Abstract
An Internet shopping mall for clothing operates a warehouse for packing and shipping products to fulfill its orders. All the products in the warehouse are put into the boxes of same brands and the boxes are stored in a row on shelves equiped in the warehouse. To make picking and managing easy, boxes of the same brands are located side by side on the shelves. When new products arrive to the warehouse for storage, the products of a brand are put into boxes and those boxes are located adjacent to the boxes of the same brand. If there is not enough space for the new coming boxes, however, some boxes of other brands should be moved away and then the new coming boxes are located adjacent in the resultant vacant spaces. We want to minimize the movement of the existing boxes of other brands to another places on the shelves during the warehousing of new coming boxes, while all the boxes of the same brand are kept side by side on the shelves. Firstly, we define the adjacency of boxes by looking the shelves as an one dimensional series of spaces to store boxes, i.e. cells, tagging the series of cells by a series of numbers starting from one, and considering any two boxes stored in the cells to be adjacent to each other if their cell numbers are continuous from one number to the other number. After that, we tried to formulate the problem into an integer programming model to obtain an optimal solution. An integer programming formulation and Branch-and-Bound technique for this problem may not be tractable because it would take too long time to solve the problem considering the number of the cells or boxes in the warehouse and the computing power of the Internet shopping mall. As an alternative approach, we designed a fast heuristic method for this reallocation problem by focusing on just the unused spaces-empty cells-on the shelves, which results in an assignment problem model. In this approach, the new coming boxes are assigned to each empty cells and then those boxes are reorganized so that the boxes of a brand are adjacent to each other. The objective of this new approach is to minimize the movement of the boxes during the reorganization process while keeping the boxes of a brand adjacent to each other. The approach, however, does not ensure the optimality of the solution in terms of the original problem, that is, the problem to minimize the movement of existing boxes while keeping boxes of the same brands adjacent to each other. Even though this heuristic method may produce a suboptimal solution, we could obtain a satisfactory solution within a satisfactory time, which are acceptable by real world experts. In order to justify the quality of the solution by the heuristic approach, we generate 100 problems randomly, in which the number of cells spans from 2,000 to 4,000, solve the problems by both of our heuristic approach and the original integer programming approach using a commercial optimization software package, and then compare the heuristic solutions with their corresponding optimal solutions in terms of solution time and the number of movement of boxes. We also implement our heuristic approach into a storage location assignment system for the Internet shopping mall.
의류 인터넷 쇼핑몰들은 판매 상품의 포장과 배송을 위한 상품 창고를 운영하고 있다. 상품들은 동일 브랜드끼리 상자에 담긴 후 선반에 일렬로 보관된다. 상품의 반출 및 상품 관리의 편의상, 상자들은 동일 브랜드끼리 묶여져 선반에 진열되어 있어야 한다. 따라서, 새로운 상품들이 입고될 경우 상품들은 동일 브랜드끼리 상자에 담긴 후 선반 위에 있는 기존 상자들 중에서 동일 브랜드의 상자 옆에 배치되어야 한다. 그런데, 선반 위의 빈 곳이 새로 입고되는 상자를 넣을 수 있을 만큼 충분하지 않다면, 옆의 다른 브랜드의 상자들을 옆으로 밀어서 공간을 확보한 후 새로운 상자를 배치함으로써 동일 브랜드 상자끼리 붙어있도록 해야 한다. 우리의 문제는 이와 같이 새로운 상품을 입고할 때 동일 브랜드의 상자들끼리 붙어 있도록 하면서 다른 브랜드의 상자를 옆으로 옮길 경우, 그 횟수를 최소화하는 것이다. 이 문제의 최적해를 구하기 위해서 우리는 이 문제를 우선 정수계획법으로 모형화하였다. 그런데, 정수계획법 문제는 분기한정법(Branch and Bound) 기법으로 해결하여야 하나, 그 경우 문제해결 시간이 너무 오래 걸리는 문제가 발생한다. 따라서, 본 연구에서는 위 재배치 문제를 할당 문제(Assignment Problem)로 완화하여 모형화함으로써 만족할만한 준최적해를 구하는 방법론을 제시하고, 실험에 의하여 그 타당성을 검토하였다. 또한, 이 방법론 하에서 실제 의류 인터넷 쇼핑몰의 컴퓨팅 환경을 고려할 때 해결 가능한 문제의 최대 크기를 도출하고, 그 크기 이내에서 입고 계획을 생성하는 시스템을 구현하였다.