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This study aims to examine the trend of industrial competition between the US and China, which is the most crucial determinant in the future development of the global economy. For decades, the global economy has strengthened the global production network based on the division of labor between countries. Thus, the ripple effect of competition between the two countries should be analyzed in terms of the global production network. Therefore, this study uses the product space model, which explains the development process of industries with comparative advantage by country. We constructed the model based on the products of HS 4-digit code for the 2010–2019 period. The analysis results on the trend of the industrial competitiveness of major countries are as follows. First, the current industrial competitiveness of China is concentrated on low-tech industries. In the case of high-tech items, China shows a tendency of lower export sophistication compared to major manufacturing powerhouses such as Germany, the US, Japan, and Korea. Second, with respect to the possibility of a future industrial structure upgrade evaluated by density, the trend of China overtaking other manufacturing powerhouses is observed. As implied by the product space model, the advancement of the industrial structure through active participation in international trade enhances the industrial competitiveness. Therefore, the outcome of US-China industrial competition depends on who ensures more openness and industrial complexity.

Due to increasing awareness on the treatment of end-of-use/life products, disassembly has been a fast-growing research area of interest for many researchers over recent decades. This paper introduces a novel lot-sizing problem that has not been studied in the literature, which is the service-parts lot-sizing with disassembly option. The disassembly option implies that the demands of service parts can be fulfilled by newly manufactured parts, but also by disassembled parts. The disassembled parts are the ones recovered after the disassembly of end-of-use/life products. The objective of the considered problem is to maximize the total profit, i.e., the revenue of selling the service parts minus the total cost of the fixed setup, production, disassembly, inventory holding, and disposal over a planning horizon. This paper proves that the single-period version of the considered problem is NP-hard and suggests a heuristic by combining a simulated annealing algorithm and a linear-programming relaxation. Computational experiment results show that the heuristic generates near-optimal solutions within reasonable computation time, which implies that the heuristic is a viable optimization tool for the service parts inventory management. In addition, sensitivity analyses indicate that deciding an appropriate price of disassembled parts and an appropriate collection amount of EOLs are very important for sustainable service parts systems.

It is highly challenging to measure the efficiency of electric vehicle charging stations (EVCSs) because factors affecting operational characteristics of EVCSs are time-varying in practice. For the efficiency measurement, environmental factors around the EVCSs can be considered because such factors affect charging behaviors of electric vehicle drivers, resulting in variations of accessibility and attractiveness for the EVCSs. Considering dynamics of the factors, this paper examines the technical efficiency of 622 electric vehicle charging stations in Seoul using data envelopment analysis (DEA). The DEA is formulated as a multi-period output-oriented constant return to scale model. Five inputs including floating population, number of nearby EVCSs, average distance of nearby EVCSs, traffic volume and traffic congestion are considered and the charging frequency of EVCSs is used as the output. The result of efficiency measurement shows that not many EVCSs has most of charging demand at certain periods of time, while the others are facing with anemic charging demand. Tobit regression analyses show that the traffic congestion negatively affects the efficiency of EVCSs, while the traffic volume and the number of nearby EVCSs are positive factors improving the efficiency around EVCSs. We draw some notable characteristics of efficient EVCSs by comparing means of the inputs related to the groups classified by K-means clustering algorithm. This analysis presents that efficient EVCSs can be generally characterized with the high number of nearby EVCSs and low level of the traffic congestion.

This paper considers the problem of deciding disassembly order quantity in a disassembly system. Returned end-of-use/life (EOL) products are disassembled to retrieve reusable parts sold to secondar...

The air transportation industry is one big network that is expected to grow continuously, and Asia-Pacific is the fastest growing region as of 2018 data. We apply weighted network analysis to explore the key network characteristics of the Asian international passenger aviation market in 2014 and 2018. For the analysis, networks are constructed based on international passengers' origin-destination pair data from 28 Asian airlines in 2014 and 2018. Previously published social network analysis (SNA) on the air transportation network largely used unweighted centrality metrics, whereas the actual situation is a weighted network. We implement Mean Associations (MA), Triangle Betweenness Centrality (TBC), and Weighted PageRank (WPR), as new weighted centrality metrics, to effectively reflect actual passenger traffic among airports beyond simple connections. Our weighted network analysis indicates that SIN, ICN, HKG, NRT, MNL, BKK, TPE, HND, PEK, and KUL are the top-ranked hub airports, followed by SGN, PVG, CAN, DEL, SYD, KIX and CGK, and that the low-cost carriers have almost fully developed a ‘hub-and-spoke’ structure over the 4-year study period and are increasing their impact on the centrality of airports in the region.

