Bullwhip and batching: An exploration

The rounding of orders to achieve a batch size is recognised as a source of the bullwhip problem within supply chains. While it is often advocated that batch sizes should be reduced as much as possible, there has been limited investigation into the impact of batching on bullwhip. Here we consider scenarios where orders are placed only in multiples of a fixed batch size, for both deterministic and stochastic demand rates. By manipulating mathematical equations, we derive a closed form expression for bullwhip when demand is deterministic. This is validated through a simple model of a production control system. An expression for bullwhip in a pass on orders scenario with stochastic demand is also derived and validated. Using simulation, we show the impact of changing batch size on bullwhip in a production control system. Our results show that a manager may achieve economies through batching while minimising the impact on bullwhip through the careful selection of the batch size.