A Superclass of Edge-Path-Tree graphs with few cliques

Edge-Path-Tree graphs are intersection graphs of Edge-Path-Tree matrices that is matrices whose columns are incidence vectors of edge-sets of paths in a given tree. Edge-Path-Tree graphs have polynomially many cliques as proved in [4] and [7]. Therefore, the problem of finding a clique of maximum weight in these graphs is solvable in strongly polynomial time. In this paper we extend this result to a proper superclass of Edge-Path-Tree graphs. Each graph in the class is defined as the intersection graph of a matrix with no submatrix in a set W of seven small forbidden submatrices. By forbidding an eighth small matrix, our result specializes to Edge-Path-Tree graph

Curriculum-based course timetabling with student flow, soft constraints, and smoothing objectives: an application to a real case study

This paper deals with curriculum-based course timetabling. In particular, we describe the results of a real application at the University of Rome “Tor Vergata.” In this regard, we developed a multi-objective mixed-integer model which attempts to optimize (i) the flow produced by the students enrolled in the lectures, (ii) soft conflicts produced by the possible overlap among compulsory and non-compulsory courses, and (iii) the number of lecture hours per curriculum within the weekdays. The model has been implemented and solved by means of a commercial solver and experiments show that the model is able to provide satisfactory solutions as compared with the real scenario under consideration

A bi-objective model for scheduling green investments in two-stage supply chains

Investing in green technologies to increase sustainability in supply chains has become a common practice for two reasons: the first is directly related to the defense of the environment and people’s health to smooth the emissions of pollutants; the second is the increasing consumer awareness of green products. Despite the higher costs of producing with green technologies and processes, there is also a higher markup on the price of products which rewards the former costs. This study proposes a mathematical model for scheduling green investments over time in a two-stage supply chain to minimize the impact of production on the environment and the economic costs deriving from the investment. The resulting bi-objective model has nonlinear constraints and is solved using a commercial solver. Given its complexity, we propose an upper-bound heuristic and a lower-bound model to reduce the optimality gap attained at a given time limit. Tests on synthetic instances have been conducted, and an example demonstrates the applicability and efficacy of the proposed model

Sustainable two stage supply chain management: A quadratic optimization approach with a quadratic constraint

Designing a supply chain to comply with environmental policy requires awareness of how work and/or production methods impact the environment and what needs to be done to reduce those environmental impacts and make the company more sustainable. This is a dynamic process that occurs at both the strategic and operational levels. However, being environmentally friendly does not necessarily mean improving the efficiency of the system at the same time. Therefore, when allocating a production budget in a supply chain that implements the green paradigm, it is necessary to figure out how to properly recover costs in order to improve both sustainability and routine operations, offsetting the negative environmental impact of logistics and production without compromising the efficiency of the processes to be executed. In this paper, we study the latter problem in detail, focusing on the CO2 emissions generated by the transportation from suppliers to production sites, and by the production activities carried out in each plant. We do this using a novel mathematical model that has a quadratic objective function and all linear constraints except one, which is also quadratic, and models the constraint on the budget that can be used for green investments caused by the increasing internal complexity created by large production flows in the production nodes of the supply network. To solve this model, we propose a multistart algorithm based on successive linear approximations. Computational results show the effectiveness of our proposal

A Bi-objective cap-and-trade model for minimising environmental impact in closed-loop supply chains

A Closed-Loop Supply Chain (CLSC) is a complex network with unique environmental features and attributes that requires specific managerial policies and strategies. Quantitative models can provide a solid basis for these policies and strategies. This study expands the work of Shoaeinaeini et al. (2021) on Green Supply Chain Management. We propose a bi-objective facility location, demand allocation, and pricing model for CLSC networks. The proposed model considers two conflicting objective functions: maximising profits and minimising emissions. We show consumer environmental awareness can predict the products’ rate of return and determine a more suitable price for new products and the acquisition price for used products. The cap-and-trade policy has been implemented at its fullest potential, allowing the trading of carbon quotas. Therefore, companies may decide to produce less to sell more quotas or vice-versa, effectively picking the most profitable option. The model is solved and tested with the commercial solver BARON. The model effectively shows the trade-off between generating profits and emission reduction. Companies are able to turn a profit while abiding by the government’s intention of reducing emissions. The comparison with a single-objective version of the model highlights that the concurrent optimisation of economic and environmental objectives yields better results. The acquisition price of used products is a value worthy of monitoring. The government should focus on policies to assist the reverse flow of used products