Evaluating the operational efficiency of electric vehicle charging stations (EVCSs) is important to understand charging network evolution and the charging behavior of electric vehicle users. However, aggregation of efficiency performance metrics poses a significant challenge to practitioners and researchers. In general, the operational efficiency of EVCSs can be measured as a complicated function of various factors with multiple criteria. Such a complex aspect of managing EVCSs becomes one of the challenging issues to measure their operational efficiency. Considering the difficulty in the efficiency measurement, this paper suggests a way to measure the operational efficiency of EVCSs based on data envelopment analysis (DEA). The DEA model is formulated as constant returns of output-oriented model with five types of inputs, four of them are the numbers of floating population and nearby charging stations, distance of nearby charging stations and traffic volume as desirable inputs and the other is the traffic speed in congestion as undesirable one. Meanwhile, the output is given by the charging frequency of EVCSs in a day. Using real-world data obtained from reliable sources, we suggest operational efficiencies of EVCSs in Seoul and discuss implications on the development of electric vehicle charging network. The result of efficiency measurement shows that most of EVCSs in Seoul are inefficient, while some districts (Nowon-gu, Dongdaemun-gu, Dongjak-gu, Songpa-gu, Guro-gu) have relatively more efficient EVCSs than the others.

In today’s multi-channel distribution environment, it is crucial for the competitiveness of retail stores and companies to improve efficiency of dedicated logistics centers (DLCs) servicing types of retail outlets such as large retail-stores, super supermarkets, and convenient stores. This paper derives efficiency improvement strategies for DLCs through efficiency analyses. To this end, this paper empirically analyzes the efficiency of DLCs by applying DEA (data envelopment analysis) approaches using real data from a Korean distribution company. In detail, this paper analyzes operations, finance, and service efficiencies of DLCs and performs a comparison analysis on the efficiency between DLCs. Finally, this paper discusses the analysis results considering the DLCs’ characteristics and derives managerial and operational implications.

The vehicle routing problem is one of the vibrant research problems for half a century. Many studies have extensively studied the vehicle routing...

In South Korea, Jeju Island has a role as a test bed for electric vehicles (EVs). All conventional cars on the island are supposed to be replaced with EVs by 2030. Accordingly, how to effectively set up EV charging stations (EVCSs) that can charge EVs is an urgent research issue. In this paper, we present a case study on planning the locations of EVCS for Jeju Island, South Korea. The objective is to determine where EVCSs to be installed so as to balance the load of EVCSs while satisfying demands. For a public service with EVCSs by some government or non-profit organization, load balancing between EVCS locations may be one of major measures to evaluate or publicize the associated service network. Nevertheless, this measure has not been receiving much attention in the related literature. Thus, we consider the measure as a constraint and an objective in a mixed integer programming model. The model also considers the maximum allowed distance that drivers would detour to recharge their EV instead of using the shortest path to their destination. To solve the problem effectively, we develop a heuristic algorithm. With the proposed heuristic algorithm, a variety of numerical analysis is conducted to identify effects of the maximum allowed detour distance and the tightness of budget for installing EVCSs. From the analysis, we discuss the effects and draw practical implications.

Owing to growing economic growth in tandem with regional economic developments on the route connecting Asia and sub-Saharan Africa (SSA), several countries in the SSA region such as South Africa have been developing container ports. This paper analyzes potential trunk line routes and transshipment flows that could be captured by potential hub ports in the SSA region. To this end, integer programing models are developed to represent liner shipping networks in the SSA region and a wide variety of numerical experiments based on realistic data are conducted for the SSA-Europe and SSA-Asia trade routes. This paper draws various meaningful policy and managerial implications through scenario analyses such as the effects of network evolution, different vessel sizes and speeds, carbon taxes and insights in association with the 21st Century Maritime Silk Road initiated by China.

