We investigate a lean inventory sharing strategy, called “Circular Bidirectional Chaining” (BDC), in a single period setting, and quantify the difference between the performance of BDC and the performance of other inventory sharing strategies for normally distributed demands. Under BDC all the locations, each facing stochastic demand, are connected in a closed loop, such that each location is allowed to cooperate laterally with exactly two adjacent locations. A location is not allowed to serve as a source and a sink of material at the same time. To consider BDC vis-à-vis other strategies, one must first optimize the proposed BDC strategy. Managing the BDC consists of two problems: determining the optimal order quantities, and, for given order quantities and demand realizations, determining how should items be transshipped. The former is a stochastic planning problem with recourse, solved via simulation-based optimization, while the latter, which is the recourse part of the former, can be interpreted as a transportation problem. Sensitivity analysis with respect to problem parameters is provided. It turns out that BDC can achieve a considerable portion of the benefits of complete pooling in around 65% of the cases, while the cost required to enable cooperation via BDC is lower than that of complete pooling.