able to handle many real-life project scheduling characteristics such as time-varying resource requirements and availabilities, activity ready times, due dates and deadlines, activity overlaps, activity start time constraints and other types of temporal constraints.     

A cost operator approach to multistage location-allocation

The multistage factory-warehouse location-allocation problem is to decide on locations of warehouses and shipping amounts from the factories through the warehouses to meet customer demands in such a way that the total fixed plus variable costs are minimized. Capacity constraints at factories and warehouses are also imposed.We present a cost operator algorithm for solving this problem. The algorithm takes into account the network structure and the submodularity of the objective function. Computational results with problems taken from the literature as well as new problems are provided.     

企业及市场经营效用函数形式研究

鉴于经营效用是企业制订战略决策和发展策略的重要影响因素,研究其基本效用类型,提出对应的函数形式,并在此基础上提出市场总体的综合经营效用测度方法。企业经营效用由自身经营效用和同业比较效用两部分线性合成,效用变量分别为企业单位盈利指标加权合成值及单位盈利水平与行业平均值的差,效用函数通过原点且单调,因此需将效用理论中对应于各种效用类型的对数函数、指数函数等进行坐标变换、旋转或对称。保守型和冒险型效用在定义域内分别为凹函数和凸函数,共组合为9种效用类型含81种基本函数形式,并给出各效用类型含义、经营特征和定价倾向。以市场份额作为各企业经营效用权重,构建幂平均效用合成模型作为市场总体综合经营效用测度。     

Optimal Market Dealing Under Constraints

We consider a market dealer acting as a liquidity provider by continuously setting bid and ask prices for an illiquid asset in a quote-driven market. The market dealer may benefit from the bid–ask spread, but has the obligation to permanently quote both prices while satisfying some liquidity and inventory constraints. The objective is to maximize the expected utility from terminal liquidation value over a finite horizon and subject to the above constraints. We characterize the value function as the unique viscosity solution to the associated Hamilton–Jacobi–Bellman equation, and further enrich our study with numerical results. The contributions of our study concern both the modelling aspects and the dynamic structure of the control strategies. Important features and constraints characterizing market making problems are no longer ignored.     

On necessary optimality conditions for infinite-horizon economic growth problems with locally unbounded instantaneous utility function

We consider a class of infinite-horizon optimal control problems that arise in studying models of optimal dynamic allocation of economic resources. In a typical problem of that kind the initial state is fixed, no constraints are imposed on the behavior of the admissible trajectories at infinity, and the objective functional is given by a discounted improper integral. Earlier, for such problems, S.M. Aseev and A.V. Kryazhimskiy in 2004–2007 and jointly with the author in 2012 developed a method of finite-horizon approximations and obtained variants of the Pontryagin maximum principle that guarantee normality of the problem and contain an explicit formula for the adjoint variable. In the present paper those results are extended to a more general situation where the instantaneous utility function need not be locally bounded from below. As an important illustrative example, we carry out a rigorous mathematical investigation of the transitional dynamics in the neoclassical model of optimal economic growth.     

Solving nonconvex economic load dispatch problem using particle swarm optimization with time varying acceleration coefficients

This article presents the design and application of an efficient hybrid heuristic search method to solve the practical economic dispatch problem considering many nonlinear characteristics of power generators, and their operational constraints, such as transmission losses, valve‐point effects, multi‐fuel options, prohibited operating zones, ramp rate limits and spinning reserve. These practical operation constraints which can usually be found at the same time in realistic power system operations make the economic load dispatch (ELD) problem a nonsmooth optimization problem having complex and nonconvex features with heavy equality and inequality constraints. A particle swarm optimization with time varying acceleration coefficients is proposed to determine optimal ELD problem in this paper. The proposed methodology easily takes care of solving nonconvex ELD problems along with different constraints like transmission losses, dynamic operation constraints, and prohibited operating zones. The proposed approach has been implemented on the 3‐machines 6‐bus, IEEE 5‐machines 14‐bus, IEEE 6‐machines 30‐bus systems and 13 thermal units power system. The proposed technique is compared with solve the ELD problem with hybrid approach by using the valve‐point effect. The comparison results prove the capability of the proposed method give significant improvements in the generation cost for the ELD problem. © 2015 Wiley Periodicals, Inc. Complexity 21: 299–308, 2016     

