Abstract
A practical distribution system that arises in the context of delivering liquefied petroleum gas (LPG) through cylinders is considered in this study. To meet all the challenging constraints, the model is explicitly considered as a simultaneous pickup and delivery single commodity truncated vehicle routing problem with the homogeneous fleet of vehicles. The aim of this problem is to find the optimal routes for the set of vehicles locating at the distributing agency (DA), which offers simultaneous pickup and delivery operations over single commodity (i.e. LPG cylinders) to a fixed subset (need not serve all delivery centers) of delivery centers at rural level. The model is designed using zero-one integer linear programming. For proper treatment of the present model, an exact Lexi-search algorithm (LSA) has been developed. A comparative study is performed between the LSA and existing results for the relaxed version of the present model. Further, the efficiency of the LSA is tested through numerical experiments over small and medium CVRP benchmark test instances. The extensive computational results have shown that the LSA is productive and revealed that the real solutions have more consistent than the integral solutions in the presence of truncation constraint.
Highlights
The physical flow is the key activity in logistics and distribution systems, which involves the distribution of supplies from manufacturer to the consumers using a fleet of vehicles through distributing agencies/centers
The proposed model physically appears VRP with simultaneous pickup and delivery tasks, but due to the assumption that the amount of filled liquefied petroleum gas (LPG) cylinders delivered to the delivery centers is same as the quantity of empty cylinders collected back from them, the truncated version of VRPSPD can be viewed as a capacitated truncated vehicle routing problem (CTVRP)
0.85 n – number of city locations; m – number of vehicles; capacity of vehicles (CV) – capacity of a vehicle, n0 – number of delivery centers to be served; Opt_Int. – optimal integral solution found by Lexi-search algorithm (LSA); Opt_Frac. – optimal fractional solution found by LSA; Error % – error percentage of solutions caused due to rounding the distance matrix entries; CPU time (s) – CPU time required to provide the optimal solution; RDC– ratio of demand to capacity
Summary
The physical flow is the key activity in logistics and distribution systems, which involves the distribution of supplies from manufacturer to the consumers using a fleet of vehicles through distributing agencies/centers. Effective distribution of LPG cylinders to the delivery centers/customers at the rural areas that undertake by any distributing agency (DA) is still a challenging problem due to practical scenarios. This motivates to adapt the truncation constraint in the context of real time distribution systems With this motivation, in this study, a truncated version of VRPSPD that simultaneously performs pickup and delivery tasks using a homogeneous fixed fleet of vehicles over a single commodity (LPG Cylinders) in the rural areas is considered. The proposed model physically appears VRP with simultaneous pickup and delivery tasks, but due to the assumption that the amount of filled LPG cylinders delivered to the delivery centers is same as the quantity of empty cylinders collected back from them, the truncated version of VRPSPD can be viewed as a capacitated truncated vehicle routing problem (CTVRP).
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