Large scale stochastic inventory routing problems with split delivery and service level constraints

A stochastic inventory routing problem (SIRP) is typically the combination of stochastic inventory control problems and NP-hard vehicle routing problems, which determines delivery volumes to the customers that the depot serves in each period, and vehicle routes to deliver the volumes. This paper aims to solve a large scale multi-period SIRP with split delivery (SIRPSD) where a customer’s delivery in each period can be split and satisfied by multiple vehicle routes if necessary. This paper considers SIRPSD under the multi-criteria of the total inventory and transportation costs, and the service levels of customers. The total inventory and transportation cost is considered as the objective of the problem to minimize, while the service levels of the warehouses and the customers are satisfied by some imposed constraints and can be adjusted according to practical requests. In order to tackle the SIRPSD with notorious computational complexity, we first propose an approximate model, which significantly reduces the number of decision variables compared to its corresponding exact model. We then develop a hybrid approach that combines the linearization of nonlinear constraints, the decomposition of the model into sub-models with Lagrangian relaxation, and a partial linearization approach for a sub model. A near optimal solution of the model found by the approach is used to construct a near optimal solution of the SIRPSD. Randomly generated instances of the problem with up to 200 customers and 5 periods and about 400 thousands decision variables where half of them are integer are examined by numerical experiments. Our approach can obtain high quality near optimal solutions within a reasonable amount of computation time on an ordinary PC

An interactive ranking-based multi-criteria choice algorithm with filtering: Applications to university selection

In this study, we develop an interactive algorithm to converge to the most preferred alternative of a decision maker (DM) among a set of discrete alternatives. The algorithm presents a limited number of alternatives to the DM and collects preference ranking of them iteratively. The preferences are modeled by a flexible and realistic preference function. To improve the performance, the alternatives presented are determined by a filtering method. We compare our algorithm with benchmark algorithms on numerous data sets from Quacquarelli Symonds, a higher education marketing company that reports annual rankings of universities under different categories. The results show that our algorithm outperforms the benchmark algorithms.Publisher's Versio

A DEA-BASED APPROACH TO RANKING MULTI-CRITERIA ALTERNATIVES

We propose a data envelopment analysis (DEA)-based approach to ranking multi-criteria alternatives. We call it "the area of the efficiency score graph" (AES) approach. Unlike the classical DEA score and D(k) measure that counts the number of DMUs (alternatives in DEA terminology) that should be removed from the set for each DMU k to become efficient, AES is not fully dependent on relative values of inputs/outputs of the alternatives in the set. It considers the change in efficiency scores of the alternatives while we delete 0, ... , D(k) number of alternatives from the set. The method avoids the negative effect of outliers and crowding in certain areas. It favors DMUs that manage to improve their efficiency scores quickly as we delete units from the set, and also alternatives that maintain high levels of efficiency scores as we delete units. We propose inclusion of weight restrictions into AES to incorporate decision maker preferences into the analysis. We apply our approach to ranking MBA programs. We provide rank lists of MBA programs by both AES and another DEA-based method for comparison. We also use AES scores to place programs in a small number of classes that are preference ordered from the best to the worst