• Journal of Korean Society of Industrial and Systems Engineering
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• v.44 no.3
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• pp.106-116
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• 2021

This paper considers a joint problem for blood inventory planning at hospitals and blood delivery planning from blood centers to hospitals, in order to alleviate the blood service imbalance between big and small hospitals being occurred in practice. The joint problem is to determine delivery timing, delivery quantity, delivery means such as medical drones and legacy blood vehicles, and inventory level to minimize inventory and delivery costs while satisfying hospitals' blood demand over a planning horizon. This problem is formulated as a mixed integer programming model by considering practical constraints such as blood lifespan and drone specification. To solve the problem, this paper employs a Lagrangian relaxation technique and suggests a time efficient Lagrangian heuristic algorithm. The performance of the suggested heuristic is evaluated by conducting computational experiments on randomly-generated problem instances, which are generated by mimicking the real data of Korean Red Cross in Seoul and other reliable sources. The results of computational experiments show that the suggested heuristic obtains near-optimal solutions in a shorter amount of time. In addition, we discuss the effect of changes in the length of blood lifespan, the number of planning periods, the number of hospitals, and drone specifications on the performance of the suggested Lagrangian heuristic.

• Journal of Korean Institute of Industrial Engineers
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• v.37 no.1
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• pp.19-29
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• 2011

Cellular network is comprised of several base stations which serve cellular shaped service area and each base station (BS) is connected to the mobile switching center (MSC). In this paper, the configuration modeling and algorithm of a cellular mobile network with the aim of minimizing the overall cost of operation (handover) and network installation cost (cabling cost and installing cost of mobile switching center) are considered. Handover and cabling cost is one of the key considerations in designing cellular telecommunication networks. For real-world applications, this configuration study covers in an integrated framework for two major decisions: locating MSC and assigning BS to MSC. The problem is expressed in an integer programming model and a heuristic algorithm based on Lagrangian relaxation is proposed to resolve the problem. Searching for the optimum solution through exact algorithm to this problem appears to be unrealistic considering the large scale nature and NP-Completeness of the problem. The suggested algorithm computes both the bound for the objective value of the problem and the feasible solution for the problem. A Lagrangian heuristics is developed to find the feasible solution. Numerical tests are performed for the effectiveness and efficiency of the proposed heuristic algorithm. Computational experiments show that the performance of the proposed heuristics is satisfactory in the quality of the generated solution.

• Journal of the Korean Institute of Intelligent Systems
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• v.20 no.6
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• pp.755-760
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• 2010

In general, Lagrangian method for discrete optimization is a kind of technique to easily manage constraints. It is traditionally used for finding upper bounds in the branch-and-bound method. In this paper, we propose a new Lagrangian search method for the 0-1 knapsack problem with multiple constraints. A novel feature of the proposed method different from existing Lagrangian approaches is that it can find high-quality lower bounds, i.e., feasible solutions, efficiently based on a new property of Lagrangian vector. We show the performance improvement of the proposed Lagrangian method over existing ones through experiments on well-known large scale benchmark data.

• Korean Management Science Review
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• v.12 no.2
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• pp.89-103
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• 1995

Traditionally, the scarce and expensive resources in communication networks has been the bandwidth of transmission facilities; accordingly, the techniques used for networking and switching have been chosen so as to optimize the efficient use of that resource. One of them is the packet switching for data communications, which is much different from the circuit switching. It allows multiple users to share the data network facilities and bandwidth, rather than providing specific amounts of dedicated bandwidth to each users. One main challenge therefore has been to design and build cost-effective packet switching networks. In this paper, we develop a mathematical programming medel and heuristic algorithm for designing the packet switching networks with hop-count constraints. To develop an efficient heuristic, we apply the Lagrangian relaxation method. Some valid inequalities, which have been known as the tight constraints, are considered to improve the bound for Lagrangian sub-problem. The computational experiments show that the performance of the proposed heuristic is very satisfactory in both the speed and the quality of design solutions generated.

• Journal of Communications and Networks
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• v.12 no.3
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• pp.246-252
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• 2010

A binary linear integer program is formulated for the problem of expanding the capacity of a fiber optic network and routing the traffic to deliver new interactive multimedia services. A two-phase Lagrangian dual search procedure and a Lagrangian heuristic are developed. Computational results show superior performance of the two-phase subgradient optimization compared with the conventional one-phase approach.