Estimation of resource requirements in optimization problems of network planning

It is well known that optimization problems of network planning concerned with non-depositable resources are as a rule non-convex. The extreme difficulties of solving non-convex optimization problems make any pre-solution analysis of such problems highly welcome. This paper is devoted to an important tool for such analysis of our class of problems. The main ideas of the paper are as follows.Jointly with a given non-convex problem Ξ we consider an adjoint convex problem Θ, which is obtained from Ξ by lifting all resource constraints. Feasible schedules of the problem Θ are called Θ-feasible for the problem Ξ. By estimation of resource requirements we understand construction of such estimates which are valied for every Θ-feasible schedule. Two kinds of estimates are considered: pointwise (i.e. for single time units) and interval (for longer time spans) ones.Much attention is paid to numerical aspects of estimation. That is why a hierarchy of upper estimates is built ranging from a rough but easily computed one to the best estimate, requiring much more sophisticated computations. Amazingly enough such hierarchy does not exist for lower estimates, the simplest of them, next in roughness to the total zero only, being the best.     

Relaxation-based algorithms for minimax optimization problems with resource allocation applications

We consider minimax optimization problems where each term in the objective function is a continuous, strictly decreasing function of a single variable and the constraints are linear. We develop relaxation-based algorithms to solve such problems. At each iteration, a relaxed minimax problem is solved, providing either an optimal solution or a better lower bound. We develop a general methodology for such relaxation schemes for the minimax optimization problem. The feasibility tests and formulation of subsequent relaxed problems can be done by using Phase I of the Simplex method and the Farkas multipliers provided by the final Simplex tableau when the corresponding problem is infeasible. Such relaxation-based algorithms are particularly attractive when the minimax optimization problem exhibits additional structure. We explore special structures for which the relaxed problem is formulated as a minimax problem with knapsack type constraints; efficient algorithms exist to solve such problems. The relaxation schemes are also adapted to solve certain resource allocation problems with substitutable resources. There, instead of Phase I of the Simplex method, a max-flow algorithm is used to test feasibility and formulate new relaxed problems.Corresponding author.Work was partially done while visiting AT&T Bell Laboratories.     

出版社书号分配的优化问题

决策问题是企业活动的重要组成,而决策往往是在市场信息不完备、企业自身数据收集和积累不足的情况下做出的.如何合理地进行决策,以达到优化资源配置的目的,是企业领导需解决的首要问题.出版社书号分配便是这样的一个例子.通过合理的假设,运用最优化原理和方法,确定目标函数为出版社的总收益,同时利用Excel对给出的调查问卷数据进行筛选处理,筛选出出版社编号为P 115的数据信息,即A出版社的信息,删除掉一些对结果影响不太大的数据列,留下包括课程名称在内的主要数字信息以供Matlab编程使用(课程名称里的汉字项以0替换,这项操作也在Excel里实现),然后分别对五年数据的四项满意指标进行处理,确定出对应课程满意度的评价准则.并对其他数据进行统计分析,依次确定出其他各个准则的约束条件,如准确度、人力资源限制等.其中根据专家评判给出目标权值,建立模糊综合评判模型,再由本题中书号和销售量的比例关系计算出2006年的每门课程书号所包含的成本与利润总和,由得出的结果设定优化模型的约束条件.最后利用M atlab软件处理数据,给出了较为合理的最优化模型的运行结果.总社根据这个结果对九个分社进行资源分配,以期达到最好的经济效益.本模型具有良好的可行性和通用性.并可推广到其他类似问题的求解中去.     

供应链金融借贷市场中均衡解的存在性研究

根据博弈论的观点,构建了多层级供应链中距离核心企业层级较远的中小企业融资模型,比较了两种类型企业(高经营能力和低经营能力)的融资特点,分析了供应链上两种类型企业在是否存在区块链技术情形下融资达到均衡解的条件。研究表明,金融机构分别以企业贷款总量和企业库存订购量作为标准来判定企业类型的情形下,在区块链技术不存在时,借贷市场中的均衡解在一定条件下存在;但在区块链技术存在时,借贷市场中的均衡解总是存在。研究结果对于金融机构降低风险提供了一个新的视角。     

Dynamic modeling of the power market and analysis of its complex behavior based on a nonlinear complementarity function

In order to accurately simulate the dynamic decision-making behaviors of market participants, a new dynamic model of power markets that considers the constraints of realistic power networks is proposed in this paper. This model is represented by discrete difference equations embedded within the optimization problem of market clearing. Compared with existing dynamic models, the remarkable characteristic of the proposed model is twofold: it accurately reflects the process of market clearing by the Independent System Operator (ISO) while considering the inherent physical characteristics of power networks, i.e., the complex network constraints; and it describes the market condition that the generation and demand sides bid simultaneously. Using a nonlinear complementary function, the complex discrete difference dynamic model is transformed into a set of familiar discrete difference algebraic equations. Then, the complex dynamic behaviors of power markets are quantitatively analyzed. Corresponding to different operating conditions of power network, such as congestion or non-congestion, the Nash equilibrium of power markets and its stability are calculated, and the periodic and even chaotic dynamic behaviors are exhibited when the market parameters are beyond the stability region of the Nash equilibrium.     

