A note on the joint economic lot size model with stochastic demand and variable lead time

This paper considers the problem of choosing optimal production policy in an integrated production‐inventory system comprising a single manufacturer and a single buyer. Two production scenarios are compared, namely continuous and lot‐for‐lot production policies, using a mathematical modelling approach and the expected total joint cost is considered as the performance measure. In addition, the lost opportunity cost due to production downtime in the lot‐for‐lot policy, including the cost of unemployment of human resources and stoppage of the production line, is incorporated into the model. Numerical experiment and sensitivity analysis in terms of setup and lost opportunity costs are provided to illustrate the theory and the percentage of difference in the expected total cost of the two policies is analysed. The presented approach helps managers to make the right decisions on the optimal production policy under different conditions, especially where expert and technical human resources and/or expensive production equipments are utilised.