On EOQ cost models with arbitrary purchase and transportation costs

Ş. İlker Birbil; Kerem Bülbül; J. B. G. Frenk; H. M. Mulder

doi:10.3934/jimo.2015.11.1211

Article Contents

2015, Volume 11, Issue 4: 1211-1245. Doi: 10.3934/jimo.2015.11.1211

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On EOQ cost models with arbitrary purchase and transportation costs

1.
Sabanci University, Manufacturing Systems and Industrial Engineering, Orhanli-Tuzla, 34956 Istanbul
2.
Manufacturing Systems and Industrial Engineering, Sabancı University, Istanbul
3.
Erasmus University Rotterdam, Postbus 1738, 3000 DR Rotterdam

Received: June 30, 2013

Revised: August 31, 2014

Published: September 2015

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Abstract

We analyze an economic order quantity cost model with unit out-of-pocket holding costs, unit opportunity costs of holding, fixed ordering costs, and general purchase-transportation costs. We identify the set of purchase-transportation cost functions for which this model is easy to solve and related to solving a one-dimensional convex minimization problem. For the remaining purchase-transportation cost functions, when this problem becomes a global optimization problem, we propose a Lipschitz optimization procedure. In particular, we give an easy procedure which determines an upper bound on the optimal cycle length. Then, using this bound, we apply a well-known technique from global optimization. Also for the class of transportation functions related to full truckload (FTL) and less-than-truckload (LTL) shipments and the well-known carload discount schedule, we specialize these results and give fast and easy algorithms to calculate the optimal lot size and the corresponding optimal order-up-to-level.

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Mathematics Subject Classification: Primary: 90B05, 90B06; Secondary: 90C26, 46N10.

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