Equitable Vessel Traffic Scheduling in a Seaport

In the global maritime transportation network, the on-time performance of cargo transportation depends largely on the service capacity and accessibility of seaports. When opportunities for infrastructure expansions are not available, seaport congestion mitigation may require effective scheduling of the vessel traffic in the port waters. Although existing works on vessel traffic scheduling focus on minimizing vessel delays, this paper studies a novel vessel traffic scheduling problem that aims to address the inter-shipping line equity issue. We develop a lexicographic optimization model that accounts for two conflicting performance measures: efficiency, which favors minimizing total vessel delay; and equity, which favors balancing the impacts of delays fairly among shipping lines. Our model allows the port operator to quantify the efficiency-equity tradeoff and make the best vessel traffic scheduling decisions. For solving the model, we develop an effective two-stage solution method in which the first stage solves two single-objective models to obtain the maximum system efficiency and equity, whereas the second stage trades between efficiency and equity and seeks the best compromise between the two conflicting objectives. We apply our model and solution method on instances generated from the operational data of the Port of Shanghai. Our computational results show that an efficiency-oriented model can lead to highly inequitable traffic plans, whereas inter-shipping line equity can be achieved at only mild losses in efficiency, indicating that the consideration of inter-shipping line equity can lead to satisfactory service at both the vessel level and the shipping line level.

Approximate and robust bounded job start scheduling for Royal Mail delivery offices

Motivated by mail delivery scheduling problems arising in Royal Mail, we study a generalization of the fundamental makespan scheduling $$P||C_{\max }$$ P | | C max problem which we call the bounded job start scheduling problem. Given a set of jobs, each specified by an integer processing time $$p_j$$ p j , that have to be executed non-preemptively by a set of m parallel identical machines, the objective is to compute a minimum makespan schedule subject to an upper bound $$g\le m$$ g ≤ m on the number of jobs that may simultaneously begin per unit of time. With perfect input knowledge, we show that Longest Processing Time First (LPT) algorithm is tightly 2-approximate. After proving that the problem is strongly $${\mathcal {N}}{\mathcal {P}}$$ N P -hard even when $$g=1$$ g = 1 , we elaborate on improving the 2-approximation ratio for this case. We distinguish the classes of long and short instances satisfying $$p_j\ge m$$ p j ≥ m and $$p_j<m$$ p j < m , respectively, for each job j. We show that LPT is 5/3-approximate for the former and optimal for the latter. Then, we explore the idea of scheduling long jobs in parallel with short jobs to obtain tightly satisfied packing and bounded job start constraints. For a broad family of instances excluding degenerate instances with many very long jobs, we derive a 1.985-approximation ratio. For general instances, we require machine augmentation to obtain better than 2-approximate schedules. In the presence of uncertain job processing times, we exploit machine augmentation and lexicographic optimization, which is useful for $$P||C_{\max }$$ P | | C max under uncertainty, to propose a two-stage robust optimization approach for bounded job start scheduling under uncertainty aiming in a low number of used machines. Given a collection of schedules of makespan $$\le D$$ ≤ D , this approach allows distinguishing which are the more robust. We substantiate both the heuristics and our recovery approach numerically using Royal Mail data. We show that for the Royal Mail application, machine augmentation, i.e., short-term van rental, is especially relevant.

A hybrid service selection optimization algorithm in internet of things

With the scale of Internet of Things (IoT) continues to increase, it brings big challenges for service selection in a large-scale IoT. For solving this problem, a service selection method based on the enhanced genetic algorithm is proposed in this paper. To decrease the scale of service selection, this paper uses the lexicographic optimization approach and quality of service (QoS) constraint relaxation technique to find the candidate service with height QoS. Then, the IoT service selection problem is transformed into a single-objective optimization problem adopting a simple weighting method, and the final composite service meeting the user's QoS needs are obtained from the candidate service. The simulation results show that the proposed algorithm can efficiently and quickly achieve a composite service satisfying user's QoS needs, and is more suitable for solving the service composite problem in large-scale IoT services.

LEXICOGRAPHIC PROBLEMS OF CONVEX OPTIMIZATION: SOLVABILITY AND OPTIMALITY CONDITIONS, CUTTING PLANE METHOD

The lexicographic approach for solving multicriteria problems consists in the strict ordering of criteria concerning relative importance and allows to obtain optimization of more important criterion due to any losses of all another, to the criteria of less importance. Hence, a lot of problems including the ones of com­plex system optimization, of stochastic programming under risk, of dynamic character, etc. may be presented in the form of lexicographic problems of opti­mization. We have revealed conditions of existence and optimality of solutions of multicriteria problems of lexicographic optimization with an unbounded convex set of feasible solutions on the basis of applying properties of a recession cone of a convex feasible set, the cone which puts in order lexicographically a feasible set with respect to optimization criteria and local tent built at the boundary points of the feasible set. The properties of lexicographic optimal solutions are described. Received conditions and properties may be successfully used while developing algorithms for finding optimal solutions of mentioned problems of lexicographic optimization. A method of finding lexicographic of optimal solutions of convex lexicographic problems is built and grounded on the basis of ideas of method of linearization and Kelley cutting-plane method.

