Xinan Yang

Choice-based demand management and vehicle routing in E-fulfillment

Attended home delivery services face the challenge of providing narrow delivery time slots to ensure customer satisfaction, while keeping the significant delivery costs under control. To that end, a firm can try to influence customers when they are booking their delivery time slot so as to steer them toward choosing slots that are expected to result in cost-effective schedules. We estimate a multinomial logit customer choice model from historic booking data and demonstrate that this can be calibrated well on a genuine e-grocer data set. We propose dynamic pricing policies based on this choice model to determine which and how much incentive (discount or charge) to offer for each time slot at the time a customer intends to make a booking. A crucial role in these dynamic pricing problems is played by the delivery cost, which is also estimated dynamically. We show in a simulation study based on real data that anticipating the likely future delivery cost of an additional order in a given location can lead to significantly increased profit as compared with current industry practice.

An approximate dynamic programming approach to attended home delivery management

We propose a new method of controlling demand through delivery time slot pricing in attended home delivery management with a focus on developing an approach suitable for industry-scale implementation. To this end, we exploit a relatively simple yet effective way of approximating delivery costs by decomposing the overall delivery problem into a collection of smaller, area-specific problems. These cost estimations serve as inputs into an approximate dynamic programming method that provides estimates of the opportunity cost associated with having a customer from a specific area book delivery in a specific time slot. These estimates depend on the area and on the delivery time slot under consideration. Using real, large-scale industry data, we estimate a demand model including a multinomial logit model of customers’ delivery time slot choice, and show in simulation studies that we can improve profits by over two per cent in all tested instances relative to using a fixed-price policy commonly encountered in e-commerce. These improvements are achieved despite making strong assumptions in estimating delivery cost. These assumptions allow us to reduce computational run-time to a level suitable for real-time decision making on delivery time slot feasibility and pricing. Our approach provides quantitative insight into the importance of incorporating expected future order displacement costs into opportunity cost estimations alongside marginal delivery costs.

An approximate dynamic programming approach for improving accuracy of lossy data compression by Bloom filters

Bloom filters are a data structure for storing data in a compressed form. They offer excellent space and time efficiency at the cost of some loss of accuracy (so-called lossy compression). This work presents a yes–no Bloom filter, which as a data structure consisting of two parts: the yes-filter which is a standard Bloom filter and the no-filter which is another Bloom filter whose purpose is to represent those objects that were recognized incorrectly by the yes-filter (that is, to recognize the false positives of the yes-filter). By querying the no-filter after an object has been recognized by the yes-filter, we get a chance of rejecting it, which improves the accuracy of data recognition in comparison with the standard Bloom filter of the same total length. A further increase in accuracy is possible if one chooses objects to include in the no-filter so that the no-filter recognizes as many as possible false positives but no true positives, thus producing the most accurate yes–no Bloom filter among all yes–no Bloom filters. This paper studies how optimization techniques can be used to maximize the number of false positives recognized by the no-filter, with the constraint being that it should recognize no true positives. To achieve this aim, an Integer Linear Program (ILP) is proposed for the optimal selection of false positives. In practice the problem size is normally large leading to intractable optimal solution. Considering the similarity of the ILP with the Multidimensional Knapsack Problem, an Approximate Dynamic Programming (ADP) model is developed making use of a reduced ILP for the value function approximation. Numerical results show the ADP model works best comparing with a number of heuristics as well as the CPLEX built-in solver (B&B), and this is what can be recommended for use in yes–no Bloom filters. In a wider context of the study of lossy compression algorithms, our research is an example showing how the arsenal of optimization methods can be applied to improving the accuracy of compressed data.

