In a two-stage serial supply chain, Periodic Flexible (PF) policies can reduce the inefficiency due to decentralization by as much as 43%. Existing literature has mostly defined and implemented ad-hoc periodic flexible policies and has not attempted to identify the optimal periodic flexible policies. In this paper, we demonstrate a general way to find the optimal PF policies through an example of periodic flexible policies of length two. In particular, we show that under the optimal policy, the retailer follows a state dependent capacitated policy or a state dependent order upto policy. Furthermore, we can approximate the optimal restricted ordering function by a piecewise linear function. Numerical examples illustrate that the optimal PF(2) policies are able to reduce the total supply chain cost by as much as 13%. The linear approximation is effective with an average error of less than 1%.
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