• Industrial Engineering and Management Systems
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• v.3 no.2
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• pp.100-115
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• 2004

The network representation and branch and bound algorithm with efficient lower and upper bounding procedures are developed to determine a global optimal production schedule on a machine that minimizes sequence-dependent setup cost and earliness/tardiness penalties. Lower bounds are obtained based on heuristic and Lagrangian relaxation. Priority dispatching rule with local improvement procedure is used to derive an initial upper bound. Two dominance criteria are incorporated in a branch and bound procedure to reduce the search space and enhance computational efficiency. The computational results indicate that the proposed procedure could optimally solve the problem with up to 40 jobs in a reasonable time using a personal computer.

• Journal of Korean Institute of Industrial Engineers
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• v.29 no.3
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• pp.206-212
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• 2003

In this paper, we propose a mathematical optimization model with a suitable algorithm to determine delivery and backlogging quantities by minimizing the total cost including the penalty costs for delay. The system has fixed transshipment costs and demands are fulfilled by some delivery units that represent the volume of delivery amount to be shipped in a single time period. Since, backlogging is allowed, demands could be delivered later at the expense of some penalty costs. The model provides the optimal decisions on when and how much to he delivered while minimizing the total costs. To solve the problem, we propose an algorithm that uses the Lagrangian dual in conjunction with some primal heuristic techniques that exploit the special structure of the problem. Finally, we present some computational test results along with comments on the further study.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.46 no.4
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• pp.238-245
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• 2023

As technologies have been more quickly developed in this 4th Industry Revolution era, their application to defense industry has been also growing. With these much advanced technologies, we attempt to use Manned-Unmanned Teaming systems in various military operations. In this study, we consider the Location-Routing Problem for reconnaissance surveillance missions of the maritime manned-unmanned surface vehicles. As a solution technique, the two-phase method is presented. In the first location phase, the p-median problem is solved to determine which nodes are used as the seeds for the manned vehicles using Lagrangian relaxation with the subgradient method. In the second routing phase, using the results obtained from the location phase, the Vehicle Routing Problems are solved to determine the search routes of the unmanned vehicles by applying the Location Based Heuristic. For three network data sets, computational experiments are conducted to show the performance of the proposed two-phase method.

• Journal of the Korean Operations Research and Management Science Society
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• v.23 no.2
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• pp.47-65
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• 1998

We consider a multiperiod capacity planning problem for determining a mix of flexible and dedicated capacities under budget restriction. These capacities are controlled by purchasing flexible machines and/or new dedicated machines and disposing old dedicated machines. Acquisition and replacement schedules are determined and operations are assigned to the flexible or dedicated machines for the objective of minimizing the sum of discounted costs of acquisition and operation of flexible machines, new dedicated machines, and old dedicated machines. In this research, the Problem is formulated as a mixed integer linear Program and solved by a Lagrangian relaxation approach. A subgradient optimization method is employed to obtain lower bounds and a multiplier adjustment method is devised to improve the bounds. We develop a linear programming based Lagrangian heuristic algorithm to find a good feasible solution of the original problem. Results of tests on randomly generated test problems show that the algorithm gives relatively good solutions in a reasonable amount of computation time.

• Journal of Korean Institute of Industrial Engineers
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• v.37 no.2
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• pp.124-131
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• 2011

In this research report, we propose a heuristic algorithm with some primal recovery strategies for capacitated facility location problems (CFLP), which is a well-known combinatorial optimization problem with applications in distribution, transportation and production planning. Many algorithms employ the branch-and-bound technique in order to solve the CFLP. There are also some different approaches which can recover primal solutions while exploiting the primal and dual structure simultaneously. One of them is a MVCD (Mean Value Cross Decomposition) ensuring convergence without solving a master problem. The MVCD was designed to handle LP-problems, but it was applied in mixed integer problems. However the MVCD has been applied to only uncapacitated facility location problems (UFLP), because it was very difficult to obtain "Integrality" property of Lagrangian dual subproblems sustaining the feasibility to primal problems. We present some heuristic strategies to recover primal feasible integer solutions, handling the accumulated primal solutions of the dual subproblem, which are used as input to the primal subproblem in the mean value cross decomposition technique, without requiring solutions to a master problem. Computational results for a set of various problem instances are reported.