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 4OR: A Quarterly Journal of Operations ResearchJournal Prestige (SJR): 0.825 Citation Impact (citeScore): 1Number of Followers: 12      Hybrid journal (It can contain Open Access articles) ISSN (Print) 1619-4500 - ISSN (Online) 1614-2411 Published by Springer-Verlag  [2469 journals]
• Challenges and opportunities in crowdsourced delivery planning and
operations

Abstract: How to best deliver goods to consumers has been a logistics question since time immemorial. However, almost all traditional delivery models involved a form of company employees, whether employees of the company manufacturing the goods or whether employees of the company transporting the goods. With the growth of the gig economy, however, a new model not involving company employees has emerged: relying on crowdsourced delivery. Crowdsourced delivery involves enlisting individuals to deliver goods and interacting with these individuals using the internet. In crowdsourced delivery, the interaction with the individuals typically occurs through a platform. Importantly, the crowdsourced couriers are not employed by the platform and this has fundamentally changed the planning and execution of the delivery of goods: the delivery capacity is no longer under (full) control of the company managing the delivery. We present the challenges this introduces, review how the research community has proposed to handle some of these challenges, and elaborate on the challenges that have not yet been addressed.
PubDate: 2022-01-21

• A note on the complexity of the bilevel bottleneck assignment problem

Abstract: We establish the NP-completeness of the variant of the bilevel assignment problem, where the leader and the follower both have bottleneck objective functions and were the follower behaves according to the optimistic rule. This result settles a problem that has been left open by Klinz & Gassner [4OR 7:379–394, 2009].
PubDate: 2021-12-31

• Acknowledgement to referees

PubDate: 2021-12-01

• Dealing with uncertainty in round robin sports scheduling

PubDate: 2021-12-01

• Sports timetabling: theoretical results and new insights in algorithm
performance

PubDate: 2021-12-01

• Comparing stage-scenario with nodal formulation for multistage stochastic
problems

Abstract: To solve real life problems under uncertainty in Economics, Finance, Energy, Transportation and Logistics, the use of stochastic optimization is widely accepted and appreciated. However, the nature of stochastic programming leads to a conflict between adaptability to reality and tractability. To formulate a multistage stochastic model, two types of formulations are typically adopted: the so-called stage-scenario formulation named also formulation with explicit non-anticipativity constraints and the so-called nodal formulation named also formulation with implicit non-anticipativity constraints. Both of them have advantages and disadvantages. This work aims at helping the scholars and practitioners to understand the two types of notation and, in particular, to reformulate with the nodal formulation a model that was originally defined with the stage-scenario formulation presenting this implementation in the algebraic language GAMS. In addition, this work presents an empirical analysis applying the two formulations both without any further decomposition to perform a fair comparison. In this way, we show that the difficulties to implement the model with the nodal formulation are somehow reworded making the problem tractable without any decomposition algorithm. Still, we remark that in some other applications the stage-scenario formulation could be more helpful to understand the structure of the problem since it allows to relax the non-anticipativity constraints.
PubDate: 2021-12-01

• Pricing and strategy selection in a closed-loop supply chain under demand
and return rate uncertainty

Abstract: Closed-loop supply chain (CLSC) decision-making involves many uncertainties, which makes the decision-making process more complex and diversified. This study considered a two-stage CLSC consisting of an original manufacturer and a third-party recycler. Without any government policy support, considering the effects of market demand, product return rate, and consumer perceived value, a CLSC decision model based on market demand with a [0,1] distribution was established. The model analyzes three situations—a manufacturer monopoly, the Cournot duopoly game, and the Stackelberg competition game—and solves them. The optimal values of decision variables such as optimal pricing, market demand, and all parties’ profits in the CLSC are obtained, and a strict mathematical proof is given. Through the model-solving process, the effects of product return rate and consumer perceived value on decision variables are analyzed; then, the profit allocation between the original manufacturer and the third-party recycler under different cooperation modes is analyzed. In addition, the four combinations of competition and cooperation are analyzed based on game theory. The Nash equilibrium solution and Pareto optimal solution of the four modes are analyzed by drawing a bimatrix Nash equilibrium table. The results indicate that the cooperation–cooperation mode is difficult to produce automatically, and government policy guidance and support are often needed to achieve Pareto optimality. Finally, a numerical example is given to validate the proposed model. In this way, the proposed model provides reliable theoretical support for the decision-making of both sides in a CLSC.
PubDate: 2021-12-01

