دانلود رایگان مقاله مدل فرایند تصمیم گیری مارکوف برای توزیع عادلانه عرضه در شرایط عدم قطعیت

abstract

 Many individuals suffering from food insecurity obtain assistance from governmental programs and nonprofit agencies such as food banks. Much of the food distributed by food banks come from donations which are received from various sources in uncertain quantities at random points in time. This paper presents a model that can assist food banks in distributing these uncertain supplies equitably and measure the performance of their distribution efforts. We formulate this decision problem as a discrete-time, discrete state Markov decision process that considers stochastic supply, deterministic demand and an equity-based objective. We investigate three different allocation rules and describe the optimal policy as a function of available inventory. We also provide county level estimates of unmet need and determine the probability distribution associated with the number of underserved counties. A numerical study is performed to show how the allocation policy and unmet need are impacted by uncertain supply and deterministic, time-varying demand. We also compare different allocation rules in terms of equity and effectiveness.

6.2. Future work

Irrespective of the work that has been done in this paper, there is still room for improvement. The model could be extended to all other branches in the FBCENC network to study branch to branch variability. One may model the donation and transfer-in with other probability distributions and analyze the associated prediction errors. Likewise, another parameter such as transfer-out can also be added and modeled, perishable items can be considered since this research only investigated the case of dry goods. Warehouse capacity constraints can also be investigated to see how that may affect the optimal policy. Furthermore, a continuous state Markov decision process can be investigated to avoid discretization and the errors that may be associated with it. We also know that in practice, while the proportional allocation rule may be optimal to achieve perfect equity, there are other constraints not incorporated in the model that may make this difficult to achieve. For example, as mentioned in Orgut et al. (2015), capacity constraints at the agency level may cause deviations from equity which cannot be avoided. In our work, we have not considered capacity constraints at the agencies. The incorporation of capacity and supply constraints is an interesting area of future research.