Improving envelopment in Data Envelopment Analysis under variable returns to scale

In a Data Envelopment Analysis model, some of the weights used to compute the efficiency of a unit can have zero or negligible value despite of the importance of the corresponding input or output. This paper offers an approach to preventing inputs and outputs from being ignored in the DEA assessment under the multiple input and output VRS environment, building on an approach introduced in Allen and Thanassoulis (2004) for single input multiple output CRS cases. The proposed method is based on the idea of introducing unobserved DMUs created by adjusting input and output levels of certain observed relatively efficient DMUs, in a manner which reflects a combination of technical information and the decision maker’s value judgements. In contrast to many alternative techniques used to constrain weights and/or improve envelopment in DEA, this approach allows one to impose local information on production trade-offs, which are in line with the general VRS technology. The suggested procedure is illustrated using real data.     

Hierarchical facility network planning model for global logistics network configurations

This paper presents a novel hierarchical network planning model for global logistics (GLs) network configurations. The proposed method, which is based on the fundamentals of integer programming and hierarchical cluster analysis methods, determines the corresponding locations, number and scope of service areas and facilities in the proposed GLs network. Therein, a multi-objective planning model is formulated that systematically minimizes network configuration cost and maximizes both operational profit and the customer satisfaction rate. Particularly, potential risk-oriented costs, such as macro-environmental-risk and micro-operational-risk costs are considered in the proposed model. Numerical results indicate that the overall system performance can be improved by up to 11.52% using the proposed approach.     

Optimal Design of Heat-Integrated Multipurpose Batch Facilities with Economic Savings in Utilities: A Mixed Integer Mathematical Formulation

The increasing importance of utilities rationalization is an aspect that must be addressed from the early steps of the industrial design procedure. This paper addresses this problem and presents a mathematical formulation for the detailed design of multi-purpose batch process facilities where heat-integration and economic savings in utilities are considered. This generalization appears as an extension of the work of Barbosa-Póvoa et al. [3] where some important design aspects were not considered. In particular, no consideration was given to the economic savings in utility requirements, while considering both the cost of the auxiliary structures (i.e. heat-exchanger through their transfer area) and the design of the utility circuits and associated piping costs. These aspects can appear quite relevant at the design level if the connectivity cost and consumption utilities account for a significant share of capital investment within the plant budget. Also, and at the operational level, heat-integration considerations often result in important plant savings. The problem is formulated as a Mixed Integer Linear Problem (MILP) where binary variables are introduced to characterise operational and topological choices, and continuous ones define the equipment capacities, as well as the amounts of material within the overall process. The applicability of the proposed model is shown via the solution of some illustrative examples.     

Network DEA efficiency in input–output models: With an application to OECD countries

We undertake network efficiency analysis within an input–output model that allows us to assess potential technical efficiency gains by comparing technologies corresponding to different economies. Input–output tables represent a network where different sectoral nodes use primary inputs (endowments) to produce intermediate input and outputs (according to sectoral technologies), and satisfy final demand (preferences). Within the input–output framework it is possible to optimize primary inputs allocation, intermediate production and final demand production by way of non-parametric data envelopment analysis (DEA) techniques. DEA allows us to model the different subtechnologies corresponding to alternative production processes, to assess efficient resource allocation among them, and to determine potential output gains if inefficiencies were dealt with. The proposed model optimizes the underlying multi-stage technologies that the input–output system comprises identifying the best practice economies. The model is applied to a set of OECD countries.     

Reliable design of a logistics network under uncertainty: A fuzzy possibilistic-queuing model

This paper proposes a bi-objective model for designing a reliable network of bi-directional facilities in logistics network under uncertainties. For this purpose, the model utilizes an effective reliability approach to find a robust logistics network design. The objectives of the model are to minimize the total costs and the expected transportation costs after failures of bi-directional facilities of the logistics network. To solve the model, a new solution approach is proposed by combining queuing theory, fuzzy possibilistic programming and fuzzy multi-objective programming. Finally, the computational experiments are provided to illustrate the effectiveness of the proposed model and solution approach.     

A time–space network based exact optimization model for multi-depot bus scheduling

The vehicle scheduling problem, arising in public transport bus companies, addresses the task of assigning buses to cover a given set of timetabled trips with consideration of practical requirements, such as multiple depots and vehicle types as well as depot capacities. An optimal schedule is characterized by minimal fleet size and minimal operational costs including costs for unloaded trips and waiting time. This paper discusses the multi-depot, multi-vehicle-type bus scheduling problem (MDVSP), involving multiple depots for vehicles and different vehicle types for timetabled trips. We use time–space-based instead of connection-based networks for MDVSP modeling. This leads to a crucial size reduction of the corresponding mathematical models compared to well-known connection-based network flow or set partitioning models. The proposed modeling approach enables us to solve real-world problem instances with thousands of scheduled trips by direct application of standard optimization software. To our knowledge, the largest problems that we solved to optimality could not be solved by any existing exact approach. The presented research results have been developed in co-operation with the provider of transportation planning software PTV AG. A software component to support planners in public transport was designed and implemented in context of this co-operation as well.     

