Fuzzy Linear Programming Formulation for Time Prediction in Product Delivery

The product delivery process is a set of steps to transport a product of an origin to a delivery point. Nowadays, there are different platforms or software based on classical algorithms for network optimization that help develop routes. Although these informatics systems provide vehicle routes, their prediction time has low accuracy compared to real times in the product distribution, since these systems do not consider the elements that affect route planning, i.e., despite providing vehicle routes, these software systems have low prediction accuracy. To address this problem, an alternative is to use artificial intelligence systems that consider the knowledge of the product delivery planning into route optimization models, thus increasing the time accuracy, but adding the challenge of having to interpret correctly the vehicle route ambiguities. Motivated by the latter, we propose a new fuzzy linear programming formulation to predict delivery times for products. Unlike previous studies, our methodology considers various parameters in the distribution process and offers an effective way to identify which parameters should be used. Our strategy combines the abstraction power of fuzzy logic and the result that provides a route optimization analysis, i.e., this work brings the best of the two worlds to address the difficult problem of shortest-route in product delivery. For that, our methodology has three steps. First, we introduce our formulation that incorporates a Fuzzy Inference System (FIS) into linear programming to achieve accurate time predictions in product delivery. Second, we propose a fuzzy adjustment coefficient to consider the uncertain factors in product distribution and the expertise of the delivery staff. Finally, we develop a Geographic Information System (GIS) to visualize the distribution route and its time. On the other hand, we evaluate this methodology in the routes of a soft drink company using statistical analyses. Experimental results are feasible and promising. For example, in real-world scenarios, our approach reduced the Mean Absolute Percentage Error (MAPE) by 56% compared to methods that utilize artificial intelligence.