Beyond the Harris’ model to optimally define lot sizes in a Make-to-Stock multi-line production system

Since 1913, the Harris’ model is adopted within intermittent production systems to size the batches to produce and purchase. For each product, the model sets the so-called Economic Order Quantity (EOQ) as the quantity optimally trading-off the cost of orders and the average stock cost. Traditionally, the EOQ from the Harris’ model is a milestone for make-to-stock (MTS) production systems. In addition, existing extensions of the base model are in the direction of including multiple actors of the supply chain, i.e. joint economic lot size, and tailored product management policies, i.e. consignment stock. A basic hypothesis behind the lot size models is that the production line productivity is higher than the average market demand so that a dynamic equilibrium becomes feasible. Nevertheless, in the case of permanent or temporary high product request, the productivity of a single production line can be insufficient. This case makes of interest the adoption of multi-line production systems. Such systems are made of parallel production lines able to produce the same product at the same final qualitative standards so that the output is a unique batch of identical products. This paper investigates MTS multi-line systems presenting two formulations of the EOQ model for the case of identical lines (1) and the case of lines with different productivity and setup cost (2). Finally, an application of the model is done with data taken from a leading company operating in the beverage packaging sector.