Search results for "Integer programming"

Comment on “A simple way to incorporate uncertainty and risk into forest harvest scheduling”

2017

In a recent research article, Robinson et al. (2016) described a method of estimating uncertainty of harvesting outcomes by analyzing the historical yield to the associated prediction for a large number of harvest operations. We agree with this analysis, and consider it a useful tool to integrate estimates of uncertainty into the optimization process. The authors attempt to manage the risk using two different methods, based on deterministic integer linear programming. The first method focused on maximizing the 10th quantile of the distribution of predicted volume subject to area constraint, while the second method focused on minimizing the variation of total quantity of volume harvested sub…

Landowner preferences and conservation prioritization: response to Nielsen et al.

2017

Decorous combinatorial lower bounds for row layout problems

2020

Abstract In this paper we consider the Double-Row Facility Layout Problem (DRFLP). Given a set of departments and pairwise transport weights between them the DRFLP asks for a non-overlapping arrangement of the departments along both sides of a common path such that the weighted sum of the center-to-center distances between the departments is minimized. Despite its broad applicability in factory planning, only small instances can be solved to optimality in reasonable time. Apart from this even deriving good lower bounds using existing integer programming formulations and branch-and-cut methods is a challenging problem. We focus here on deriving combinatorial lower bounds which can be compute…

Decomposition and Mean-Field Approach to Mixed Integer Optimal Compensation Problems

2016

Mixed integer optimal compensation deals with optimization problems with integer- and real-valued control variables to compensate disturbances in dynamic systems. The mixed integer nature of controls could lead to intractability in problems of large dimensions. To address this challenge, we introduce a decomposition method which turns the original n-dimensional optimization problem into n independent scalar problems of lot sizing form. Each of these problems can be viewed as a two-player zero-sum game, which introduces some element of conservatism. Each scalar problem is then reformulated as a shortest path one and solved through linear programming over a receding horizon, a step that mirro…

Variable Fixing for Two-Arc Sequences in Branch-Price-and-Cut Algorithms on Path-Based Models

2020

Variable fixing by reduced costs is a popular technique for accelerating the solution process of mixed-integer linear programs. For vehicle-routing problems solved by branch-price-and-cut algorithms, it is possible to fix to zero the variables associated with all routes containing at least one arc from a subset of arcs determined according to the dual solution of a linear relaxation. This is equivalent to removing these arcs from the network used to generate the routes. In this paper, we extend this technique to routes containing sequences of two arcs. Such sequences or their arcs cannot be removed directly from the network because routes traversing only one arc of a sequence might still b…

A more efficient cutting planes approach for the green vehicle routing problem with capacitated alternative fuel stations

2021

AbstractThe Green Vehicle Routing Problem with Capacitated Alternative Fuel Stations assumes that, at each station, the number of vehicles simultaneously refueling cannot exceed the number of available pumps. The state-of-the-art solution method, based on the generation of all feasible non-dominated paths, performs well only with up to 2 pumps. In fact, it needs cloning the paths between every pair of pumps. To overcome this issue, in this paper, we propose new path-based MILP models without cloning paths, for both the scenario with private stations (i.e., owned by the fleet manager) and that with public stations. Then, a more efficient cutting plane approach is designed for addressing both…

Exact solution of the soft-clustered vehicle-routing problem

2020

Abstract The soft-clustered vehicle-routing problem (SoftCluVRP) extends the classical capacitated vehicle-routing problem by one additional constraint: The customers are partitioned into clusters and feasible routes must respect the soft-cluster constraint, that is, all customers of the same cluster must be served by the same vehicle. In this article, we design and analyze different branch-and-price algorithms for the exact solution of the SoftCluVRP. The algorithms differ in the way the column-generation subproblem, a variant of the shortest-path problem with resource constraints (SPPRC), is solved. The standard approach for SPPRCs is based on dynamic-programming labeling algorithms. We s…

New exact methods for the time-invariant berth allocation and quay crane assignment problem

2019

Abstract Efficient management of operations in seaport container terminals has become a critical issue, due to the increase in maritime traffic and the strong competition between ports. In this paper we focus on two seaside operational problems: the Berth Allocation Problem and the Quay Crane Assignment Problem, which are considered in an integrated way. For the continuous BACAP problem with time-invariant crane assignment we propose a new mixed integer linear model in which the vessels can be moored at any position on the quay, not requiring any quay discretization. The model is enhanced by adding several families of valid inequalities. The resulting model is able to solve instances with u…

The berth allocation problem in terminals with irregular layouts

2019

As international trade thrives, terminals attempt to obtain higher revenue while coping with an increased complexity with regard to terminal management operations. One of the most prevalent problems such terminals face is the Berth Allocation Problem (BAP), which concerns allocating vessels to a set of berths and time slots while simultaneously minimizing objectives such as total stay time or total assignment cost. Complex layouts of real terminals introduce spatial constraints which limit the mooring and departure of vessels. Although significant research has been conducted regarding the BAP, these real-world restrictions have not been taken into account in a general way. The present work …

Determining the best shipper sizes for sending products to customers

2014

A distribution company has to send products, packed into shippers, from the warehouse to retail shops. The number of different shipper types is regarded as a parameter given by the user, who is looking for a balance between transportation costs and stock and procurement costs. The problem is to decide the sizes of the shipper types to keep at the warehouse so as to minimize the cost of meeting the forecasted demand over the planning horizon. In this paper, we describe an integer linear programming formulation for the problem and obtaining feasible solutions. Other models, based on multiknapsack and p-median and facility location models, are for obtaining lower bounds. We study several ways …