This paper aims to provide a practical method for forecasting potential container cargo volume that can be induced by a port development project on a container transport network by combining port choice and an autoregressive integrated moving average (ARIMA) model. The entrance channel improvement plan for Incheon New Port in South Korea is used as a case study. Based on the stated preference data collected from domestic shippers, a discrete choice analysis is performed to estimate the future market share of three major ports in South Korea: Busan, Gwangyang, and Incheon. The estimated market share of Incheon New Port is used to forecast its future container volume derived by the ARIMA model and the potential port development scenarios.

This paper discusses a case of truck sharing as an application of the sharing economy. This case study examines a real mixed feed company with multiple factories. In this company’s operation, bulk trucks located in a factory had not previously been shared for delivery with other factories to their pre-assigned customers of stock farms. Therefore, this paper suggests a new delivery system that facilitates truck-sharing and analyzes its effects on the transport cost and trucks’ CO2 emissions. To this end, this paper develops vehicle routing models to represent the current delivery practice and the new truck-shared delivery (TSD). In addition, models are developed for a carbon control policy of an emission trading scheme (ETS) and the effects of the ETS on truck-sharing are investigated. Numerical analysis is conducted to identify the effects of the TSD and the carbon control policy and draw practical implications.

This study addresses the problem of determining the ship speed and bunkering ports in a ship route. All of the previous research has investigated the ship speed optimization issues by assuming that the ship navigates at constant speed or by ignoring the bunkering port decision. In this study, the problem of determining the variable speed and bunkering port is formulated mathematically with a nonlinear program in order to minimize the bunker fuel, ship time costs, and carbon tax imposed on greenhouse gas emissions. This study then provides a Lagrangian heuristic by deriving a property for a relaxed problem. The performance of the heuristic is evaluated and analysed using the data obtained from the literature, real practice and random generation.

Owing to high fuel costs and environmental regulations, the optimization of ship speed to minimize fuel consumption and reduce carbon emissions has become a hot issue in the maritime industry. In this paper, we study the sailing speed optimization problem for a ship operating on a route having a specified sequence of calling ports with time windows for calling time. The considered problem can be formulated as a non-linear program. We derive the intrinsic properties of the problem and develop an optimal algorithm based on the properties. Computational experiments show that the developed algorithm in this paper is efficient in finding an optimal solution.

In semiconductor wafer fabrication facilities, order-lot pegging is the process of assigning wafer lots to orders and meeting the due dates of orders is considered one of the most important operational issues. In many cases of order-lot pegging, some orders cannot be fulfilled with the current wafers in the lots being processed, necessitating the release of additional new wafer lots into the wafer fabrication facility. In this paper, we propose a simultaneous decision model for order-lot pegging and wafer release planning in semiconductor wafer fabrication facilities, and develop a Lagrangian heuristic for solving the model. The results of computational experiments conducted using randomly generated problem instances that mimic actual field data from a Korea semiconductor wafer fabrication facility indicate that the performance of the Lagrangian heuristic is superior to that of a practical greedy algorithm for practical-sized problem instances. The results also point to how sensitivity analysis can be use...

This article analyzes an intermodal transportation network for international container cargoes in Korea. The actual transportation situation in Korea is formulated by a linear programming model. The model is validated first by comparing the model output with actual performance, and then the model is extended by incorporating various externalities arising from inland transport modes such as air pollution, congestion, accidents, noise pollution, and wear and tear. Moreover, the model is extended for assessing the effects of complying with carbon taxation and emission trading schemes, which loom large in international shipping communities. Test results of the models using the data obtained from reliable sources are presented and policy directions are discussed from an environmental perspective.

We study the ship speed optimization problem with the objective of minimizing the total fuel consumption. We consider multiple time windows for each port call as constraints and formulate the problem as a nonlinear mixed integer program. We derive intrinsic properties of the problem and develop an exact algorithm based on the properties. Computational experiments show that the suggested algorithm is very efficient in finding an optimal solution.

This paper provides an algorithm to minimize the fixed ordering, purchase, and inventory-carrying costs associated with bunker fuel together with ship time costs; and environmental costs associated with greenhouse gas emissions. It determines the optimum ship speed, bunkering ports, and amounts of bunker fuel for a given ship’s route. To solve the problem, we use an epsilon-optimal algorithm by deriving a property. The algorithm is illustrated by applying it to typical sample data obtained and the effects of bunker prices, carbon taxes, and ship time costs on the ship speed are analyzed. The results indicate that the ship speed and CO2 emissions are highly sensitive to the factors considered.

