A Generalized Bin Packing Problem for parcel delivery in last-mile logistics

Abstract In this paper, we present a new problem arising at a tactical level of setting a last-mile parcel delivery service in a city by considering different Transportation Companies (TC), which differ in cost and service quality. The courier must decide which TCs to select for the service in order to minimize the total cost and maximize the total service quality. We show that the problem can be modeled as a new packing problem, the Generalized Bin Packing Problem with bin-dependent item profits (GBPPI), where the items are the parcels to deliver and the bins are the TCs. The aim of the GBPPI is to select the appropriate fleet from TCs and determine the optimal assignment of parcels to vehicles such that the overall net cost is minimized. This cost takes into account both transportation costs and service quality. We provide a Mixed Integer Programming formulation of the problem, which is the starting point for the development of efficient heuristics that can address the GBPPI for instances involving up to 1000 items. Extensive computational tests show the accuracy of the proposed methods. Finally, we present a last-mile logistics case study of an international courier which addresses this problem

The Generalized Bin Packing Problem with bin-dependent item profits

In this paper, we introduce the Generalized Bin Packing Problem with bin-dependent item profits (GBPPI), a variant of the Generalized Bin Packing Problem. In GBPPI, various bin types are available with their own capacities and costs. A set of compulsory and non-compulsory items are also given, with volume and bin-dependent profits. The aim of GBPPI is to determine an assignment of items to bins such that the overall net cost is minimized. The importance of GBPPI is confirmed by a number of applications. The introduction of bin-dependent item profits enables the application of GBPPI to cross-country and multi-modal transportation problems at strategic and tactical levels as well as in last-mile logistic environments. Having provided a Mixed Integer Programming formulation of the problem, we introduce efficient heuristics that can effectively address GBPPI for instances involving up to 1000 items and problems with a mixed objective function. Extensive computational tests demonstrate the accuracy of the proposed heuristics. Finally, we present a case study of a well-known international courier operating in northern Italy. The problem approached by the international courier is GBPPI. In this case study, our methodology outperforms the policies of the company

Solving Bin Packing Problems Using VRPSolver Models

International audienceWe propose branch-cut-and-price algorithms for the classic bin packing problem and also for the following related problems: vector packing, variable sized bin packing and variable sized bin packing with optional items. The algorithms are defined as models for VRPSolver, a generic solver for vehicle routing problems. In that way, a simple parameterization enables the use of several branch-cut-and-price advanced elements: automatic stabilization by smoothing, limited-memory rank-1 cuts, enumeration, hierarchical strong branching and limited discrepancy search diving heuristics. As an original theoretical contribution, we prove that the branching over accumulated resource consumption (Gélinas et al. 1995), that does not increase the difficulty of the pricing subproblem, is sufficient for those bin packing models. Extensive computational results on instances from the literature show that the VRPSolver models have a performance that is very robust over all those problems, being often superior to the existing exact algorithms on the hardest instances. Several instances could be solved to optimality for the first time

Relaxations and exact solution of the variable sized bin packing problem

Due to copyright restrictions, the access to the full text of this article is only available via subscription.We address a generalization of the classical one-dimensional bin packing problem with unequal bin sizes and costs. We investigate lower bounds for this problem as well as exact algorithms. The main contribution of this paper is to show that embedding a tight network flow-based lower bound, dominance rules, as well as an effective knapsack-based heuristic in a branch-and-bound algorithm yields very good performance. In addition, we show that the particular case with all weight items larger than a third the largest bin capacity can be restated and solved in polynomial-time as a maximum-weight matching problem in a nonbipartite graph. We report the results of extensive computational experiments that provide evidence that large randomly generated instances are optimally solved within moderate CPU times.Fatimah Alnijris’ Research Chair for Advanced Manufacturing Technolog