• Inductive linearization for binary quadratic programs with linear
constraints

Abstract: A linearization technique for binary quadratic programs (BQPs) that comprise linear constraints is presented. The technique, called “inductive linearization”, extends concepts for BQPs with particular equation constraints, that have been referred to as “compact linearization” before, to the general case. Quadratic terms may occur in the objective function, in the set of constraints, or in both. For several relevant applications, the linear programming relaxations obtained from applying the technique are proven to be at least as strong as the one obtained with a well-known classical linearization. It is also shown how to obtain an inductive linearization automatically. This might be used, e.g., by general-purpose mixed-integer programming solvers.
PubDate: 2021-12-01

• A binary search algorithm for the general coupled task scheduling problem

Abstract: The coupled task scheduling problem aims to schedule a set of jobs, each with at least two tasks and there is an exact delay period between two consecutive tasks, on a set of machines to optimize a performance criterion. We study the problem of scheduling a set of coupled jobs to be processed on a single machine with the objective of minimizing the makespan, which is known to be strongly NP-hard. We obtain competitive lower bounds for the problem through different procedures, including solving 0-1 knapsack problems. We obtain an upper bound by applying a heuristic algorithm. We then propose a binary search heuristic algorithm for the coupled task scheduling problem. We perform extensive computational experiments and show that the proposed method is able to obtain quality solutions. The results also indicate that the proposed solution method outperforms the standard exact solver Gurobi.
PubDate: 2021-12-01

• Scanning integer points with lex-inequalities: a finite cutting plane
algorithm for integer programming with linear objective

Abstract: We consider the integer points in a unimodular cone K ordered by a lexicographic rule defined by a lattice basis. To each integer point x in K we associate a family of inequalities (lex-inequalities) that define the convex hull of the integer points in K that are not lexicographically smaller than x. The family of lex-inequalities contains the Chvátal–Gomory cuts, but does not contain and is not contained in the family of split cuts. This provides a finite cutting plane method to solve the integer program $$\min \{cx: x\in S\cap \mathbb {Z}^n\}$$ , where $$S\subset \mathbb {R}^n$$ is a compact set and $$c\in \mathbb {Z}^n$$ . We analyze the number of iterations of our algorithm.
PubDate: 2021-12-01

• Mixed integer programming formulations for the generalized traveling
salesman problem with time windows

Abstract: The generalized traveling salesman problem with time windows (GTSPTW) is defined on a directed graph where the vertex set is partitioned into clusters. One cluster contains only the depot. Each vertex is associated with a time window, during which the visit must take place if the vertex is visited. The objective is to find a minimum cost tour starting and ending at the depot such that each cluster is visited exactly once and time constraints are respected, i.e., for each cluster, a single vertex is visited during its time window. In this paper, four mixed integer linear programming formulations for the GTSPTW are proposed and compared. They are based on different definitions of variables. All the formulations are compact, which means the number of decision variables and constraints is polynomial with respect to the size of the instance. Dominance relations between their linear relaxations are established theoretically. Computational experiments are conducted to compare the linear relaxations and branch-and-bound performances of the four formulations. The results show that two formulations are better than the other ones.
PubDate: 2021-12-01

• A competitive optimization approach for data clustering and orthogonal
non-negative matrix factorization