This paper presents a case study on the problems which result when loading air containers onto DHL and Air Hong Kong air express carriers. Problems often arise when trying to determine which containers should be loaded and where the containers should be located in an aircraft in order for it to maintain stability. The objective of this activity is to maximize the revenue obtained from delivering containers. We will present an integer programming model which will attempt to optimally solve the problem. Computational experiments which have been done on a number of randomly generated test instances show that the integer programming model can be a viable tool for generating loading plans within the companies since optimal or near-optimal solutions were obtained during the test instances within a reasonable amount of computation time.

The strategic location of city logistics facilities may help to establish more efficient urban logistics systems, reduce social and environmental costs of urban freight transport, and improve urban traffic conditions. In addition, it may allow a number of shippers or freight carriers to jointly operate freight vehicles and terminals or information systems while allowing them to have the capability to provide higher levels of services to their customers. This paper considers the problem of selecting a location for a city logistics facility while considering linguistic factors. This paper identifies the important factors in the selection of a location for a city logistics facility by performing a case study which applies the analytic hierarchy process method on data from Chongqing, China. The optimal location in Chongqing is then determined by using the fuzzy synthetic evaluation method. The results of this paper are expected to help municipal governments select appropriate locations for city logistics facilities and quantify the advantages and disadvantages of alternative locations.

H maritime company in Korea had a long history of difficulty in obtaining enough empty containers to transport its commodities. Despite efforts to resolve the problem, the repositioning of empty containers between depots was still planned manually, which consumed much worker time. To automate the generation of reposition plans, we developed a planning system to optimize the company’s reposition of empty containers between global depots with a linear programming model functioning as a key decision engine in the system. The model determines the route, volume and mode of transportation for repositioning empty containers from depots with surplus containers to those requiring containers, as well as the empty space of ships generated from the unloading or loading of full and empty containers. The system has been in operation in the company’s global network since March 2008.

We consider the problem of determining the lot sizes that satisfy the demands of remanufactured products over a given planning horizon with discrete time periods. Remanufacturing, in which used or end-of-life products are restored to like-new condition, typically consists of disassembly, reprocessing and reassembly processes, and hence the lot sizes are determined for each of the three processes. The objective is to minimise the sum of setup and inventory holding costs occurring at the three processes. To represent the problem mathematically, we suggest a mixed integer programming model by combining the existing ones for disassembly and assembly systems. After proving that the problem is NP-hard, we suggest two dynamic programming based heuristics, called the aggregation and the decomposition type heuristics in this paper. Computational experiments were done on various test instances, and the results show that the two heuristics give near-optimal solutions in a short amount of computation time. Also, the ...

Dynamic lot sizing is the problem of determining the quantity and timing of ordering items while satisfying the demand over a finite planning horizon. This paper considers the problem with two practical considerations: minimum order size and lost sales. The minimum order size is the minimum amount of items that should be purchased and lost sales involve situations in which sales are lost because items are not on hand or when it becomes more economical to lose the sale rather than making the sale. The objective is to minimize the costs of ordering, item , inventory holding and lost sale over the planning horizon. To solve the problem, we suggest a heuristic algorithm by considering trade-offs between cost factors. Computational experiments on randomly generated test instances show that the algorithm quickly obtains near-optimal solutions.

This paper considers disassembly scheduling, which is the problem of determining the quantity and timing of the end-of-use/life products to be disassembled while satisfying the demand for their parts obtained from disassembling the products over a planning horizon. This paper focuses on the problem with stochastic demand of parts/modules, capacity restrictions on disassembly resources, and multiple product types with a two-level product structure. The two-level product structure implies that an end-of-use/life product is hierarchically decomposed into two levels where the first level corresponds to the parts/modules and the second level corresponds to the product. We formulate the problem as a stochastic inventory model and to solve the problem we propose a Lagrangian heuristic algorithm as well as an optimisation algorithm for the sub-problems obtained from Lagrangian decomposition. The test results on randomly generated problems show that the Lagrangian heuristic algorithm demonstrates good performance in terms of solution quality and time.

