• Journal of applied mathematics & informatics
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• 제31권3_4호
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• pp.469-477
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• 2013

Pattabiraman and Paulraja [K. Pattabiraman, P. Paulraja, Vertex and edge PI indices of the generalized hierarchical product of graphs, Discrete Appl. Math. 160 (2012) 1376- 1384] obtained exact formulas for the vertex and edge PI indices of generalized hierarchical product of graphs. The aim of this note is to improve the main results of this paper.

• 산업공학
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• 제13권3호
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• pp.378-387
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• 2000

As the globalization of manufacturing companies continues, the scope of dependence between these companies and distributors, and other suppliers are growing very rapidly since no one company manufactures or distributes the whole product by themselves. And, the need to increase the efficiency of the whole supply chain is increasing. This paper deals with a multi-plant lot-sizing problem(MPLSP) which happens in a decentralized manufacturing system of a supply chain. In this study, we assume that the whole supply chain is driven by a single source of independent demand and many levels of dependent demands among manufacturing systems in the supply chain. We consider setup cost, transportation cost and time, and inventory holding cost as a decision factor in the MPLSP. The MPLSP is decomposed into two sub-problems: a planning problem of the whole supply chain and a lot-sizing problem of each manufacturing system. The supply chain planning problem becomes a pure linear programming problem and a Generalized Goal Decomposition method is used to solve the problem. Its result is used as a goal of the lot-sizing problem. The lot-sizing problem is solved using the CPLEX package, and then the coefficients of the planning problem are updated reflecting the lot-sizing solution. This procedure is repeated until termination criteria are met. The whole solution process is similar to Lagrangian relaxation method in the sense that the solutions are approaching the optimum in a recursive manner. Through experiments, the proposed closed-loop hierarchical planning and traditional hierarchical planning are compared to optimal solution, and it is shown that the proposed method is a very viable alternative for solving production planning problems of decentralized manufacturing systems and in other areas.

• 농촌계획
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• 제16권3호
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• pp.43-49
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• 2010

This study generalized and systemized the unit-project items of 176 project districts for the rural village comprehensive development projects (RVCDP). This paper surveyed opinions of III answerers (7 specialists, 43 agents of Korea Rural Community corporation, and 61 agents of local government of cities and counties) in order to determine the classification system and their corresponding weighting values of the project items using analytic hierarchy process (AHP) method. From the results extracted by project plans of 176 project districts for 5 years from 2004 to 2008, this study decided a hierarchical system for unit-project items of RVCDP by AHP method, which consisted of three steps: 4 items for 1st step, 13 items for 2nd step, and 52 items for 3rd step. The first step contains 4 items of Strength of Rural-urban Exchange & Regional Capability (RURC), Green-income Infrastructure & Facility (GIF), Culture-health-welfare Facility, and Eco-environment & Landscape facility (ELF). In the survey of weighting values with AHP method, the analysis result for the first step showed that in opinion of specialists, GIF is more important than the others while in opinion of the other agents, RURC is more important. In the second step, Product Facility is more important in the specialists, whereas Strength of Resident Capability is the most important in the other agents. Analyzed unit project items as the third step, all answerers evaluated that the Education and Excursion for Rural Resident Capability has the highest weighting values.