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October  2015, 11(4): 1211-1245. doi: 10.3934/jimo.2015.11.1211

## 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, Turkey 3 Erasmus University Rotterdam, Postbus 1738, 3000 DR Rotterdam, Netherlands

Received  July 2013 Revised  September 2014 Published  March 2015

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.
Citation: Ş. İlker Birbil, Kerem Bülbül, J. B. G. Frenk, H. M. Mulder. On EOQ cost models with arbitrary purchase and transportation costs. Journal of Industrial & Management Optimization, 2015, 11 (4) : 1211-1245. doi: 10.3934/jimo.2015.11.1211
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