基于弹性区带架构的多目标设施布局问题研究

为解决设施面积不等的连续型设施布局问题,建立了基于弹性区带架构布置形式,以物料搬运成本最小、邻近关系最大、距离要求满足度最大的多目标设施布局模型。模型中考虑了区域内的横向、纵向过道,对设施的长宽比进行了限制,使得结果更符合实际情况。为克服传统多目标单一化方法需要人为设置子目标函数权重、主观性过强的缺陷,采用基于带有精英保留策略的非支配排序遗传算法(NSGA Ⅱ)的多目标优化算法求解模型,设计了相应的编码方式、交叉算子、变异算子、罚函数。最后通过某物流园区的实例分析证明了模型与方法的有效性。     

An Inventory-Location Model: Formulation, Solution Algorithm and Computational Results

We introduce a distribution center (DC) location model that incorporates working inventory and safety stock inventory costs at the distribution centers. In addition, the model incorporates transport costs from the suppliers to the DCs that explicitly reflect economies of scale through the use of a fixed cost term. The model is formulated as a non-linear integer-programming problem. Model properties are outlined. A Lagrangian relaxation solution algorithm is proposed. By exploiting the structure of the problem we can find a low-order polynomial algorithm for the non-linear integer programming problem that must be solved in solving the Lagrangian relaxation subproblems. A number of heuristics are outlined for finding good feasible solutions. In addition, we describe two variable forcing rules that prove to be very effective at forcing candidate sites into and out of the solution. The algorithms are tested on problems with 88 and 150 retailers. Computation times are consistently below one minute and compare favorably with those of an earlier proposed set partitioning approach for this model (Shen, 2000; Shen, Coullard and Daskin, 2000). Finally, we discuss the sensitivity of the results to changes in key parameters including the fixed cost of placing orders. Significant reductions in these costs might be expected from e-commerce technologies. The model suggests that as these costs decrease it is optimal to locate additional facilities.     

An integrated approach to dynamic plant location and capacity planning

We consider a dynamic capacitated plant location problem in which capacities of opened plants are determined by acquisition and/or disposal of multiple types of facilities. We determine the opening schedule of plants, allocations of customers' demands and plans for acquisition and/or disposal of plant capacities that minimise the sum of discounted fixed costs for opening plants, delivery costs of products, and acquisition and operation costs of facilities. The dynamic capacitated plant location problem is formulated as a mixed integer linear program and solved by a heuristic algorithm based on Lagrangian relaxation and a cut and branch algorithm which uses Gomory cuts. Several solution properties of the relaxed problem are found and used to develop efficient solution procedures for the relaxed problem. A subgradient optimisation method is employed to obtain better lower bounds. The heuristic algorithm is tested on randomly generated test problems and results show that the algorithm finds good solutions in a reasonable amount of computation time.     

A Simple Model for Computing the Trade-Offs between Plant Capacity and Operating Strategies

A method is presented for determining the optimal capacity of a production system which encounters a strong seasonal demand for its output. A model is developed for analysing the trade-offs between plant capacity and different production strategies. The production strategies are computed by linear programming for a range of plant capacities and a given demand pattern. The annual capital costs of the plant are calculated as a function of plant capacity and the two costs are added in order to determine the plant capacity corresponding to the least cost.     

A model of the direct interaction of elements of a tightly coupled system

A maximin mathematical model describing the process of changing the quality indicators of products manufactured by facilities of a complex production system interconnected by multiple feedbacks is considered. Necessary and sufficient conditions for the monotone growth of these indicators are found. For the proposed new technologies utilized on some of these facilities, consistency conditions with the technologies used on other facilities are determined. For finding the optimal control of this process, it is recommended to use parallel computations.     

Algorithms for the generalized quadratic assignment problem combining Lagrangean decomposition and the Reformulation-Linearization Technique

In this paper, we propose two exact algorithms for the GQAP (generalized quadratic assignment problem). In this problem, given M facilities and N locations, the facility space requirements, the location available space, the facility installation costs, the flows between facilities, and the distance costs between locations, one must assign each facility to exactly one location so that each location has sufficient space for all facilities assigned to it and the sum of the products of the facility flows by the corresponding distance costs plus the sum of the installation costs is minimized. This problem generalizes the well-known quadratic assignment problem (QAP). Both exact algorithms combine a previously proposed branch-and-bound scheme with a new Lagrangean relaxation procedure over a known RLT (Reformulation-Linearization Technique) formulation. We also apply transformational lower bounding techniques to improve the performance of the new procedure. We report detailed experimental results where 19 out of 21 instances with up to 35 facilities are solved in up to a few days of running time. Six of these instances were open.     

