Optimal logistics strategy to distribute medicines in clinics and hospitals

Abstract

This document presents a methodology for the optimal selection of the vehicle fleet necessary to distribute medical products from the company's storage center to many intermediate transfer nodes, and from these to a group of public hospitals. The problem addressed is a real case presented by a company that provides logistics services in the Mexican Republic. An algorithm that incorporates three modified mathematical models was designed for its solution. A version of the Dijkstra algorithm was modified for the solution to develop the clustering of nodes (clinics) within the system. A modified version of the model of the traveling salesman generated the routes of the transports and the sequence of distribution of the products. Finally, a model of mixed integer linear programming provided the quantities and characteristics of the transports to buy.

An exact viscosity solution to a Hamilton–Jacobi–Bellman quasi-variational inequality for animal population management

“…1. Note that Cadenillas [17] proved the verification theorem (Theorem 3.1 in the literature), which states that the solution to HJBQVI (12) under the QVI control (16) through (18) is in fact the value function (11) and the QVI control is the optimal impulse control. Thus, if we could solve the HJBQVI (12), then we are able to obtain the optimal impulse control.…”

“…The boundary condition for the HJBQVI is V (0) = 0, which means that no problem arises when there is no population. The left part in "min" operator in the HJBQVI (12) corresponds to the situation where no intervention should be performed, while the right part corresponds to the situation where the intervention should be performed immediately. The following lemma gives the upper and lower bound of V .…”

“…Stochastic optimal control theory [10] has been applied to population and resource management problems [1,[11][12][13][14]. In reality, there are fixed costs besides proportional costs when some interventions are performed for management of animal population.…”

A model for the location and scheduling of the operation of second-generation ethanol biorefineries

“…The process becomes iterative until it reaches the convergence. For the design of the clusters the method mentioned in [19] is used. Here, the use of radial distribution was used due to the transportation costs of the product and the characteristics of it.…”

“…The variety of applications covers from the location of banks [3,7,10,11,22,23] industrial facilities [2,4,8,19,25]. A review on location of facilities and supply chain can be found in [16].…”