Mixed Reserve Decisions For Emergency Supplies

Ensuring sufficient emergency supplies is the key to an effective response to potential sudden events.Emergency management organizations in many countries keep physical stocks,which can be directly accessed.However,due to objective factors such as the perishable nature of emergency supplies and the uncertainty of sudden events,physical stocks only are not suitable for responding to sudden events.In practice,the expiration of supplies due to excess reserves or the shortage of supplies due to insufficient reserves has become a huge challenge for governments.Although it has become a consensus among academia,industry,and government authorities to build a reserve system that combines multiple reserve methods of emergency supplies,most existing studies still focus on reserving physical stocks of emergency supplies and ignore the mixed reserve decision problem that combines multiple reserve methods.Therefore,it is of great theoretical and practical significance to study the mixed reserve decisions of emergency supplies.This dissertation explores the mixed reserve decisions of emergency supplies under multiple scenarios.First,considering that the current research on the mixed reserve decisions mainly focuses on the physical stock and production capacity reserve for the single product,while the emergency management often involves the joint reserves of multiple supplies,this dissertation explores the "mixed reserve decisions of physical and production capacity for emergency supplies";then,based on the practical situation that Chinese cities mainly hold their emergency supplies in physical stocks and capital reserves,this dissertation explores the "mixed reserve decisions of physical and capital for emergency supplies";next,in order to overcome the disadvantages of each of the three reserve methods,this dissertation explores the "mixed reserve decisions of physical,production capacity and capital for emergency supplies";finally,considering social donation as an important source of supplying emergency supplies,this dissertation explores the "mixed reserve decisions for emergency supplies considering social donations".This dissertation can provide theoretical support and decision-making tools for relevant government departments to scientifically determine the mixed reserve decisions for emergency supplies.Specifically,the main contents and results of this dissertation are as follows:(1)First,this dissertation considers the scenario of joint reserves of multiple emergency supplies.We establish a mixed reserve model of physical and production capacity,and derive the optimal reserve strategy and corresponding closed-form solution for each supply.Further,considering that physical stocks are always constrained by the budget in practice,we establish a mixed reserve model with the budget constraint for physical stocks,and obtain the combination of strategies for multiple supplies.We also develop a solution algorithm to solve the model with a budget constraint for physical stocks by the binary method.By comparing the optimal reserve strategy for physical stocks with and without a budget constraint,this dissertation finds that once a certain threshold for the physical stock budget is passed,the budget constraint is not binding and the optimal solution is the same as the solution to the no-budget constraint for physical stocks.This dissertation also finds that the presence of the physical reserve budget constraint suppresses the effect of the cost parameter on the optimal physical stock level and amplifies the effect on the optimal reserve capacity production rate,but also amplifies the effect on the expected long-term average cost,and an appropriate increase in the physical stock budget is beneficial for improving the reserve efficiency for emergency supplies.(2)Second,based on the fact of emergency reserve management in China,this dissertation takes physical stock and capital reserve as the research objects,and focuses on the following questions: i)What is the optimal mixed reserve strategy of physical and capital before the outbreak? ii)How to deploy physical stocks and capital reserves during the emergency relief phase? iii)How to reasonably adjust physical stocks and capital reserves when the key characteristics change? This dissertation establishes a mixed reserve model of physical and capital,and a procurement and deployment model during the emergency relief phase.We derive the optimal mixed reserve strategy and deployment strategy of physical and capital.Through sensitivity analysis,this dissertation finds that the optimal capital reserve level always increases with the uncertainty of demand,but the optimal physical stock level may decrease with it.This dissertation also finds numerically that capital reserves become more cost-effective than physical stocks once the penalty cost exceeds a certain threshold.In addition,the cost savings from capital reserves can indeed be substantial and effective.(3)Third,considering that it is difficult for the government to effectively respond to the disaster by relying only on a single reserve method or a combination of two reserve methods in practice,this dissertation further explores the mixed reserve decisions of three reserve methods: physical,production capacity and capital.We derive the optimal reserve strategies in closed form and their boundary conditions.Accordingly to the characteristics of different kinds of emergency supplies,the corresponding reserve strategy is suggested through the sensitivity analysis: for diet security supplies,e.g.food,and mineral water,the production capacity reserve should be increased appropriately to cope with the increase in the emergency purchase price;for medicines with short shelf life and narrow scope of indications,the capital reserve should be increased as a priority;for medical protective equipment and daily necessities,e.g.masks,protective clothing,and tents,the physical stock is more important than the production capacity reserve and capital reserve.The numerical studies further show that the total reserve level of emergency supplies increases with the probability of sudden events as long as building reserves,while the optimal production capacity and capital reserve levels may decrease with the probability.(4)Forth,since the social donation is an important source of emergency supplies in the rescue practices,this dissertation establishes a mixed reserve model of three reserve methods considering social donations.We characterize the different sudden events in the model by using the probability of sudden events,the demand distribution of supplies,and the social donation quantity.After theoretical and numerical studies,we find that improving the ability of processing donated supplies and social mobilization can not only improve the timeliness of emergency response,but also be critical to reducing the reserve cost of emergency supplies,especially when responding to the sudden events with higher intensity.Moreover,owing to the great uncertainty of the social donation quantity,this dissertation also establishes a mixed reserve model of emergency supplies considering random donations.We determine the set of implicit functions for the optimal solution.Through numerical studies,we find that the total reserve level of emergency supplies increases slightly with the uncertainty of donation quantity,and the government would increase the capital reserves to migrate the negative effect of uncertainty of donation quantity.The main innovations of this dissertation are as follows:(1)This dissertation proposes a mixed reserve model of physical and production capacity for multiple items,which makes up for the shortage of current research on mixed reserve only for a single product.This dissertation characterizes the production capacity reserve through the reserve capacity production rate,enriching the related research on production capacity reserve in the field of emergency management.(2)This dissertation explores the reserve,procurement,and deployment problem of emergency supplies in a comprehensive way,and establishes the mixed reserve model of physical and capital,as well as the procurement and deployment model over the emergency relief phase.This dissertation overcomes the current limitations of the lack of a theoretical basis for quantifying capital reserves.(3)This dissertation develops the mixed reserve model of three methods of emergency supplies,which could narrow the research gaps that there are only qualitative descriptions and quantitative studies on partial reserve methods,and expand the quantitative research in the field of emergency supplies reserve.(4)This dissertation considers the social donations of emergency supplies and the multiple potential sudden events over the reserve cycle,and establishes a mixed reserve model of three methods of emergency supplies considering social donations,which fills a gap in current quantitative research on social donation,especially the lack of research on how social donation impacts the mixed reserve decisions.The research findings can provide decision-making guidelines for relevant government departments to better manage emergency supplies reserves.