Several extensions of the presented work are possible.
1. Infinite Horizon: As noted earlier, our focus in this dissertation is on the-oretical analysis of the optimal inventory and/or transportation policies with consideration of realistic transportation cost. All models investigated are over a finite horizon. Usually for a finite-period dynamic system, although the
poli-cies in different periods have the same structure, the parameters that define the policy can be very different from each other. However, for a supply chain system that needs to make frequent decisions over many time periods, it would be more convenient to have a stationary policy. Here, “stationary” means the policy parameters do not vary from period to period. Therefore, it is worth-while to show the optimality of the characterized policies in the infinite horizon discounted and average cost cases.
2. Solution Methods: Although the analytical results regarding the structure of the optimal policies have a theoretical value, to strengthen the practical contri-bution of this research, solution methods or algorithms for efficient calculation of the policy values need to be developed. It is known that the computational lim-itations on stochastic dynamic programming have made it very difficult to find the optimal values of the policy parameters, even if it is a conceptually power-ful technique. In addition, incorporation of time-windows, explicit consideration of general freight cost structures, and cargo capacity constraints increase the computational requirements for this class of problems. Therefore, designing a well-formed approximate algorithm is a possible future research avenue. When a solution method is available, the advantages of the optimal policy over those suboptimal, yet practical policies can also be evaluated.
3. Generalized Transportation Cost in Integrated Model: In Chapter V, the transportation cost is presented as the summation of a fixed setup cost and a linear variable cost. Clearly, this cost structure ignores the impact of transportation cost and capacity related to delivery of orders; thereby, also ignoring possible transportation scale economies achievable via optimization.
An interesting generalization is to investigate the transportation costs for single
or multiple capacitated trucks, or common carriage transportation in both the inbound and outbound logistics of the integrated replenishment and shipment model.
4. Multiple Items: It would also be of interest to consider multiple products that have different demand distributions, procurement costs (hence, different inventory holding costs), and customer waiting costs. As mentioned previously, shipment consolidation can be applied to combine orders of the same item or-dered by the customers at different time, or the orders of different items oror-dered at the same time (more accurately, during a sufficiently short period). In such a supply chain system, we need to consider the proper dispatch schedules to reduce the total cost of transportation and waiting.
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