4.3 Article

The integrated uncapacitated lot sizing and bin packing problem

Journal

RAIRO-OPERATIONS RESEARCH
Volume 55, Issue 3, Pages 1197-1212

Publisher

EDP SCIENCES S A
DOI: 10.1051/ro/2021049

Keywords

Integrated production-delivering problems; lot sizing; bin packing; Heuristics

Funding

  1. Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior {Brasil (CAPES)}
  2. Brazilian National Council for Scientific and Technological Development (CNPq)
  3. Foundation for Support of Research of the State of Minas Gerais, Brazil (FAPEMIG)
  4. Fundep

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In the integrated uncapacitated lot sizing and bin packing problem, decisions regarding replenishment from suppliers and delivery of client orders need to be coupled to minimize total costs. Proposed methods including mixed integer linear programming formulations and heuristics efficiently achieve small optimality gaps in reduced computational times.
In the integrated uncapacitated lot sizing and bin packing problem, we have to couple lot sizing decisions of replenishment from single product suppliers with bin packing decisions in the delivery of client orders. A client order is composed of quantities of each product, and the quantities of such an order must be delivered all together no later than a given period. The quantities of an order must all be packed in the same bin, and may be delivered in advance if it is advantageous in terms of costs. We assume a large enough set of homogeneous bins available at each period. The costs involved are setup and inventory holding costs and the cost to use a bin as well. All costs are variable in the planning horizon, and the objective is to minimize the total cost incurred. We propose mixed integer linear programming formulations and a combinatorial relaxation where it is no longer necessary to keep track of the specific bin where each order is packed. An aggregate delivering capacity is computed instead. We also propose heuristics using different strategies to couple the lot sizing and the bin packing subproblems. Computational experiments on instances with different configurations showed that the proposed methods are efficient ways to obtain small optimality gaps in reduced computational times.

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