تصمیم گیری موجودی برای تامین اضطراری بر اساس پیش بینی تعداد دفعات طوفان

This paper addresses a stochastic inventory control problem for manufacturing and retail firms who face challenging procurement and production decisions associated with hurricane seasons. Specifically, the paper presents a control policy in which stocking decisions are based on a hurricane forecast model that predicts the number of landfall hurricanes for an ensuing hurricane season. The multi-period inventory control problem is formulated as a stochastic programming model with recourse where demand during each pre-hurricane season period is represented as a convolution of the current period's demand and an updated estimate of demand for the ensuing hurricane season. Due to the computational challenges associated with solving stochastic programming problems, recent scenario reduction techniques are discussed and illustrated through an example problem. The proposed model specifies cost minimizing inventory strategies for simultaneously meeting stochastic demands that occur prior to the hurricane season while proactively preparing for potential demand surge during the season.

Planning inventories of supplies for the hurricane season can be challenging. For instance, in 2004, manufacturing and retail firms experienced stock-outs because they were not prepared for responding to the demand caused by several hurricanes that swept through southeastern United States. In 2005, these firms again experienced shortages due to the extreme demand surge caused by Hurricane Katrina. These experiences motivated firms to be pro-active and more aggressive in their approach to stocking hurricane supplies in 200. However, large amounts of excess inventory was commonplace because of an inactive season. This paper introduces stochastic programming methodologies to investigate proactive inventory planning for the hurricane season based on an expert hurricane count prediction model. Demand predictions for the hurricane season during the pre-hurricane season planning horizon are assumed to evolve according to a discrete-time Markov chain. The approach allows the inventory manager to adjust inventory decisions as new information regarding the hurricane season and realizations of pre-hurricane season demands are acquired. The stochastic inventory model is characterized by multiple periods before the hurricane season in which the inventory manager has the option to adjust the target inventory level of emergency supplies that should be available at the beginning of the ensuing hurricane season. During these pre-hurricane season months, manufacturing and retail organizations determine inventory levels that account for stochastic demands that occur during each period prior to the hurricane season as well as stochastic demand that will occur at the beginning of the season. The hurricane season demand predictions are revised at the beginning of each pre-hurricane season planning period, and these demand predictions are correlated to landfall hurricane count rate predictions. This multi-period stochastic inventory problem is formulated as a stochastic programming model. The solution specifies cost minimizing order/production quantities in which the decision-maker (DM) has flexibility to adjust the inventory policy based on updated hurricane season demand information and as pre-season demand realizations occur. The paper is organized as follows: In Section 2, related work from the academic literature is reviewed. In Section 3, the stochastic programming model is presented followed by a discussion of how demand scenarios are constructed, which also includes a description of the selected hurricane count prediction model. In Section 4, optimal and heuristic scenario reduction strategies are discussed and illustrated through numerical examples. Finally, in Section 5, the paper is summarized, and ideas for further research are presented.

This paper explores a stochastic inventory problem in which predictions associated with the ensuing hurricane's season demand distribution evolves according to a Markov chain. The states of the Markov chain represent predicted hurricane count rates for the ensuing season, and hurricane season demand forecasts are assumed to be proportional to these rates. The system is formulated as a multi-stage stochastic programming model with recourse. The underlying demand distribution is developed such that both the pre-hurricane season demand and the hurricane season demand are considered at each pre-hurricane season decision epoch. The demand distributions associated with each pre-hurricane season period are assumed to be known to the inventory manager at the beginning of the planning horizon. However, the hurricane season demand distribution is based on periodic information updating. The hurricane landfall count rate predictive probabilities, which are used to define the hurricane season demand distribution as a Markov chain, are estimated via a widely accepted hurricane prediction model developed by Elsner and Jagger (2004). From an academic perspective, the modeling approach presented in this paper is novel in that it accounts for information updates regarding the demand surge that will occur at the beginning of the season. It also accounts for demand uncertainties during each period prior to the season. This approach introduces the notion of reserving stock in a multi-period inventory problem with stochastic demands in anticipation of a possible demand surge in a future and terminal period. From a practitioner's perspective, the proposed model enables inventory managers to determine an appropriate stock level that should be available at the beginning of the hurricane season while simultaneously determining stock levels for pre-hurricane season demand periods. The model also allows production/procurement decisions to be altered as necessary during the planning horizon. A comparison of the results of our model to that of a basic stochastic programming model for multi-period inventory control suggests that cost savings can be realized in the long run. This can be achieved by reserving stock during the pre-season periods in preparation for the seasonal demand surge. This approach seems reasonable when inventory holding costs are inexpensive, procurement/production costs are increasingly expensive as the season approaches, and the demand surge during the season is significant. Under these circumstances, it is more beneficial to have large order/production quantities during the earlier periods and carry extra inventory than to have large quantities close to the beginning of the season. Further, it is better to keep low inventories during the early stages of the pre-season planning periods. In real-world applications, the stochastic demand process is likely to consist of many scenarios and/or stages. For these situations, the stochastic programming approach becomes less efficient and requires the implementation of other methodologies. In this paper, the scenario reduction approach introduced by Heitsch and Römisch (2003) is implemented to find the optimal set of scenarios to represent the underlying distribution. It is determined that the optimal scenario reduction method results in approximately 44% accuracy when at least half of the scenarios are removed. However, as the problem gets larger, the running time of the algorithm substantially increases. For future study, it would be beneficial to develop approximations of a demand process described by many scenarios through the implementation of the scenario generators. It is also worth exploring the quality of the reduced scenario model where the discrete demand process is represented by many scenarios. Additionally, a case can be developed in which a different demand distribution is introduced for each state. Finally, the existence of an optimal state-dependent base-stock policy can be investigated. These extensions would require additional modeling approaches and solution techniques. Although this paper is presented from the perspective of the profit driven private sector firm, seasonal prediction of hurricane landfalls is also of interest to government and service organizations. For example, military organizations and electric power companies often pre-position manpower and equipment in anticipation of a potential hurricane event. This pre-positioning decision also inherits the risk of over-preparation and under-preparation with respect to the demand induced by the hurricane event. Not-for-profit service organizations such as the American Red Cross face similar risks and decisions related to stocking and staffing evacuation shelters. The approach to demand forecasting presented in this paper seems to have potential for helping organizations make effective supply chain related decisions within the context of emergency supplies and hurricane seasons. In closing, perhaps the proposed modeling approach could be adapted to accommodate other kinds of predictable disasters such as floods and wildfire.