Linear programming model applied to the resource schedulling at queue systems

The pressure to maintain (or increase) the level of competitiveness in companies leads to an ever-increasing requirement for effective management supported by the variety of existing resources, which tend to interfere into the work of the manager. Particularly, in the case of waiting queues, the most relevant aspect is the combination of the number of multitasking servers assigned to attend and the demand that varies over the course of a day's work. The main objective is to meet the expectations created by the client regarding the opinion of the service that was provided. The contribution that this work proposes to give consists in planning the number of servers adapted to a given demand, not forgetting the valuation associated with the release of resources to perform other tasks related to the business. We use linear programming to determine the optimal number of the servers to serve customers, depending on their hourly availability to fulfill this function and the estimated demand. The model is submitted to four distinct real scenarios, each one reflecting a certain service reality, so that we can evaluate its behavior and possible gains against real situations occurring under the same conditions. The results show the credibility of the model since it reveals in conditions very similar to those of a real situation (translated in one of the scenarios), very little relevant differences.