Journal of Korean Society of Industrial and Systems Engineering (산업경영시스템학회지)

Society of Korea Industrial and System Engineering (한국산업경영시스템학회)
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An Approximation Approach for A Multi-Product Continuous Review Inventory Problem with Budget Constraint

예산의 계약이 있는 다품종 연속적 재고 관리 문제에서 추정을 통한 해법

  • Lee, Dong-Ju (Dept. of Industrial Systems Engineering Kongju National University) ;
  • Yoo, Jae-Wook (R&D Innovation Team, Technology Strategy Office, Corporate Technology Operations, Samsung Electronics) ;
  • Lee, Moon-Su (School of Industrial Management Korea University of Technology and Education)
  • 이동주 (공주대학교 산업시스템공학과) ;
  • 유재욱 (삼성전자 기술총괄 CTO전략실 개발혁신팀) ;
  • 이문수 (한국기술교육대학교 산업경영학부)
  • Published : 2008.12.31
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Abstract

Most approaches for continuous review inventory problem need tables for loss function and cumulative standard normal distribution. Furthermore, it is time-consuming to calculate order quantity (Q) and reorder point (r) iteratively until required values are converged. The purpose of this paper is to develop a direct method to get the solution without any tables. We used approximation approaches for loss function and cumulative standard normal distribution. The proposed method can get the solution directly without any iterative procedure for Q, r and without any tables. The performance of the proposed approach is tested by using numerical examples. The budget constraint of this paper assumes that purchasing costs are paid at the time an order is arrived. This constraint can be easily replaced by capacity constraint or budget constraint in which' purchasing costs are paid at the time an order is placed.

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References

  1. Abdel-Malek, L. L., and Areeratchakul N.; "A quadratic programming approach to the multi-product newsvendor problem with side constraint," European Journal of Operational Research, 176：1607-1619, 2007 https://doi.org/10.1016/j.ejor.2005.11.002
  2. Bagby, R. J.; "Calculating Normal Probabilities," Amer. Math. Monthly, 102：46-49, 1995 https://doi.org/10.2307/2974857
  3. Byrkett, D. L.; "An Empirical Evaluation of Further Approximations to An Approximate Continuous Review Inventory Model," Naval Research Logistics Quarterly, 28：169-180, 1981 https://doi.org/10.1002/nav.3800280114
  4. Das C.; "Some Adis for Lot-Size Inventory Control under Normal Lead Time Demand," AIEE Transactions, 7：77-79, 1975 https://doi.org/10.1080/05695557508974989
  5. Das C.; "On the Solution of Some Approximate Continuous Review Inventory Models," Naval Research Logistics Quarterly, 32：301-313, 1985 https://doi.org/10.1002/nav.3800320210
  6. Ghalebsaz-Jeddi, B., Shultes B. C., Haji R.; "A multi- product continuous review inventory system with stochastic demand, backorders, and a budget constraint," European Journal of Operational Research, 158：456-469, 2004 https://doi.org/10.1016/S0377-2217(03)00363-1
  7. Herron, D. P.; "Inventory Management for Minimum Cost," Management Science, 14：B219-235, 1967 https://doi.org/10.1287/mnsc.14.4.B219
  8. Johnson, A. and Montgomery D. C.; "Operations Research in Production Planning, Scheduling, and Inventory Control," Wiley, New York. 1974
  9. Moon, I. and Silver E. A.; "The multi-item newsvendor problem with a budget constraint and fixed ordering costs," Journal of the Operational Research Society, 51：602-608, 2000 https://doi.org/10.1057/palgrave.jors.2600938
  10. Patel, J. K. and Read, C. B.; "Handbook of the Normal Distribution," Dekker, New York, 1982
  11. Wang, T-Y and Hu J-M; "An inventory control system for products with optional components under service level and budget constraints," European Journal of Operational Research, 189：41-58, 2008 https://doi.org/10.1016/j.ejor.2007.05.025
  12. Weisstein, E. W.; "Normal Distribution Function," From MathWorld-A Wolfram Web Resource, http://mathwo rld.wolfram.com/NormalDistributionFunction.html