Deakin University

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

conference contribution
posted on 2013-01-01, 00:00 authored by Asef NazariAsef Nazari, Simon Dunstall, Andreas T Ernst
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.



Modelling and Simulation Society of Australia and New Zealand. Congress (20th : 2013 : Adelaide, S. Aust.)


Modelling and Simulation Society of Australia and New Zealand Congress


57 - 63


Modelling and Simulation Society of Australia and New Zealand


Adelaide, S. Aust.

Place of publication

Canberra, A.C.T.

Start date


End date






Publication classification

E1.1 Full written paper - refereed

Copyright notice

2013, MSSANZ


J Piantadosi, R Anderssen, J Boland

Title of proceedings

MODSIM2013 : Adapting to change: the multiple roles of modelling : Proceedings of the 20th International Congress on Modelling and Simulation