Container packing problem for stochastic inventory and optimal ordering through integer programming

Asef Nazari, Simon Dunstall, Andreas T Ernst

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review


A supplier to a major manufacturing company is trying to cope with a probabilistic inventory management problem that has stochasticity in demand, material consumption rate, delivery times and other logistics-related parameters. Based on the specialized nature of the finished goods, the input materials are imported from Asia and carried in refrigerated containers that are subject to size and weight limits. The material should be used within a few weeks of receipt; otherwise the rate of manufacturing faults increases drastically. Unsatisfied demand (stockout) can be recovered expensively through the use of air transportation. The stochastic inventory problem with variable demand and lead time along with the optimal packing of containers are modelled as a stochastic optimisation problem. The solution to this problem expresses the optimal order size for raw materials considering all the stochasticities and other logistic limitations by minimizing the expected cost of stockout and over-supply. In addition, the optimal packing of pallets of raw materials into the containers is calculated simultaneously. In this paper, along with the modeling of the probabilistic inventory problem,we develop integer programming models for the optimal container loading and compare the numerical outputs.
Original languageEnglish
Title of host publicationMODSIM2013, 20th International Congress on Modelling and Simulation
EditorsJ Piantadosi, R S Anderssen, J Boland
Place of PublicationCanberra ACT Australia
PublisherModelling and Simulation Society of Australia and New Zealand (MSSANZ)
Number of pages7
ISBN (Electronic)9780987214331
Publication statusPublished - 2013
Externally publishedYes
EventInternational Congress on Modelling and Simulation 2013: Adapting to Change: the multiple roles of modelling - Adelaide Convention Centre, Adelaide, Australia
Duration: 1 Dec 20136 Dec 2013
Conference number: 20th


ConferenceInternational Congress on Modelling and Simulation 2013
Abbreviated titleMODSIM 2013
Internet address


  • Integer programming
  • stochastic optimisation
  • container packing
  • optimal ordering
  • stochastic inventory

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