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The aim of city logistics is to fully optimize the urban freight movement with respect to the public and private costs and benefits including the fuel consumption and environmental costs. Most of the urban freight movement is primarily based on the truck traffic, which contributes to many urban traffic-related problems such as traffic congestion, parking issues, accidents and environmental problems. To counter these issues, city logistics suggests many measures and policies to reduce the number of trucks, their mileage and their idling times. The Vehicle Routing and scheduling Problem with Time Windows (VRPTW) is a typical route optimization technique employed in city logistics. It is also used to evaluate other city logistics measures relating to infrastructure planning and development (for example, optimal location of logistics terminals) and infrastructure management (such as, cooperative delivery systems). Most of the city logistics-related research utilizes the soft time windows variant of the VRPTW (abbreviated as VRPSTW), whereby an early arrival is penalized equal to the opportunity cost lost due to waiting and a high late arrival penalty is imposed on delayed service (delivery/pickup of goods). However, most of the exact optimization research has been directed towards the Vehicle Routing and scheduling Problem with Hard Time Windows (VRPHTW), though it lacks the practicality found in real life problems because of stringent restriction on even slight delays. Furthermore, these exact techniques allow waiting at no penalty cost in VRPHTW, which results in more waiting time as compared to the cases when waiting is penalized or even when waiting is allowed at no cost along with penalized late arrivals. On the other hand, mostly heuristics (approximate) solutions have been used for the VRPSTW in city logistics-related research (for example see, Yamda et al., 2) , Duin et al., 6) ).

VEHICLE ROUTING PROBLEM WITH SOFT TIME WINDOWS AND PATH CHOICE