The optimal control of batched production and its effect on demand amplification

We review the control theoretic approaches made to solving aggregate production–inventory problems, highlighting some of their common failings. One of these is the inability to realistically model batch production costs. By applying a novel optimal control algorithm to a differential equation model of a production–inventory system we successfully mimic these cost structures and find optimal responses to fluctuations in demand. We then examine how the various penalty costs qualitatively affect the response of the system. The second part of the paper deals with the supply chain phenomenon of demand amplification, the tendency of small fluctuations in demand at the retailer end of the supply chain to be amplified as they are communicated down the chain. By considering our production–inventory system to be part of a supply chain we examine the effect of batch sizes on demand amplification under the assumption of the rational behaviour of supply chain players.