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Joint decisions on inventory replenishment and emission reduction investment under different emission regulations

Carbon emission regulation policies have emerged as mechanisms to control firms’ carbon emissions. To meet regulatory requirements, firms can make changes in their production planning decisions or invest in green technologies. In this study, we analyse a retailer’s joint decisions on inventory replenishment and carbon emission reduction investment under three carbon emission regulation policies. Particularly, we extend the economic order quantity model to consider carbon emissions reduction investment availability under carbon cap, tax and cap-and-trade policies. We analytically show that carbon emission reduction investment opportunities, additional to reducing emissions as per regulations, further reduce carbon emissions while reducing costs. We also provide an analytical comparison between various investment opportunities and compare different carbon emission regulation policies in terms of costs and emissions. We document the results of a numerical study to further illustrate the effects of investment availability and regulation parameters.

Robust berth scheduling at marine container terminals via hierarchical optimization

In this paper, we present a mathematical model and a solution approach for the discrete berth scheduling problem, where vessel arrival and handling times are not known with certainty. The proposed model provides a robust berth schedule by minimizing the average and the range of the total service times required for serving all vessels at a marine container terminal. Particularly, a bi-objective optimization problem is formulated such that each of the two objective functions contains another optimization problem in its definition. A heuristic algorithm is proposed to solve the resulting robust berth scheduling problem. Simulation is utilized to evaluate the proposed berth scheduling policy as well as to compare it to three vessel service policies usually adopted in practice for scheduling under uncertainty.

Analysis of different approaches to cross-dock truck scheduling with truck arrival time uncertainty

This paper studies scheduling of inbound trucks at the inbound doors of a cross-dock facility under truck arrival time uncertainty. Arrival time of an inbound truck is considered to be unknown. In particular, the cross-dock operator only acknowledges the arrival time window of each truck, i.e., the lower and upper bounds of any inbound trucks arrival time. In absence of any additional information, the cross-dock operator may use three approaches to determine a scheduling strategy: deterministic approach (which assumes expected truck arrival times are equal to their mid-arrival time windows), pessimistic approach (which assumes the worst truck arrivals will be realized), and optimistic approach (which assumes the best truck arrivals will be realized). In this paper, a bi-level optimization problem is formulated for pessimistic and optimistic approaches. We discuss a Genetic Algorithm (GA) to solve the truck-to-door assignments for given truck arrival times, which solves the deterministic approach. Then the GA is modified to solve the bi-level formulations of the pessimistic and the optimistic approaches. Our numerical studies show that an hybrid approach regarding the pessimistic and the optimistic approaches may outperform all of the three approaches in certain cases.

Economic and environmental comparison of grouping strategies in coordinated multi-item inventory systems

The increasing concerns for sustainability throughout supply chains are enforcing managers to plan their operations considering not only economic but also environmental performance. Inventory management is one of the main determinants of the costs incurred and emissions generated throughout supply chains as it defines the level of logistical operations, freight transportation, and warehousing activities. In this study, we analyze a multi-item inventory control system with coordinated shipments. In particular, we revisit the well-known deterministic joint replenishment problem (JRP) with economic and environmental objectives under indirect and direct grouping strategies. We formulate and develop solution methods for each bi-objective JRP and compare direct and indirect grouping strategies with respect to their economic as well as environmental performance. A set of numerical studies is presented to examine the settings where a specific grouping strategy can be economically and environmentally better than the other.

Military system of systems architecting with individual system contracts

This paper studies the process of architecting a System of Systems (SoS) where the SoS architect can negotiate with individual systems. Particularly, the SoS architect aims to select a set of systems to provide a set of capabilities required for the SoS as well as the interfaces that enable communications amongst the selected systems. The SoS architect regards a set of three objectives: cost and deadline minimization and performance maximization. The performance levels of the capabilities provided by a system can be improved through additional funds contracted by the SoS architect. The system decides on how to use the allocated funds. We model the resulting Stackelberg game between the SoS architect and the individual systems as a multi-objective multi-level optimization problem. Three evolutionary heuristic methods are proposed and compared in a set of numerical studies. Further numerical studies illustrate the benefits of the modeling approach compared to system contracting after system selection.

