5. Conclusions This paper considere

5. Conclusions
This paper considered postal logistics network design with realistic restrictions. We developed mathematical models for hybrid hub-and-spoke postal logistics network designs by considering the transportation network and vehicle operations with realistic restrictions. We considered 24 MPCs and one or more ECs, and we used real data (e.g., distance data, mail-received data, maildelivered data, and transportation rate data) by simultaneously considering the locations and allocations. The mathematical models have been coded and solved by ILOG OPL Development Studio 5.5 with the ILOG CPLEX 11.0 engine. The computational times of all of the models were less than about 10 s. The computational experiments demonstrate the usefulness of the mathematical models that were developed. Moreover, the proposed scenarios are very useful in decision making for postal logistics network designers and operators. The network problem occurs in postal logistics is more complex and diverse than that for general logistics. Moreover, the amount of data is enormous which makes the decision makers difficult to design the network. It was impossible to compute the restrictions on vehicle capacity, assignment of vehicles in accordance with transportation rates, and delivery quantities to each EC (Exchange Center) manually. If one uses our model for postal logistics, one can easily design the optimal network for the existing facilities. Moreover, one can use this 0 10 20 30 40 50 60 70 10,235 10,240 10,245 10,250 10,255 10,260 10,265 10,270 10,275 123456 Number of vehicles (MPCs-ECs) Number of vehicles (MPCs-MPCs) Scenarios # of vehicles (MPCs-MPCs) # of vehicles (MPCs-ECs) Fig. 8. Comparison of the number of vehicles traveling MPCs–MPCs and MPCs–EC. 5518 J.-H. Lee, I. Moon / Expert Systems with Applications 41 (2014) 5509–5519 model to design the optimal network to minimize total costs by observing facility capacities and various practical restrictions when new ECs are being constructed. In addition, the models can be applied to the multi-item supply chain and to parcel delivery service companies and, in general, can also be applied to develop robust solutions in uncertain and dynamic decision situations. Further studies can explore several different directions. First, we may develop an integrated mathematical model that considers D&PSs and all types of mail. Second, we can develop a user-friendly decision support system that applies the developed mathematical models. Third, we can develop a simulation model by changing some parameters into random variables. Fourth, we may consider other objective functions, such as service time, service level, and the mail processing rate. Acknowledgements The authors are grateful for the useful comments from two anonymous referees. This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. 2012R1A2A2A01012355).