To alleviate harm to the environment, short sea shipping (SSS) is gaining popularity in transportation policy formulation as an alternative transport mode for ecofriendly and cost-efficient transportation. There have been no studies of how to optimize intermodal container movement incorporating environmental aspects into SSS networks. This paper analyzes an intermodal transportation problem of international container cargoes while incorporating the external costs of the modes into an optimization model in South Korea. The objective of the problem is to minimize the total logistic costs, that is, shipping and land transportation costs, as well as external costs such as air pollutants (particulate matter, nitrogen oxide, sulfur dioxide, and volatile organic compounds) and greenhouse gases (carbon dioxide). The results of the model show a strong foundation for encouraging more environmentally friendly modes, such as SSS and rail, and a well-balanced modal shift if transport policy is formulated in this direction.

This paper considers a multimodal transportation problem, which is the problem of determining the transportation flow, i.e. volume of container cargoes, and the transportation mode in each trade route, for the objective of minimizing the sum of shipping and inland transportation costs. The problem takes account of two restrictions: maximum cargo volumes capacitated at each seaport and maximum number of vehicles available at each transportation mode. To solve optimally the problem, this paper employs a mixed integer programming, which is an operations research technique. A case study is performed on the container cargo data in Korea and we draw several implications to improve efficiency in the transportation of international trade cargoes in Korea.

Disassembly scheduling, one of the important operational problems in disassembly systems, can be generally defined as the problem of determining the quantity and timing of the end-of-use/life products while satisfying the demand of their parts over a planning horizon. This paper presents a literature review on this planning problem in disassembly systems. First, the basic form of the problem is defined with a mathematical formulation. To characterize the differences between assembly and disassembly processes, the effects of the divergence property are also explained with respect to the zero inventory property, indispensable surplus inventory, and mathematical representation. Then, we review the existing research articles on the basic problem and its generalizations. A systematic scheme for classifying problems is also suggested. Finally, we suggest several future research directions.

This paper considers the problem of determining the disassembly schedule (quantity and timing) of products in order to satisfy the demand of their parts or components over a finite planning horizon. The objective is to minimize the sum of set-up, disassembly operation, and inventory holding costs. As an extension of the uncapacitated versions of the problem, we consider the resource capacity restrictions over the planning horizon. An integer program is suggested to describe the problem mathematically, and to solve the problem, a heuristic is developed using a Lagrangean relaxation technique together with a method to find a good feasible solution while considering the trade-offs among different costs. The effectiveness of the algorithm is tested on a number of randomly generated problems and the test results show that the heuristic suggested in this paper can give near optimal solutions within a short amount of computation time.

Disassembly scheduling, one of the important operational problems in disassembly systems, is the problem of determining the timing and quantity of disassembling used or end-of-life products to satisfy the demand of their parts or components over a given planning horizon. This paper focuses on the case of single product type without parts commonality while the resource capacity restrictions are considered explicitly. The problem is formulated as an integer programming model with the objective of minimizing the number of products disassembled, and a solution algorithm is suggested after deriving its optimal solution properties. Computational experiments are done on various test problems, and the results show that the algorithm suggested in this paper gives optimal solutions for the test problems within a very short amount of computation time.

Disassembly scheduling is one of the important planning problems in disassembly systems, and generally defined as the problem of determining the quantity and timing of disassembling products in order to satisfy the demand of their parts or components over a planning horizon. This paper focuses on the case of multiple product types with parts commonality for the objective of minimizing the sum of set-up, disassembly operation and inventory-holding costs, and it suggests a two-phase heuristic in which an initial solution is obtained using a linear-programming relaxation, and then improved by perturbing the initial solution using a dynamic programming algorithm with look-ahead check. Computational experiments are done on a number of randomly generated test problems and the results show that the heuristic suggested in this paper can give near-optimal solutions within a short computation time.

This paper focuses on an arc-welding robot scheduling problem, which is the problem of determining the sequence of welding operations while avoiding heat-caused distortion for the objective of minimizing the time required to complete a given set of welding operations. Each welding operation is specified by a weld line with two end points, each of which can be a possible starting point of the welding operation for that weld line. Because of the heat-caused distortion, there must be a certain period of time (delay) between welding operations associated with weld lines near each other. We develop several heuristic algorithms, in which heuristics for the travelling salesman problem are modified to cope with characteristics of the problem considered here. To show the performance of the heuristics suggested in this paper, computational experiments are performed on a number of randomly generated test problems and results are reported.

