Question: Read article A dial-a-ride problem for client transportation in a health-care organization A vehicle routing problem (VRP) is a generalization of the traveling salesman problem

Read article "A dial-a-ride problem for client transportation in a health-care organization" A vehicle routing problem (VRP) is a generalization of the traveling salesman problem (TSP), we defined in the class. Actually, a VRP is a TSP with multiple capacitated vehicles. Each vehicle serves certain customers in a subtour. The dial-a ride problem is the VRP for the transportation of people. 1. What is the problem addressed in this paper? What is the current practice in dealing with transportation needs across the CAB centers and what new practice is tested/proposed in this work? 2. Briefly, in a few sentences (avoid symbols and equations as much as possible), describe the mathematical model developed in this paper. In particular, what is(are) the objective(s), the sets, the decision variables, and the types of constraints in the model. Which are the flow balance equations (constraints #)? 3. The problem is represented by a network and the decision variables are unit flows representing the vehicles. What are the nodes and arcs of the network? 4. What type of optimization model and what algorithm(s)/software were used to solve it? What was the maximum problem size that could be solved by the exact method (branch and bound for integer programming implemented in the lingo software) versus the heuristic approach implemented in a C++ code? How accurate was the heuristic approach as compared with the exact approach? 5. Which were the recommendations for CAB based on the results of this study? 6. And some flavor of multi-objective considerations... In this problem we have two objectives: (a) to minimize total vehicle traveling time (TVT) and (b) to minimize total client inconvenience time (TCIT). Actually, by minimizing the weighted sum of them, we try to find solutions that are the best tradeoffs between these two conflicting objectives, Now, given two solution alternatives, A and B, if A has both lower TVT and TCIT we say that A dominates B (better with respect to all objectives). If A performs better with respect to one objective and B performs better with respect to the other objective then no one dominates the other. Look at Fig. 4 and explain why Policy 2 performs better in a multi-objective sense?

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