The incorporation of fixed cost and multilevel capacities into the discrete and continuous single source capacitated facility location problem

In this study we investigate the single source location problem with the presence of several possible capacities and the opening (fixed) cost of a facility that is depended on the capacity used and the area where the facility is located. Mathematical models of the problem for both the discrete and the continuous cases using the Rectilinear and Euclidean distances are produced. Our aim is to find the optimal number of open facilities, their corresponding locations, and their respective capacities alongside the assignment of the customers to the open facilities in order to minimise the total fixed and transportation costs. For relatively large problems, two solution methods are proposed namely an iterative matheuristic approach and VNS-based matheuristic technique. Dataset from the literature is adapted to assess our proposed methods. To assess the performance of the proposed solution methods, the exact method is first applied to small size instances where optimal solutions can be identified or lower and upper bounds can be recorded. Results obtained by the proposed solution methods are also reported for the larger instances.

     

Consolidating Facilities for the Connecticut Department of Transportation: a Case-Study

The Connecticut Department of Transportation (ConnDOT) was charged with investigating the possibility of reducing costs by operating with fewer than 13 equipment repair facilities. Using a mixed-integer programming model, we helped ConnDOT identify options for achieving savings without sacrificing quality of service. A key feature of the model is that it establishes repair capacities based on the past performance of benchmark facilities within the system. As we developed recommendation, we gave serious consideration to factors outside the context of the model and to feedback received from ConnDOT personnel. Ultimately, we proposed two options-one containing ten facilities and the other 11. The net present values of savings offered by these options are estimated at over $5.0 million and $3.1 million, respectively. While the 11-facility option is lower in savings,it has advantages in that it: (1) satisfies concerns highlighted by ConnDOT Maintenance; (2) is easier to implement than the ten-facility option; and (3) represents less of a current commitment, which is beneficial if future consideration of additional changes is likely. These advantages contributed to the 11-facility option being the one most widely preferred within ConnDOT.     

Heuristics for assessing emergency transshipments

It is not uncommon for organizations with multiple stock-keeping facilities to have some locations facing shortages while others have excess inventory. This paper examines emergency transshipments of product as an approach to solve this problem. Specifically, two heuristics are developed to assist managers in determining when stock transfers should be made. The heuristics produce critical values for on-hand inventory levels above which transshipments minimize overall expected costs. They also provide insight into the factors affecting transshipment usage.     

Electric load forecasting methods: Tools for decision making

For decision makers in the electricity sector, the decision process is complex with several different levels that have to be taken into consideration. These comprise for instance the planning of facilities and an optimal day-to-day operation of the power plant. These decisions address widely different time-horizons and aspects of the system. For accomplishing these tasks load forecasts are very important. Therefore, finding an appropriate approach and model is at core of the decision process. Due to the deregulation of energy markets, load forecasting has gained even more importance. In this article, we give an overview over the various models and methods used to predict future load demands.     

MILP-based approaches for medium-term planning of single-stage continuous multiproduct plants with parallel units

In this paper, we address the problem of medium-term planning of single-stage continuous multiproduct plants with multiple processing units in parallel. Sequence-dependent changeover times and costs occur when switching from one type of product to another. A traveling salesman problem (TSP)-based mixed-integer linear programming (MILP) model is proposed based on a hybrid discrete/continuous time representation. We develop additional constraints and variables to ensure that subtours do not occur in the solution. The model is successfully applied to an example of a polymer processing plant to illustrate its applicability. In order to solve larger model instances and planning horizons, a rolling horizon approach is developed to reduce the computational expense. Finally, the proposed model is compared to a recently published approach through literature examples, and the results show that the computational performance of the proposed model is superior.     

Integrated facility location and production scheduling in multi-generation energy systems

In this paper, we investigate the energy system design problems with the multi-generation technologies, i.e., simultaneous generation of multiple types of energy. Our results illustrate the economic value of multi-generation technologies to reduce spatio-temporal demand uncertainty by risk pooling both within and across different facilities.     

Dismantling of nuclear power plants at optimal NPV

Today, worldwide far more than 100 nuclear power plants, which have been decommissioned in the recent years, are waiting for their complete dismantling. Since the dismantling of a single reactor causes costs of up to one billion Euros and lasts up to 15 years, the elaboration of a scheduling approach helping to optimize the net present value of a dismantling project seems to be worthwhile. In this paper we present a resource-constrained project scheduling approach optimizing the total discounted disbursements of dismantling a nuclear power plant. For the corresponding NP-hard optimization problem, we introduce an appropriate project scheduling model with minimum and maximum time lags, renewable and cumulative resources as well as multiple execution modes. To solve this model, we introduce a relaxation-based enumeration approach that delivers optimal solutions for problem instances containing up to 50 activities.     

A cover-based competitive location model

In this paper we propose a new approach to estimating market share captured by competing facilities. The approach is based on cover location models. Each competing facility has a ‘sphere of influence’ determined by its attractiveness level. More attractive facilities have a larger radius of the sphere of influence. The buying power of a customer within the sphere of influence of several facilities is equally divided among the competing facilities. The buying power of a customer within the sphere of influence of no facility is lost. Assuming the presence of competition in the area, the objective is to add a number of new facilities to a chain of existing facilities in such a way that the increase of market share captured by the chain is maximized. The model is formulated and analysed. Optimal and heuristic solution algorithms are designed. Computational experiments demonstrate the effectiveness of the proposed algorithms.