A Mixed-integer Linear Programming Model for Solving Multi-item Uncapacitated Lot-sizing Problems with Storage Capacities Limitations: A Case Study of an Apparel Manufacturing Company

Abstract

This study aimed to use a mixed-integer linear programming model to solve the multi-item uncapacitated lot size problem with storage capacity limitations for apparel manufacturing. In real-world operations, sometimes the storage capacity of cloth rolls can be insufficient at any given time. This would be because the sum of the remaining cloth rolls from the previous period and the receiving cloth rolls from the existing period would be a vast number. Furthermore, the extra cloth on the rolls would have to be carried and kept in the production line. Consequently, this caused the late issue of the distribution of the material, the loss of the cloth rolls, and the failure to count the cloth rolls. As a result, we conducted a multi-item cloth roll replenishment plan to meet the production line's demand and keep all the inventory and receiving cloth rolls. Using mixed-integer linear programming, the multi-item lot size of each period and the sum of the cloth, ordering, and holding costs was calculated, including the number of occupied cloth racks that did not exceed the number of available cloth racks in the cloth storage. Then, this result was compared with the calculation of a mixed-integer linear programming model based on the procurement policies of a case study company. This study used OpenSolver and GAMS/CPLEX software to calculate the solutions. The results found that in using the procurement policy, we could provide the maximum number of occupied cloth racks, about 368 racks, or 2.78 times the racks on the available shelves of the cloth storage. The result of the proposed model indicated that the number of occupied cloth racks to be installed did not exceed the number of available racks on the shelves. The total cost of the model of the procurement policy was less than the proposed model by about 0.26 percent because ordering occurred only about 25 times.