Porous silicon materials have been shown to have bright prospects for applications in light emitting, solar cell, as well as light- and chemical-sensing devices. In this report, structures of porous silicon prepared by anodic etching in HF-based solution with various etching times were studied in detail by Atomic Force Microscopy and Small Angle X -ray Scattering technique using the high energy beam line at Pohang Light Source in Korea. The results showed the coexistence of the various pores with nanometer and submicrometer scales. For nanameter size pores, the mixed ones with two different shapes were identified: the larger ones in cylindrical shape and the smaller ones in spherical shape. Volume fractions of the cylindrical and the spherical pores were about equal and remained unchanged at all etching times investigated. On the whole uniform values of the specific surface area and of the size parameters of the pores were observed except for the larger specific surface area for the sample with the short etching time. The results implies that etching process causes the inner surfaces to become smoother while new pores are being generated. In all SAXS data at large Q vectors, Porod slope of -4 was observed, which supports the fact that the pores have smooth surfaces.

This paper focuses on the problem of determining the ordering and disassembly schedules of used or end-of-life products while satisfying the demand of their parts/components over a planning horizon. To represent and optimally solve the basic case of the problem, an integer programming model is suggested for the objective of minimizing the sum of purchase, set-up, inventory holding and disassembly operation costs. Then, the basic model is extended to consider more general cases with parts commonality, i.e. single and multiple product types with parts commonality. Computational experiments done on the problems obtained from the literature and a number of randomly generated test problems show that the integer programming models suggested in this paper work well up to medium-sized test problems.

The lanthanide complexes have been applied as emitting materials and have been anticipated to exhibit high efficiency along with a narrow emission spectrum since both singlet and triplet excitons of ligands are involved in the luminescence process. With increasing current, however, the quantum efficiencies have decreased significantly due to the triplet–triplet annihilation. The effect of the energy levels of singlet and triplet states of ligands have been studied and the efficient energy transfer mechanism to overcome triplet–triplet annihilation is proposed. The calculation shows that the triplet state as well as the singlet state of the ligand affects the quantum efficiency.

We consider the problem of determining the disassembly schedules of used products while satisfying the demand of their parts/components over a planning horizon. The case of multiple product types with parts commonality is considered for the objective of minimizing the sum of setup, disassembly operation, and inventory holding costs. A heuristic algorithm is proposed using the linear programming relaxation approach. Test results of the case study on the data obtained from a disassembly shop show that the heuristic algorithm suggested in this paper works well for practical problems.

This paper considers the problem of determining the quantity and timing of disassembling used or end-of-life products in order to satisfy the demand of their parts or components over a finite planning horizon. We focus on the case of single product type without parts commonality, i.e., assembly product structure. The objective is to minimize the sum of setup, disassembly operation, and inventory holding costs. Several properties of optimal solutions are derived, and then a branch and bound algorithm is developed based on the Lagrangian relaxation technique. Results of computational experiments on randomly generated test problems show that the algorithm finds the optimal solutions in a reasonable amount of computation time.

Disassembly scheduling is the problem of determining the timing and quantity of disassembling used products to satisfy the demands of their parts or components over the planning horizon. This paper focuses on the case of single product type without parts commonality while the resource capacity restrictions are explicitly considered. The problem is formulated as an integer program for the objective of minimizing the number of products to be disassembled, and an optimal algorithm, after deriving the properties of the problem, is suggested. Computational experiments are done on randomly generated test problems, and the results are reported.

We consider the problem of determining the disassembly schedule (quantity and timing) of products in order to satisfy the demand of their parts or components over a finite planning horizon. This paper focuses on the capacitated version of the problem for the objective of minimizing the sum of setup, disassembly operation, and inventory holding costs. The problem is formulated as an integer program, and to solve the problem, a Lagrangean heuristic algorithm is developed after reformulating the integer program. To show the performance of the heuristic algorithm, computational experiments are done on randomly generated test problems, and the test results show that the algorithm suggested in this paper works well.

This paper addresses the problem of determining the ship speed, fleet size, and chartered ship number subject to environmental regulations consisting of a carbon tax and an emission trading scheme. The objective of the problem is to minimise bunker consumption cost, ship operating cost, ship charterage and either the carbon tax or the revenue/cost of selling/purchasing CO2 emissions permits. We formulate the problems as non-linear programmes by considering the two regulations independently. This study also suggests Lagrangian heuristics to solve the problems. A case study is performed to evaluate the applicability of the heuristics.