A multi-objective military system of systems architecting problem with inflexible and flexible systems: formulation and solution methods

System of systems (SoS) architecting is the process of bringing together and connecting a set of systems so that the collection of the systems, i.e., the SoS is equipped with a set of required capabilities. A system is defined as inflexible in case it contributes to the SoS with all of the capabilities it can provide. On the other hand, a flexible system can collaborate with the SoS architect in the capabilities it will provide. In this study, we formulate and analyze a SoS architecting problem representing a military mission planning problem with inflexible and flexible systems as a multi-objective mixed-integer-linear optimization model. We discuss applications of an exact and an evolutionary method for generating and approximating the Pareto front of this model, respectively. Furthermore, we propose a decomposition approach, which decomposes the problem into smaller sub-problems by adding equality constraints, to improve both the exact and the evolutionary methods. Results from a set of numerical studies suggest that the proposed decomposition approach reduces the computational time for generating the exact Pareto front as well as it reduces the computational time for approximating the Pareto front while not resulting in a worse approximated Pareto front. The proposed decomposition approach can be easily used for different problems with different exact and heuristic methods and thus is a promising tool to improve the computational time of solving multi-objective combinatorial problems. Furthermore, a sample scenario is presented to illustrate the effects of system flexibility.

On the Flexibility of Systems in System of Systems Architecting

Abstract System of Systems (SoS) architecting requires analyzing a set of individual but interconnected systems simultaneously in order to build a communicating SoS, which can provide the capabilities needed. In general, the systems can provide a set of capabilities and the SoS architect needs to decide which systems to include in the SoS so that each capability is provided by at least one system. In this case, the systems are inflexible, i.e., a selected system will contribute to the SoS with all the capabilities it can provide. On the other hand, if SoS architect can incentivize systems to contribute specific capabilities instead of all its capabilities, it might be possible to build a better SoS in terms of not only one objective but all objectives considered. In this study, we compare SoS architecting with inflexible and flexible systems and quantify the value of the flexibility of the systems for a military application. Two evolutionary algorithms are constructed for the SoS architecting with inflexible and flexible systems for the resulting multi-objective optimization problems. These evolutionary algorithms output a set of Pareto efficient SoSs for the architect. Upon comparing the Pareto fronts of inflexible and flexible models, we quantify the value of systems’ flexibilities. It is demonstrated that SoS architecting with flexible systems can improve performance while decreasing costs.

A mathematical modeling approach to resource allocation for railroad-highway crossing safety upgrades

State Departments of Transportation (S-DOTs) periodically allocate budget for safety upgrades at railroad-highway crossings. Efficient resource allocation is crucial for reducing accidents at railroad-highway crossings and increasing railroad as well as highway transportation safety. While a specific method is not restricted to S-DOTs, sorting type of procedures are recommended by the Federal Railroad Administration (FRA), United States Department of Transportation for the resource allocation problem. In this study, a generic mathematical model is proposed for the resource allocation problem for railroad-highway crossing safety upgrades. The proposed approach is compared to sorting based methods for safety upgrades of public at-grade railroad-highway crossings in Tennessee. The comparison shows that the proposed mathematical modeling approach is more efficient than sorting methods in reducing accidents and severity.

Integrated districting, fleet composition, and inventory planning for a multi-retailer distribution system

We study an integrated districting, fleet composition, and inventory planning problem for a multi-retailer distribution system. In particular, we analyze the districting decisions for a set of retailers such that the retailers within the same district share truck capacity for their shipment requirements. The number of trucks of each type dedicated to a retailer district and retailer inventory planning decisions are jointly determined in a district formation problem. We provide a mixed-integer-nonlinear programming formulation for this problem and develop a column generation based heuristic approach for its set partitioning formulation. To do so, we first characterize important properties of the optimal fleet composition and inventory planning decisions for a given retailer district. Then, we utilize these properties within a branch-and-price method to solve the integrated districting, fleet composition, and inventory planning problem. A set of numerical studies demonstrates the efficiency of the solution methods discussed for the investigated subproblems. An additional set of numerical studies compares the branch-and-price method to a commercial solver and an evolutionary heuristic method. Further numerical studies illustrate the economic as well as environmental benefits of the integrated modeling approach for various settings.