Remy Spliet

The discrete time window assignment vehicle routing problem

In this paper we introduce the discrete time window assignment vehicle routing problem (DTWAVRP) that can be viewed as a two-stage stochastic optimization problem. Given a set of customers that must be visited on the same day regularly within some period of time, the first-stage decisions are to assign to each customer a time window from a set of candidate time windows before demand is known. In the second stage, when demand is revealed for each day of the time period, vehicle routes satisfying vehicle capacity and the assigned time windows are constructed. The objective of the DTWAVRP is to minimize the expected total transportation cost. To solve this problem, we develop an exact branch-price-and-cut algorithm and derive from it five column generation heuristics that allow to solve larger instances than those solved by the exact algorithm. We illustrate the performance of these algorithms by means of computational experiments performed on randomly generated instances.

The vehicle rescheduling problem

The capacitated vehicle routing problem (CVRP) is the problem of finding a routing schedule to satisfy demand by supplying goods stored at the depot, such that the traveling costs are minimized. For operational purposes, in many practical applications a long term routing schedule is made, often based on average demand. When demand substantially differs from the average, constructing a new schedule is beneficial. The vehicle rescheduling problem (VRSP) is the problem of finding a new schedule that not only minimizes the total traveling costs but also minimizes the costs of deviating from the original schedule. In this paper a mathematical programming formulation of the rescheduling problem is presented as well as a heuristic solution method referred to as the two-phase heuristic. We provide sufficiency conditions for which it produces the optimal solution. Finally, we perform computational experiments to study the performance of the two-phase heuristic.

Preference inference with general additive value models and holistic pair-wise statements

Additive multi-attribute value models and additive utility models with discrete outcome sets are widely applied in both descriptive and normative decision analysis. Their non-parametric application allows preference inference by analyzing sets of general additive value functions compatible with the observed or elicited holistic pair-wise preference statements. In this paper, we provide necessary and sufficient conditions for the preference inference based on a single preference statement, and sufficient conditions for the inference based on multiple preference statements. In our computational experiments all inferences could be made with these conditions. Moreover, our analysis suggests that the non-parametric analyses of general additive value models are unlikely to be useful by themselves for decision support in contexts where the decision maker preferences are elicited in the form of holistic pair-wise statements.

The Time Window Assignment Vehicle Routing Problem with Time-Dependent Travel Times

In this paper, we introduce the time window assignment vehicle routing problem TWAVRP with time-dependent travel times. It is the problem of assigning time windows to customers before their demand is known and creating vehicle routes adhering to these time windows after demand becomes known. The goal is to assign the time windows in such a way that the expected transportation costs are minimized. We develop a branch-price-and-cut algorithm to solve this problem to optimality. The pricing problem that has to be solved is a new variant of the shortest path problem, which includes a capacity constraint, time-dependent travel times, time window constraints on both the nodes and on the arcs, and linear node costs. For solving the pricing problem, we develop an exact labeling algorithm and a tabu search heuristic. Furthermore, we present new valid inequalities, which are specifically designed for the TWAVRP with time-dependent travel times. Finally, we present results of numerical experiments to illustrate the performance of the algorithm.

The driver assignment vehicle routing problem

We introduce the driver assignment vehicle routing problem, DAVRP. In this problem, drivers are assigned to customers before demand is known, and after demand is known a routing schedule has to be made such that every driver visits at least a fraction α of its assigned customers. We present a solution procedure to investigate how much transportation costs increase by adhering to the driver assignments. Furthermore, we distinguish between the case in which customers that are not visited by their assigned driver are visited by backup drivers only, and the case in which slack capacity of regular drivers is utilized to visit these customers. We use randomly generated instances of the DAVRP to provide examples where the difference in transportation costs is substantial.

A Branch-and-Price Approach for a Ship Routing Problem with Multiple Products and Inventory Constraints

In the oil industry, different oil components are blended in a refinery to fuel products. These products are transported to different harbors by ship. Due to the limited storage capacity at the harbors and the undesirability of a stock-out, inventory levels at the harbors have to be taken into account during the construction of the ship routes. In this paper, we give a detailed description of this problem, which we call the ship routing problem with multiple products and inventory constraints. Furthermore, we formulate this problem as a generalized set-covering problem, and we present a Branch-and-Price algorithm to solve it. The pricing problems have a very complex nature. We discuss a dynamic programming algorithm to solve them to optimality.

Shared Capacity Routing Problem − An omni-channel retail study

More and more retailers allow customers to order goods online and then pick them up in a store. In this setting, these orders are typically served from a dedicated warehouse. This often means that the stores are visited by different vehicles to replenish the store inventory and to supply the pick-up points. Motivated by a collaboration with an omni-channel grocery retailer in the Netherlands, we study how to best share capacity between the routes associated with these different sales channels. As operational constraints prevent jointly planning the routes, we consider the replenishment routes as fixed when planning the routes to serve the pick-up orders. An order can be transferred to the replenishment route, if capacity allows. We consider the problem of deciding which customer orders to transfer and which to deliver directly such that the total costs are minimized. We present an exact and a heuristic approach to solve this problem. Computational experiments on both real-world and artificial instances show that substantial savings can be achieved by sharing vehicle capacity across different channels.

Shared Capacity Routing Problem – An Omni-channel Retail Study

More and more retailers allow customers to order goods online and then pick them up in a store. In this setting, these orders are typically served from a dedicated warehouse. This often means that the stores are visited by different vehicles to replenish the store inventory and to supply the pick-up points. Motivated by a collaboration with an omni- channel grocery retailer in the Netherlands, we study how to best share capacity between the routes associated with these different sales channels. As operational constraints prevent jointly planning the routes, we consider the replenishment routes as fixed when planning the routes to serve the pick-up orders. An order can be transferred to the replenishment route, if capacity allows. We consider the problem of deciding which customer orders to transfer and which to deliver directly such that the total costs are minimized. We present an exact and heuristic approach to solve this problem. Computational experiments on both real-world and artificial instances show that substantial savings can be achieved by sharing vehicle capacity across different channels.