A Dynamic Strategy for Home Pick-Up Service with Uncertain Customer Requests and Its Implementation

Abstract

In this paper, a home service problem is studied, where a capacitated vehicle collects customers’ parcels in one pick-up tour. We consider a situation where customers, who have scheduled their services in advance, may call to cancel their appointments, and customers, who do not have appointments, also need to be visited if they request for services as long as the capacity is allowed. To handle those changes that occurred over the tour, a dynamic strategy will be needed to guide the vehicle to visit customers in an efficient way. Aimed at minimizing the vehicle’s total expected travel distance, we model this problem as a multi-dimensional Markov Decision Process (MDP) with finite exponential scale state space. We exactly solve this MDP via dynamic programming, where the computing complexity is exponential. In order to avoid complexity continually increasing, we aim to develop a fast looking-up method for one already-examined state’s record. Although generally this will result in a huge waste of memory, by exploiting critical structural properties of the state space, we obtain an O ( 1 ) looking-up method without any waste of memory. Computational experiments demonstrate the effectiveness of our model and the developed solution method. For larger instances, two well-performed heuristics are proposed.

GRASP‐based request allocation and MDP‐based vehicle routing in home pick‐up service with service continuity consideration

“…Specifically, those modifications include two aspects. First, in Wu et al [16], the state space is divided into five groups and costs of states are computed for those groups one by one, shown as Steps 2-5 of Algorithm 1 in Wu et al [16]. However, in this paper, we do not divide the state space but compute state cost directly, which makes coding implementation much easier.…”

“…However, in this paper, we do not divide the state space but compute state cost directly, which makes coding implementation much easier. Second, in Wu et al [16], there is an amount of onrun calculation for state transfer probabilities, which is very time-consuming. In this paper, we conduct those calculations in preparation calculation phase, together with index value calculation at Step 0 of Algorithm 1 in Wu et al [16].…”

“…Second, in Wu et al [16], there is an amount of onrun calculation for state transfer probabilities, which is very time-consuming. In this paper, we conduct those calculations in preparation calculation phase, together with index value calculation at Step 0 of Algorithm 1 in Wu et al [16]. Note that "preparation calculation" is a calculation task that can be conducted before P-customers ( i ) and M-customers ( i ) are realized.…”

“…As illustrated in Wu et al [16], based on a well-designed data structure for storing the costs of the exponential-size states, the MDP can be exactly solved on instances up to the size of Certainly, if more time can be consumed, instances with larger size will also be exactly solved. In addition, by adopting the same analysis as Wu et al [16], we can get total time complexity of the DP method is O(𝒸…”

“…Next we will describe the problem studied in this paper explicitly. Wu et al [16] study a single-courier home parcel pickup problem. In this study, instead of focusing on a single courier 1 , we consider a more practical situation in that a fixed group of couriers are responsible for parcel pick-up service within one certain urban region.…”