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

Society of Korea Industrial and System Engineering (한국산업경영시스템학회)
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An Inventory Problem with Lead Time Proportional to Lot Size and Space Constraint

로트크기에 비례하는 리드타임과 공간 제약을 고려한 재고관리 정책

  • Lee, Dongju (Dept. of Industrial & Systems Engineering, Kongju National University)
  • 이동주 (공주대학교 산업시스템공학과)
  • Received : 2015.10.12
  • Accepted : 2015.12.03
  • Published : 2015.12.31
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Abstract

This paper is concerned with the single vendor single buyer integrated production inventory problem. To make this problem more practical, space restriction and lead time proportional to lot size are considered. Since the space for the inventory is limited in most practical inventory system, the space restriction for the inventory of a vendor and a buyer is considered. As product's quantity to be manufactured by the vendor is increased, the lead time for the order is usually increased. Therefore, lead time for the product is proportional to the order quantity by the buyer. Demand is assumed to be stochastic and the continuous review inventory policy is used by the buyer. If the buyer places an order, then the vendor will start to manufacture products and the products will be transferred to the buyer with equal shipments many times. The mathematical formulation with space restriction for the inventory of a vendor and a buyer is suggested in this paper. This problem is constrained nonlinear integer programming problem. Order quantity, reorder points for the buyer, and the number of shipments are required to be determined. A Lagrangian relaxation approach, a popular solution method for constrained problem, is developed to find lower bound of this problem. Since a Lagrangian relaxation approach cannot guarantee the feasible solution, the solution method based on the Lagrangian relaxation approach is proposed to provide with a good feasible solution. Total costs by the proposed method are pretty close to those by the Lagrangian relaxation approach. Sensitivity analysis for space restriction for the vendor and the buyer is done to figure out the relationships between parameters.

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References

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