The impact of lot-sizing in multiple product environments with congestion

• We consider a multiproduct dynamic lot sizing model in the presence of queueing behaviour.
• Setup costs are not required as the capacity implications of setups are directly captured in the model.
• Approximately optimal solutions are obtained and compared to a conventional lot sizing model without congestion.
• Proposed model yields significantly better cycle time and WIP performance than conventional models.

We present a production planning model for a multiple product single machine dynamic lot-sizing problem with congestion. Using queuing models, we develop a set of functions to capture the nonlinear relationship between the output, lot sizes and available work in process inventory levels of all products in the system. We then embed these functions in a nonlinear optimization model with continuous variables, and construct an approximate solution to the original problem by rounding the resulting fractional solution. Computational experiments show that our model with congestion provides significantly better flow time and inventory performance than a benchmark model that does not consider the effects of congestion. These advantages arise from the use of multiple smaller lots in a period instead of a single large lot as suggested by conventional fixed-charge models without congestion.