This thesis consists of two essays. The first essay is on capacity pooling and cost sharing among independent firms in the presence of congestion. We analyze the benefit of production/service capacity sharing for a set of independent firms. Firms have the choice of either operating their own production/service facilities or investing in a facility that is shared. Facilities are modeled as queueing systems with finite service rates. Firms decide on capacity levels (the service rate) to minimize delay costs and capacity investment costs possibly subject to service level constraints. If firms decide to operate a shared facility they must also decide on a scheme for sharing the costs. We formulate the problem as a cooperative game and identify a cost allocation that is in the core. The allocation rule charges every firm the cost of capacity for which it is directly responsible, its own delay cost, and a fraction of buffer capacity cost that is consistent with its contribution to this cost. In settings where unit delay costs are private information, the cooperative capacity sharing game becomes embedded with a non-cooperative information reporting game. We show how a cost allocation rule can be designed to induce all firms to report truthfully this information. Moreover, we show that, under this allocation rule, truth telling is a dominant strategy, with each firm reporting truthfully its private information regardless of the reporting decisions of other firms.
The second essay is on a customer-item decomposition approach to inventory problems. We consider inventory systems with periodic review, correlated, non-stationary stochastic demand and correlated, non-stationary stochastic and sequential leadtimes. We treat systems with both single and multiple stages. We use the customer-item decomposition approach to decompose the associated inventory control problem into sub-problems, each involving a single customer-item pair. We then formulate each subproblem as an optimal stopping problem. We use properties that arise from this formulation to show that the optimal policy is a state-dependent base-stock policy and to show, for the case of positive demand, that the optimal policy can be obtained via an algorithm whose complexity is polynomial in the length of the planning horizon. We also use the formulation to construct myopic heuristics which lead to explicit solutions for the optimal policy in the form of a critical fractile. We characterize conditions under which the myopic heuristics are optimal. We show how the results can be extended to systems with advance demand information and batch ordering.