In an emerging trend in the grocery industry, multiple suppliers and retailers share a warehouse to facilitate horizontal collaboration, in order to lower transportation costs and increase outbound delivery frequencies. Typically, these systems (sometimes known as Mixing and Consolidation Centers) are operated in a decentralized manner, with little effort to coordinate shipments from multiple suppliers with shipments to multiple retailers. Indeed, implementing coordination in this setting, where potential competitors are using the same logistics resources, could be very challenging. In this thesis, we characterizes the loss due to this decentralized operation, in order to develop insight into the value of making the extra effort and investment necessary to imple- ment some form of coordinated control. To do this, we consider a setting where several suppliers ship to several retailers through a shared warehouse, so that outbound trucks from the warehouse contain the products of multiple suppliers. We extend the classic one warehouse multi-retailer analysis of Roundy (1985) to incorporate multiple suppli- ers and per truck outbound transportation cost from the warehouse, and develop a cost lower bound on centralized operation as benchmark. We then analyze decentralized versions of the system, in which each retailer and each supplier maximizes his or her own utility in a variety of settings, and we analytically bound the ratio of the cost of decentralized to centralized operation, to bound the loss due to decentralization. We find that easy-to-implement decentralized policies are efficient and effective in this set- ting, suggesting that centralization (and thus, coordination effort intended to lead to some of the benefit of centralization) does not bring significant benefits. In a compu- tational study, we explore how system parameters impact the relative performance of this system under centralized and decentralized control. Finally, we consider a stochas- tic version of this model of decentralized collaboration, where we assume independent Poisson demand occurs at each retailer for all products. To coordinate replenishment, each retailer follows an aggregate (Q,S) policy, i.e., an order is placed to raise inventory position to S whenever total demand since the last order at that retailer reaches Q.

In this setting demand at the warehouse can be well-approximated by a compound Poisson process, and thus inventory at the warehouse is managed via an (s,S) policy. We develop optimal and heuristic algorithms to optimize parameter settings in this model.