Abstract: Partitioning a given data-set into subsets based on similarity among the data is called clustering. Clustering is a major task in data mining and machine learning having many applications such as text retrieval, pattern recognition, and web mining. Here, we briefly review some clustering related problems (k-means, normalized k-cut, orthogonal non-negative matrix factorization, ONMF, and isoperimetry) and describe their connections. We formulate the relaxed mean version of the isoperimetry problem as an optimization problem with non-negative orthogonal constraints. We first make use of a gradient-based optimization algorithm to solve this kind of a problem, and then apply a post-processing technique to extract a solution of the clustering problem. Also, we propose a simplified approach to improve upon solution of the 2-dimensional clustering problem, using the N-nearest neighbor graph. Inspired by this technique, we apply a multilevel method for clustering a given data-set to reduce the size of the problem by grouping a number of similar vertices. The number is determined based on two values, namely, the maximum and the average of the edge weights of the vertices connected to a selected vertex. In addition, using the connections between ONMF and k-means and between k-means and the isoperimetry problem, we propose an algorithm to solve the ONMF problem. A comparative performance analysis of our approach with other related methods shows outperformance of our approach, in terms of the obtained misclassification error rate and Rand index, on both benchmark and randomly generated problems as well as hard synthetic data-sets.
PubDate: 2021-12-01

• A branch-cut-and-price algorithm for the cumulative capacitated vehicle
routing problem

Abstract: The Cumulative Capacitated Vehicle Routing Problem is a variant of the classic routing problem in which the objective function is to minimize the sum of arrival times to customers. This article proposes a model for the problem that uses position indexes in order to calculate the contribution of the travel time of an edge to the arrival times of the remaining customers on a route. The model is implemented and solved by the branch-cut-and-price (BCP) algorithm in the VRPSolver package. Computational experiments indicate that the proposed BCP model is superior to the literature, being able to solve many open instances. Good results were also obtained for the Multi-Depot variant of the problem.
PubDate: 2021-11-26

• A study on sequential minimal optimization methods for standard quadratic
problems

Abstract: In this work, we consider the relevant class of Standard Quadratic Programming problems and we propose a simple and quick decomposition algorithm, which sequentially updates, at each iteration, two variables chosen by a suitable selection rule. The main features of the algorithm are the following: (1) the two variables are updated by solving a subproblem that, although nonconvex, can be analytically solved; (2) the adopted selection rule guarantees convergence towards stationary points of the problem. Then, the proposed Sequential Minimal Optimization algorithm, which optimizes the smallest possible sub-problem at each step, can be used as efficient local solver within a global optimization strategy. We performed extensive computational experiments and the obtained results show that the proposed decomposition algorithm, equipped with a simple multi-start strategy, is a valuable alternative to the state-of-the-art algorithms for Standard Quadratic Optimization Problems.
PubDate: 2021-11-11

• Correction to: Inductive linearization for binary quadratic programs with
linear constraints

PubDate: 2021-10-07

• An iterative solution technique for capacitated two-stage time
minimization transportation problem

Abstract: Capacitated two-stage time minimization transportation problem is an important optimization problem arising in industries. In literature, there is only one approach to solving this problem, but it has a deficiency of resulting in memory overflow in implementation on computer for large scale instances. In this paper, this problem is reduced to a series of finding the feasible flow in a network with lower and upper arc capacities, and two iterative algorithms are proposed as more robust solution method for this problem as compared to the existing approach. It is proved that both iterative algorithms find the optimal solution to this problem in a polynomial time. Due to fully utilizing the network structure characteristics inherent to this problem, both iterative algorithms have the advantage of easy implementation on computer and high computational efficiency, and successfully overcome the deficiency of existing approach. Computational experiments validate that as compared to the existing approach, both iterative algorithms are efficient and more robust method to solve this problem, where one iterative algorithm significantly outperforms the other in terms of computational time, especially for large scale instances.
PubDate: 2021-09-18

• Benefits of horizontal cooperation in supply chains

PubDate: 2021-09-13

• Simulation and optimisation of emergency department operations

PubDate: 2021-09-01

• Models and algorithms for decomposition problems

PubDate: 2021-09-01

• Frank–Wolfe and friends: a journey into projection-free first-order
optimization methods

Abstract: Invented some 65 years ago in a seminal paper by Marguerite Straus-Frank and Philip Wolfe, the Frank–Wolfe method recently enjoys a remarkable revival, fuelled by the need of fast and reliable first-order optimization methods in Data Science and other relevant application areas. This review tries to explain the success of this approach by illustrating versatility and applicability in a wide range of contexts, combined with an account on recent progress in variants, improving on both the speed and efficiency of this surprisingly simple principle of first-order optimization.
PubDate: 2021-09-01

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