## 1 Introduction  
In these modern days, demands for delivery services are growing rapidly, especially with the growth of the e-commerce market. The expansion greatly increases demands for direct-to-customer deliveries. The last leg of the direct-to-customer supply chain, also known as the last-mile logistics, is the delivery of products from outlets to customers. Indeed, this part of logistics may incur more costs than other parts of management costs [1] as it involves multiple aspects such as security when encountering not-at-home recipients, greenhouse gas emissions, a lack of critical mass in some areas which may require additional vehicles to make delivery and add extra costs to the courier, etc. Urban logistics are also facing several salient difficulties such as access regulation, road restriction, parking conditions and environmental pollution [2]. In addition to the costs of the last-mile logistics, customer services also play a major role in increasing customer loyalty, which subsequently increases company market share. The driver's experience is another key to efficient delivery operations which result in gaining consumer preferences for logistics services. Driver's local knowledge or expertise may also influence their decisions when there are road traffic accidents or abnormal traffic congestion in the area. Managing last-mile logistics is indeed difficult to achieve optimum performance, especially with a large number of delivery locations. It is normal practice for managers to assign areas to a driver based on their local area experience. However, because delivery demands for each day in the assigned area may differ greatly, the driver may not be able to complete all deliveries in the area before the end of their scheduled shift. Therefore, day-to-day management should consider flexible delivery area in order to reallocate workload of a high demand zone to other zones. We denote the term _vehicle time_ as the length of time a vehicle takes to start its journey from the depot until returning back to the depot to finish the whole day journey. The most common problem that managers usually face in the urban logistics is unbalanced vehicle times as logistics demands change each day. A solution with _vehicle time violations_ is referred to the case when some vehicles cannot return to the depot in time. This may result in failed deliveries and the delivery attempts must be made in the following day, adding extra cost to the total logistics operation. Therefore, the last-mile logistics planning should avoid assigning too many delivery jobs or creating too large coverage area for one vehicle. Finding a solution to a problem of balancing vehicle time for the urban logistics is not an easy task. Ideally, one can embed the problem into the classical optimization problem with a secondary objective to minimize vehicle time variance. This additional term is a nonlinear polynomial function which is much more difficult to solve. In addition, the fact that travel times in a real-world situation depend on traffic congestion complicates the problem even further. Traffic congestion has become a common problem in many big cities. There have been numerous reports that Bangkok traffic jams are among world's worst [3]. Congestion delays are very costly in logistics industries especially for those with time sensitive services such as express delivery products. The majority of traffic delays are predictable [4]. The demand for transport at peak hours contributes directly to a large number of on-road vehicles. These predictable delays, however, may not be avoided if severe traffic congestion occurs all day--which is what happens in Bangkok. Therefore, Bangkok logistics industries utilize multiple transportation modes, such as motorbikes, vans and trucks, in order to accelerate delivery services. Normally, routing problems consider timely and cost-effective deliveries with the shortest routes and the lowest number of active vehicles.