This paper presents joint economic lot size (JELS) models under stochastic demand for single-vendor single-buyer system by synchronising ordering, production and raw material procurement cycles. We consider variable production rate and partial backorder in the proposed model. An iterative procedure is employed to determine simultaneously safety factor, delivery lot size, delivery frequency, production batch, raw material lot size and production rate for minimising total cost. We investigate the behaviour of the model with the use of numerical analysis. Our study indicates that considering variable production rate in the model results in lower total cost compared to the case where the production rate is assumed to be fixed. Our study also shows that the increase in demand uncertainty leads to higher total costs, but the buyer absorbed most of the increase. In addition, we also show that the minimum total cost is obtained when the shortages are fully, rather than partially, backordered.

Original languageEnglish
Pages (from-to)91-108
Number of pages18
JournalInternational Journal of Operational Research
Issue number1
Publication statusPublished - 2014


  • Inventory
  • JELS
  • Joint economic lot size
  • Supply chain
  • Variable production rate


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