A multi-stage joint economic lot size model with lead time penalty costs

•We study a multi-stage supply chain with penalty costs for long lead times.•Performance of a stage is strongest related to first-tier customers and first-tier suppliers.•The allocation of transportation costs in the chain only has a minor influence on total costs.•Lead time can be reduced by sorting the production capacities of the stages in a descending order.

This paper studies the case of a multi-stage supply chain where equal- and unequal-sized batches are transported between the stages and where penalty costs are imposed for long lead times. Unlike earlier works, this paper does not restrict the number of stages to a given value, but rather analyses a general case of the model. First, an analytical model of the supply chain is developed and the properties of the model are discussed. Secondly, a simulation study is conducted to analyse the behaviour of the model. The results of our analysis indicate that the performance of upstream stages of the supply chain is more critical to the performance of the supply chain than the performance of downstream stages. Furthermore, our findings show that a supply chain stage may improve its position significantly by coordinating its behaviour with its direct neighbours in the supply chain.