Existence of solutions and solving method of lexicographic problem of convex optimization with the linear criteria functions

Among vector problems, the lexicographic ones constitute a broad significant class of problems of optimization. Lexicographic ordering is applied to establish rules of subordination and priority. Hence, a lot of problems including the ones of complex system optimization, of stochastic programming under a risk, of the dynamic character, etc. may be presented in the form of lexicographic problems of optimization. We have revealed the conditions of existence of solutions of multicriteria of lexicographic optimization problems with an unbounded set of feasible solutions on the basis of applying the properties of a recession cone of a con vex feasible set, the cone which puts it in order lexicographically with respect to optimization criteria. The obtained conditions may be successfully used while developing algorithms for finding the optimal solutions of the mentioned problems of lexicographic optimization. A method of finding the optimal solutions of convex lexico graphic problems with the linear functions of criteria is built and grounded on the basis of ideas of the method of linearization and the Kelley cutting plane method.

Addressing Cooperation between Mobile Operators in Telecommunication Networks via Optimization: A Lexicographic Approach and Case Study in Colombia

Cooperation between Telecommunications (Telco) operators has been limited both by regulation and competition in previous years. However, cooperation could not only allow an overall growth in quality of service (QoS) but also may benefit companies with under exploited nodes in their network infrastructure. This way, both fully deployed infrastructure by single Telco companies, as well as smaller companies with increasing service demand but low infrastructure deployment could potentially benefit from cooperation agreements. This article proposes a lexicographic mixed-integer linear optimization model for Telco cooperation composed by two phases: Phase 1 maximizes the number of services connected to the current infrastructure assuming cooperation between operators while Phase 2 minimizes the costs of connecting such services. We built a simple base scenario that allowed us to validate the intuition behind our model. Furthermore, to demonstrate the applicability of our lexicographic optimization model for cooperation between mobile operators, we present a real-world case study in a rural area in Colombia that allowed us to find the marginal costs of additional national roaming connections, as well as marginal profits under the cooperation schema. Our results could help mobile operators to benefit from cooperation and, since the model adapts to the local necessities of the company, cooperation could be restricted to any desired level.

Tropical Lexicographic Optimization: Synchronizing Timed Event Graphs

Tropical Algebra is used to model the dynamics of Timed Event Graphs (TEG), a particular class of Timed Discrete-Event System (TDES) in which we are interested only in synchronization and delay phenomena. Whenever this TEG has control inputs, we can use them to control the synchronization of the system to achieve some objective. Thus, this paper formulates a framework based on tropical algebra and lexicographic optimization to synchronize a TEG when dealing with many synchronization objectives that are ranked in previous priority order. We call this kind of problem the Tropical Lexicographic Synchronization Optimization (TLSO). This work develops a solution to this problem, based on Tropical Fractional Linear Programming (TFLP) and lexicographic optimization concepts. In this way, the basics of tropical algebra are determined, including essential terms to this paper, such as left and right residuations, and the following stages of the solution to the TLSO problem are explained. Therefore, this work presents a general framework based on structured algebraic models with application to TEG synchronization. By synchronization, we mean balancing and organizing events chronologically in order to achieve the desired goal. So, we are dealing with concepts closely related to symmetry ones. An illustrative numerical example is presented, which demonstrates the implementation of the proposed algorithms. The acquired results confirm the efficiency of the proposed methodology. Codes used for implementing the algorithms are listed in the appendix section of the article.

Conflict Management in University Examination Timetabling Problem: A case study of summer school mid-terms

Aim: This study is on tackling Examination Timetabling Problem (ETP) of the Faculty of Economics And Administrative Sciences (FEAS) of the Ankara HBV University summer school, where the courses of fall and spring semesters are offered simultaneously and regulations on restricting enrollments in inter-department electives or in-department courses of distinct years are relaxed. Thus, the complexity of the nature of the ETP problem is exacerbated. The direct heuristics based on successive assignments that the university normally adopts was proven inadequate for assuming standard regulations hence, another approach we explain in this paper was needed. Design / Research methods: The ETP was formulated as a Linear Mixed-Integer Program (LMIP) and decomposed into three stages; timetabling exams, room assignment, student allocation. To manage the conflict between the stakeholders of the examination procedure, a lexicographic optimization process based on the priority of the parties was undertaken. Conclusions / findings: After a recursive timetabling process based on a trial-and-error method a clash-free timetable was generated and, a room assignment plan that minimizes the total number of proctoring duties, usage of higher floor rooms and total crowdedness of rooms respectively was put into action. Therefore no student group experienced any clashing exams, the faculty members saved time that can be spent on research instead, since the room usage was better planned the costs (elevator usage, lighting, air conditioning, the labor of the janitors) were assumed to be decreased. Originality / value of the article: Each examination period bares a different ETP due to its problem-specific nature (number of courses offered, structure of student enrollments, availability of rooms, etc.). Summer schools provide a more irregular structure that demands special attention, a trial-and-error reformulation of the ETP in our case. In addition, the traditional formulations of the ETP, to the extent we have been able to scan, do not include the minimization of the crowdedness of the rooms. Thus, in creating a more comfortable environment, easier to monitor exams and, ability in handling unexpected dysfunctionalities (broken classroom equipment, etc.) this study is novel. Limitations of the research: The algorithms to solve an ETP formulated as an LMIP are of high complexity therefore, we are not able to assert the optimality of our suggested solutions acquired within time limitations. Keywords: examination timetabling, group decision making, lexicographic optimization, linear mixed-integer programming JEL: C44, C61, M12