Robust Berth Allocation Using a Hybrid Approach Combining Branch-and-Cut and the Genetic Algorithm

Seaside operations at container ports often suffer from uncertainty due to events such as the variation in arrival and/or processing time of vessels, weather conditions and others. Finding a robust plan which can accommodate this uncertainty is therefore desirable to port operators. This paper suggests ways to generate robust berth allocation plans in container terminals. The problem is first formulated as a mixed-integer programming model whose main objective is to minimize the total tardiness of vessel departure time. It is then solved exactly and approximately. Experimental results show that only small instances of the proposed model can be solved exactly. To handle large instances in reasonable times, the Genetic Algorithm (GA) is used. However, it does not guarantee optimality and often the approximate solutions returned are of low quality. A hybrid meta-heuristic which combines Branch-and-Cut (B&C) as implemented in CPLEX, with the GA as we implement it here, is therefore suggested. This hybrid method retains the accuracy of Branch-and-Cut and the efficiency of GA. Numerical results obtained with the three approaches on a representative set of instances of the problem are reported.

Combined quay crane assignment and quay crane scheduling with crane inter-vessel movement and non-interference constraints

Integrated models of the quay crane assignment problem (QCAP) and the quay crane scheduling problem (QCSP) exist. However, they have shortcomings in that some do not allow movement of quay cranes between vessels, others do not take into account precedence relationships between tasks, and yet others do not avoid interference between quay cranes. Here, an integrated and comprehensive optimization model that combines the two distinct QCAP and QCSP problems which deals with the issues raised is put forward. The model is of the mixed-integer programming type with the objective being to minimize the difference between tardiness cost and earliness income based on finishing time and requested departure time for a vessel. Because of the extent of the model and the potential for even small problems to lead to large instances, exact methods can be prohibitive in computational time. For this reason an adapted genetic algorithm (GA) is implemented to cope with this computational burden. Experimental results obtained with branch-and-cut as implemented in CPLEX and GA for small to large-scale problem instances are presented. The paper also includes a review of the relevant literature.

An efficient mixed integer programming model for pairing containers in inland transportation based on the assignment of orders

The inland transportation takes a significant portion of the total cost that arises from intermodal transportation. In addition, there are many parties (shipping lines, haulage companies, customers) who share this operation as well as many restrictions that increase the complexity of this problem and make it NP-hard. Therefore, it is important to create an efficient strategy to manage this process in a way to ensure all parties are satisfied. This paper investigates the pairing of containers/orders in drayage transportation from the perspective of delivering paired containers on 40-ft truck and/or individual containers on 20-ft truck, between a single port and a list of customer locations. An assignment mixed integer linear programming model is formulated, which solves the problem of how to combine orders in delivery to save the total transportation cost when orders with both single and multiple destinations exist. In opposition to the traditional models relying on the vehicle routing problem with simultaneous pickups and deliveries and time windows formulation, this model falls into the assignment problem category which is more efficient to solve on large size instances. Another merit for the proposed model is that it can be implemented on different variants of the container drayage problem: import only, import–inland and import–inland–export. Results show that in all cases the pairing of containers yields less cost compared to the individual delivery and decreases empty tours. The proposed model can be solved to optimality efficiently (within half hour) for over 300 orders.

Approximate dynamic programming with Bézier Curves/Surfaces for Top-percentile Traffic Routing

Multi-homing is used by Internet Service Providers (ISPs) to connect to the Internet via different network providers. This study develops a routing strategy under multi-homing in the case where network providers charge ISPs according to top-percentile pricing (i.e. based on the θth highest volume of traffic shipped). We call this problem the Top-percentile Traffic Routing Problem (TpTRP).

An evolutionary approach to a combined mixed integer programming model of seaside operations as arise in container ports

This paper puts forward an integrated optimisation model that combines three distinct problems, namely berth allocation, quay crane assignment, and quay crane scheduling that arise in container ports. Each one of these problems is difficult to solve in its own right. However, solving them individually leads almost surely to sub-optimal solutions. Hence, it is desirable to solve them in a combined form. The model is of the mixed-integer programming type with the objective being to minimize the tardiness of vessels and reduce the cost of berthing. Experimental results show that relatively small instances of the proposed model can be solved exactly using CPLEX. Large scale instances, however, can only be solved in reasonable times using heuristics. Here, an implementation of the genetic algorithm is considered. The effectiveness of this implementation is tested against CPLEX on small to medium size instances of the combined model. Larger size instances were also solved with the genetic algorithm, showing that this approach is capable of finding the optimal or near optimal solutions in realistic times.