Optimal scheduling of batch industrial facilities

An increasing interest in batch processing has been evident in recent years. This renewed interest is explained by the inherent flexibility of such plants that permits a high level of response to uncertain market conditions and requirements. This level of response does require the use of efficient tools to help the decision-making process at the design and operational level. This paper presents a Mixed Integer Linear Program (MILP) model to optimise the scheduling of batch facilities subject to changeovers and distribution constraints so as to guarantee a pre-defined objective. Such an objective can be defined as the minimum orders' total lateness or the maximum distribution units loading capacity, among others. A continuous-time representation is used as well as the concept of job predecessor and successor to effectively handle changeovers. Facilities having non-identical parallel units/lines, sequence-dependent orders, finite release times for units and orders, restrictions on the suitability of jobs to lines/units and different possible destinations to available distribution units are also considered. Based on these characteristics the proposed model is able to determine the optimal allocation of jobs to production lines/units, the sequence of jobs on every line/unit and the starting and completion production times of each order. Also, the usage and allocation of the distribution resources (eg trucks) to orders and destinations are obtained based on their availability and suitability to the orders. The model led to the development of a prototype information system that can be used as a tool to help the decision-making process at the operational plant level.Finally, the applicability of the proposed system/formulation is shown through the resolution of an industrial real case where the production of polymers is performed.     

An exact algorithm for solving a capacitated location-routing problem

In location-routing problems, the objective is to locate one or many depots within a set of sites (representing customer locations or cities) and to construct delivery routes from the selected depot or depots to the remaining sites at least system cost. The objective function is the sum of depot operating costs, vehicle acquisition costs and routing costs. This paper considers one such problem in which a weight is assigned to each site and where sites are to be visited by vehicles having a given capacity. The solution must be such that the sum of the weights of sites visited on any given route does not exceed the capacity of the visiting vehicle. The formulation of an integer linear program for this problem involves degree constraints, generalized subtour elimination constraints, and chain barring constraints. An exact algorithm, using initial relaxation of most of the problem constraints, is presented which is capable of solving problems with up to twenty sites within a reasonable number of iterations.     

需求导向的容量设施竞争选址问题研究

客户意愿与容量限制是竞争设施选址问题中两个重要的影响因素,在考虑客户意愿与设施容量共同作用条件下,建立了最小化企业总成本以及每个客户费用为目标的竞争设施选址问题优化模型,通过设计需求导向服务分配机制解决设施与客户之间服务关系分配问题,结合模拟退火思想提出了求解模型的算法。最后利用数值例子分析了需求导向服务分配机制以及目标权重、预算限额等参数对于选址决策的影响,其中考虑需求导向因素会适当增加企业的总成本,但可以减少客户所付出的费用从而增强对客户的吸引力;另外企业的预算限额对于企业的设施选址决策有着重要的影响,企业所能获取的市场份额与其选址预算限额呈正相关的关系;而客户所需付出的总费用与企业提供服务的总成本两者之间则呈负相关的关系,因此需要通过服务质量与成本之间的权衡实现最理想的选址决策。     

Epsilon-Ritz Method for Solving a Class of Fractional Constrained Optimization Problems

In this paper, epsilon and Ritz methods are applied for solving a general class of fractional constrained optimization problems. The goal is to minimize a functional subject to a number of constraints. The functional and constraints can have multiple dependent variables, multiorder fractional derivatives, and a group of initial and boundary conditions. The fractional derivative in the problem is in the Caputo sense. The constrained optimization problems include isoperimetric fractional variational problems (IFVPs) and fractional optimal control problems (FOCPs). In the presented approach, first by implementing epsilon method, we transform the given constrained optimization problem into an unconstrained problem, then by applying Ritz method and polynomial basis functions, we reduce the optimization problem to the problem of optimizing a real value function. The choice of polynomial basis functions provides the method with such a flexibility that initial and boundary conditions can be easily imposed. The convergence of the method is analytically studied and some illustrative examples including IFVPs and FOCPs are presented to demonstrate validity and applicability of the new technique.