Table 3.3 Total distance for
the three modes C subset R subset RC subset
PTP mode 848.393 986.365 654.8171
MMTS mode 352.8543 581.8270 311.9578 Mixed mode 477.8886 665.5658 395.03989
Table 3.4 Total timeliness
for the three modes C subset R subset RC subset
PTP mode 1 1 1
MMTS mode 0.8264 0.6310 0.8602
Mixed mode 0.9393 0.8478 0.9188
diction between these two pure modes can be equilibrated in the mixed-collaborative mode. For instance, the total average of the timeliness in the MMTS mode is merely 77.3%. To the three subsets C, R and RC, when the mixed-collaborative mode is adopted, the total distance is respectively increased by 14.7, 8.49 and 12.7%, as compared to the MMTS mode (Table3.3). However, the total timeliness is respec- tively improved by 11.29, 21.68 and 5.86% (Table3.4), which makes the total aver- age of the timeliness in the mixed-collaborative mode 90.2%, and achieves a 12.9%
improvement compared to the MMTS mode. This will be a much more appropriate solution for the actual relief activities.
As introduced in Sect.3.3.1, emergency distribution in an anti-bioterrorism system is more complex, and differs from business logistics. Computational experiments and result analysis in this section show that the mixed-collaborative distribution model is expected to be an effective decision-making tool when a bioterror attack is suffered.
Both of the two problems have been solved by such a mixed-collaborative method.
Therefore, this method can be adopted by the emergency command center, and the traditional emergency distribution planning based on the decision makers’ experience would be improved.
(2) As both of these two pure distribution modes may be infeasible in a real-life situation, we propose a mixed-collaborative mode, which can equilibrate the contradiction between these two pure modes. To verify the validity and the feasibility of the mixed-collaborative mode, we compare it with the two pure distribution modes from both aspects of distance and timeliness.
(3) To facilitate the comparison process, we propose a relative measure method of timeliness for the different distribution modes.
Besides, we offer a newly modified GA for solving the problems. To obtain more accurate results, we can increase the number of generations and the population size so as to expand the coding scale and search the optimization solution in a larger space.
It’s also necessary to point out some limitations of this research. First of all, the programming models in this chapter are discrete, and do not consider that emergency resources distributed at an earlier stage will affect the demand later. Second, only homogeneous vehicle and hard time windows are considered in this chapter, which limits the practical implications of the method. Third, we assume that the infected area can be isolated from other areas to avoid the spread of the disease. Actually, this is very difficult. All these areas of improvement represent our future research directions.
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Chapter 4
Epidemic Logistics with Demand
Information Updating Model I: Medical Resource Is Enough
In this chapter, we present a discrete time-space network model for allocating med- ical resource following an epidemic outbreak. It couples a forecasting mechanism for dynamic demand of medical resource based on an epidemic diffusion model and a multi-stage programming model for optimal allocation and transport of such resource. In this chapter, we present a discrete time-space network model for allo- cating medical resource following an epidemic outbreak. It couples a forecasting mechanism for dynamic demand of medical resource based on an epidemic diffusion model and a multi-stage programming model for optimal allocation and transport of such resource. At each stage, the linear programming solves for a cost minimizing resource allocation solution subject to a time-varying demand that is forecasted by a recursion model. The rationale that the medical resource allocated in early periods will take effect in subduing the spread of epidemic and thus impact the demand in later periods has been incorporated in such recursion model. We compare the pro- posed medical resource allocation mode with other operation modes in practice, and find that our model is superior to any of them in less waste of resource and less logis- tic cost. The results may provide some practical guidelines for a decision-maker who is in charge of medical resource allocation in an epidemics control effort.