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In this chapter, we present a discrete time-space network model for allocating 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. In this chapter, we present a discrete time-space network model for allocating 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 proposed 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 logistic 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.

In this chapter, we present two optimization models for optimizing the epidemic-logistics network. In the first one, we formulate the problem of emergency materials distribution with time windows to be a multiple traveling salesman problem. Knowledge of graph theory is used to transform the MTSP to be a TSP, then such TSP route is analyzed and proved to be the optimal Hamilton route theoretically. Besides, a new hybrid genetic algorithm is designed for solving the problem. In the second one, we propose an improved location-allocation model with an emphasis on maximizing the emergency service level. We formulate the problem to be a mixed-integer nonlinear programming model and develop an effective algorithm to solve the model. In this chapter, we present two optimization models for optimizing the epidemic-logistics network. In the first one, we formulate the problem of emergency materials distribution with time windows to be a multiple traveling salesman problem. Knowledge of graph theory is used to transform the MTSP to be a TSP, then such TSP route is analyzed and proved to be the optimal Hamilton route theoretically. Besides, a new hybrid genetic algorithm is designed for solving the problem. In the second one, we propose an improved location-allocation model with an emphasis on maximizing the emergency service level. We formulate the problem to be a mixed-integer nonlinear programming model and develop an effective algorithm to solve the model.

This chapter presents a dynamic logistics model for medical resources allocation that can be used to control an epidemic diffusion. It couples a forecasting mechanism, constructed for the demand of a medicine in the course of such epidemic diffusion, and a logistics planning system to satisfy the forecasted demand and minimize the total cost. The forecasting mechanism is a time discretized version of the SEIR model that is widely employed in predicting the trajectory of an epidemic diffusion. The logistics planning system is formulated as a mixed 0–1 integer programming problem characterizing the decision-making at various levels of hospitals, distribution centers, pharmaceutical plants, and the transportation in between them. The model is built as a closed-loop cycle, comprising forecast phase, planning phase, execution phase, and adjustment phase. The parameters of the forecasting mechanism are adjusted in reflection of the real data collected in the execution phase by solving a quadratic programming problem. A numerical example is presented to verify efficiency of the model.

This chapter is a continuous work of Chap. 6. In this chapter, a three-level and dynamic linear programming model for allocating medical resources based on epidemic diffusion model is proposed. The epidemic diffusion model is used to construct the forecasting mechanism for dynamic demand of medical resources. Heuristic algorithm coupled with MATLAB mathematical programming solver is adopted to solve the model. A numerical example is presented for testing the model’s practical applicability. The main contribution of the present study is that a discrete time-space network model to study the medical resources allocation problem when an epidemic outbreak is formulated. It takes consideration of the time evolution and dynamic nature of the demand, which is different from most existing researches on medical resources allocation. In our model, the medicine logistics operation problem has been decomposed into several mutually correlated sub-problems, and then be solved systematically in the same decision scheme. Thus, the result will be much more suitable for real operations. Moreover, in our model, the rationale that the medical resources allocated in early periods will take effect in subduing the spread of the epidemic spread and thus impact the demand in later periods has been for the first time incorporated. A win-win emergency rescue effect is achieved by the integrated and dynamic optimization model. The total rescue cost is controlled effectively, and meanwhile, inventory level in each urban health departments is restored and raised gradually.

Generally, medicine order and delivery are operated based on the previous experiences. First of all, estimating the average annual demands of hospital storage center. Second, planning a medical goods order and delivery schedule based on the annual average demands as well as establishing the period of ordering and delivering. Third, in the process of operating, medical system supplies goods according to the re-order point and safe stock. In this chapter, we propose three time-space network models for medicine order and shipment, which may help improve the effectiveness when managing the medicine in hospitals.

In this chapter, we construct a unique forecasting model for the demand of emergency resources based on the epidemic diffusion rule when suffering a bioterror attack. In what follows, we focus on how to deliver emergency resources to the epidemic areas. We find that both the pure point-to-point delivery mode and the pure multi-depot, multiple traveling salesmen delivery system are difficult to operate in an actual emergency situation. Thus, we propose a mixed-collaborative distribution mode, which can equilibrate the contradiction between these two pure modes. A special time window for the mixed-collaborative mode is designed. A genetic algorithm is adopted to solve the optimization model. To verify the validity and the feasibility of the mixed-collaborative mode, we compare it with these two pure distribution modes from both aspects of total distance and timeliness.

Medical resources scheduling affects the medical institution’s operation cost, customer satisfaction and medical service quality. Therefore, a lean arrangement of medical resources order and shipment is quite necessary and important. In this chapter, we propose two optimal models for medical resources order and shipment in community health service centers (CHSCs), with a dual emphasis on minimizing the total operation cost and improving the operation level in practice. The first planning model is a deterministic planning model (DM). Systematically, it considers constraints including the lead time of the suppliers, the storage capacity of the medical institutions, and the integrated shipment planning in the dimensions of time and space. The problem is a multi-commodities flow problem and is formulated as a mixed 0–1 integer programming model.

CANDU6 reactor power control programs include flux mapping programs and reactor power regulation programs. For reactor power control, the step of reactor power set point change is redoubled as the step is calculated by the slow program and executed by the fast program; this affects the reactor power control precision. For flux mapping, due to logic error and inappropriate initial setting, failure of a single flux signal may result into a wide range of signals reporting failure, or overflow at specific reactor power levels. This paper studies the causes of these problems and correspondent improvements made to solve these problems.