Integrating transportation and inventory decisions in multi-warehouse multi-retailer system with stochastic demand

Two major cost components in distribution system are inventory and transportation cost. For convenience, the inventory and transportation decisions are determined as two disjointed decisions which result in a high system total cost. Unifying these two decisions can lead to reduction in the system total cost.; This dissertation considers the problem of multiple capacitated warehouses supplying multiple retailers with stochastic demand. Its purpose is to develop analytical models and solution approaches for optimizing a commodity flow in a distribution system under uncertain demand based on the sum of inventory and transportation costs. The research aims to establish improved decision-making methods that integrate inventory replenishing policy and transportation strategy.; The developed model formulation extends the simple single-period stochastic inventory problem (newsboy or newsvendor problem) to incorporate the transportation cost into the objective function. In addition, the capacity constraints are added to impose over-supplying at warehouses. Two forms of the transportation cost functions are considered: linear and fixed charge cost functions.; The Lagrange multiplier method is employed to solve the linear transportation cost model. This method works well only with small problems. In the fixed charge cost model, the dynamic slope scaling procedure (DSSP) is employed to develop the scenario-based heuristic. The DSSP is an effective and efficient approach to estimate an optimal solution to a fixed charge network flow problem. Based on a set of test problems, computational results show that the DSSP scenario-based heuristic obtains the solution in reasonable computational time. This obtained solution to the approximated problem (scenario-based model) is used to evaluate the true objective value in the original non-linear problem, which gives the upper bound to the original problem. Since the optimal solution to the original problem is unknown, the conclusion on the upper bound quality cannot be established. Alternatively, the gap between upper bound and lower bound can be used as a criterion. The best lower bound is obtained by the development of Lagrangian relaxation model. Computational experiments show that the performance of the DSSP heuristic is excellent, based on a set of test problems.; Finally, we improve the DSSP heuristic by employing the Lagrangian relaxation method to solve a linear transportation cost and eliminate scenario generating work. Based on a set of test problems, the Lagrangian relaxation-based heuristic provides a better solution in less computational time than the scenario-based heuristic.