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Keywords:

  • optimal lot-size;
  • batch-storage network;
  • backlogging cost;
  • lost sales cost

Product shortages, which cause backlogging and/or lost sales costs commonly occur in the chemical industries, especially in the commodity polymer business. Shortage costs in a supply chain optimization model are studied under the framework of a generalized batch-storage network. A classical economic order quantity model with backlogging costs suggested an optimal time delay and final product delivery lot size. A product shortage can be mitigated by advancing production/transportation or by purchasing a substitute product from a third party as well as by a product delivery delay in the supply chain network. Optimal solutions that consider all means for recovering shortage are more complicated than the classical case. Four solutions are identified depending on the parametric range and variable bounds. The optimal capacity for production/transportation processes associated with a product in shortage can differ from that of a product not in shortage. An illustrative example is presented in support of the analytical results. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2454–2470, 2013