Abstract
This work considers the distribution of goods with stochastic shortages from factories to stores. It is assumed that in the process of shipping the goods to various stores, some proportion of the goods will be damaged (which will lead to shortage of goods in transit). The cost of the damaged goods is added to the cost of the shipment. A proportion of the total expected cost of the shortage goods is assumed to be recovered and should be deducted from the total cost of the shipment. In order to determine the minimum transportation costs for the operation, we adopt dynamic optimization principles. The optimal transportation cost and optimal control policies of shipping the goods from factories to stores were obtained. We find that the optimal costs of the goods recovered could be determined. It was further found that the optimum costs of distributing the goods with minimum and maximum error bounds coincide only at infinity.
Highlights
A distribution company plans to minimize the cost of distributing q kinds of products from m number of factories to n number of stores
We find that the optimal costs of the goods recovered could be determined
We have considered distribution of goods with stochastic shortages from factories to stores
Summary
A distribution company plans to minimize the cost of distributing q kinds of products from m number of factories to n number of stores. Powell and Van Roy [10] studied and applied approximate dynamic programming to high-dimensional resource allocation problems in area of managing a fleet of trucks. Cogill et al [13] considered the problem of computing decentralized policies for stochastic systems with finite state and action spaces They presented an algorithm based on linear programming and used this algorithm to obtain a decentralized policy from a function with special structure that approximates the optimal centralized Q-function. Ozbay et al [16] proposed mathematical programming models with probabilistic constraints in order to address incident response and resource allocation problems for traffic incident management They considered the resource allocation problem by assuming that the stochastic distribution of incidents over a network is given and introduced a mathematical model to determine the number of service vehicles allocated to each depot to meet the requirements of the potential incidents by taking into account the stochastic nature of the resource requirement and incident occurrence probabilities.
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