A New Lower Bound for the Resource-Constrained Project Scheduling Problem with Generalized Precedence Relations

In this paper we propose a new lower bound for the resource constrained project scheduling problem with generalized precedence relationships. The lower bound is based on a relaxation of the resource constraints among independent activities and on a solution of the relaxed problem suitably represented by means of an AON acyclic network. Computational results are presented and confirmed a better practical performance of the proposed method with respect to the those present in the literatur

A Quadratic-Linear Bilevel Programming Approach to Green Supply Chain Management

Green Supply Chain Management requires coordinated decisions between the strategic and operational organization layers to address strict green goals. Furthermore, linking CO2 emissions to supply chain operations is not always easy. This study proposes a new mathematical model to minimize CO2 emissions in a three-layered supply chain. The model foresees using a financial budget to mitigate emissions contributions and optimize supply chain operations planning. The three-stage supply chain analyzed has inbound logistics and handling operations at the intermediate level. We assume that these operations contribute to emissions quadratically. The resulting bilevel programming problem is solved by transforming it into a nonlinear mixed-integer program by applying the Karush-Kuhn-Tucker conditions. We show, on different sets of synthetic data and on a case study, how our proposal produces solutions with a different flow of goods than a modified linear model version. This results in lower CO2 emissions and more efficient budget expenditure

Unregulated Cap-and-Trade Model for Sustainable Supply Chain Management

Cap-and-trade models have been largely studied in the literature when it comes to reducing emissions in a supply chain. In this paper, further pursuing the goal of analyzing the effectiveness of cap-and-trade strategies in reducing emissions in supply chains, we propose a mathematical model for sustainable supply chain management. This optimization program aims at reducing emissions and supply chain costs in an unregulated scenario w.r.t. the cap definition, i.e., trading CO2 is allowed but no formal limit on the CO2 emissions is imposed. Also, we considered an initial budget for technological investments by the facilities in the considered supply chain, allowing plants to reduce their unit production emissions at a different unit production cost. For this model, differently from what exists in the literature, we derive some theoretical conditions guaranteeing that, if obeyed, the emissions over time have a non-increasing trend meaning that decreasing caps over time can be attained with a self-regulated scenario. Computational results show the effectiveness of our approach

An Exact algorithm to minimize the makespan in project scheduling with scarce resources and feeding precedence relations

In this paper we study an extension of the Resource-Constrained Project Scheduling Problem (RCPSP) with minimum makespan objective by introducing as precedence constraints the so called “Feeding Precedences” (FP). For the RCPSP with FP we propose a new mathematical formulation and a branch and bound algorithm exploiting the latter formulation. The exact algorithm takes advantage also of a lower bound based on a Lagrangian relaxation of the same formulation. A computational experimentation on randomly generated instances and a comparison with the results achieved by a commercial solver, show that the proposed approach is able to behave satisfactorily

Minimizing the completion time of a project under resource constraints and feeding precedence relations: a Lagrangian relaxation based lower bound

In this paper we study an extension of the classical Resource-Constrained Project Scheduling Problem (RCPSP) with minimum makespan objective by introducing a further type of precedence constraints denoted as “Feeding Precedences” (FP). This kind of problem happens in that production planning environment, like make-to-order manufacturing, when the effort associated with the execution of an activity is not univocally related to its duration percentage and the traditional finish-to-start prece- dence constraints or the generalized precedence relations cannot completely represent the overlapping among activities. In this context we need to introduce in the RCPSP the FP constraints. For this problem we propose a new mathematical formulation and define a lower bound based on a resource constraints Lagrangian relaxation. A computational experimentation on randomly generated instances of sizes of up to 100 activities show a better performance of this lower bound with respect to others. More- over, for the optimally solved instances, its value is very close to the optimal one