# MASc Thesis Seminar | Ajitesh Rajiv Singla | Optimization Models for the Perishable Inventory Routing Problem

Tuesday, August 6, 2019 — 11:00 AM EDT

Candidate: Ajitesh Rajiv Singla

Title: Optimization Models for the Perishable Inventory Routing Problem.

Date: August 6, 2019

Time: 11:00 am

Place: CPH 4335

Supervisor(s): Bookbinder, James  and Joe Naoum-Sawaya

Abstract

In this thesis, three models for the perishable inventory routing model are explored. First, an inventory routing problem with one perishable product and known (deterministic) demands is considered in the context of consignment inventory. The profit of the supplier is maximized, with the supplier owning all the inventory until it is sold. The supplier gives a fixed percentage discount on the selling price of the product as it deteriorates. The shelf life and the number of vehicles is also fixed.

Computational results, comparing the perishable inventory routing problem (PIRP) with the standard inventory routing problem (IRP), are presented. Based on the calculations using the branch-and-cut algorithm we conclude that adding perishability to the IRP leads to better inventory management, and fresher products are delivered to the customers. The PIRP model was also solved using the Benders Decomposition algorithm. However, those results were not satisfactory in comparison to the branch-and-cut algorithm.

Second, the PIRP model is extended to consider uncertain (stochastic) demands (SPIRP). This is done to make the model more comparative to a real-life problem. Several demand scenarios are created within a fixed range to capture the uncertainty with respect to the perishable product. It is assumed here that the demand scenarios are equally probable, since estimating the actual probability is difficult. Results are generated comparing the model solutions by the branch-and-cut and Benders Decomposition algorithms. We infer that, even when demand scenarios enable easy decomposition of the problem, the Benders performs worse than the branch-and-cut algorithm.

Third, a robust formulation to the SPIRP is proposed to resolve the above-mentioned limitations. The aim of adding robustness to the SPIRP is to be able to use a small number of scenarios, without the worry of accurately estimating the correct probability, but still obtain solutions that are competitive with modeling a large number of scenarios in the case of SPIRP. An innovative way of formulating the robust counterpart of the SPIRP is developed, keeping the probability of each demand scenario uncertain. An algorithm is devised to compare the effectiveness of the robust model to the deterministic, and stochastic models.

Computational results compare the average profit values generated by the three models. It is concluded that while the deterministic model captures no uncertainty, the stochastic model with many scenarios accounts for the most demand uncertainty; the robust model through the use of far fewer scenarios, can treat a significant uncertainty in demand. Another interpretation of the results is that an increased number of robust scenarios has a significant effect on the average profit values of that model.

Location
CPH - Carl A. Pollock Hall
Room 4335
200 University Avenue West

Waterloo, ON N2L 3G1

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