Incorporating location,routing and inventory decisions in supply chain network design

This paper for the first time presents a novel model to simultaneously optimize location, allocation, capacity, inventory, and routing decisions in a stochastic supply chain system. Each customer’s demand is uncertain and follows a normal distribution, and each distribution center maintains a certain amount of safety stock. To solve the model, first we present an exact solution method by casting the problem as a mixed integer convex program, and then we establish a heuristic method based on a hybridization of Tabu Search and Simulated Annealing. The results show that the proposed heuristic is considerably efficient and effective for a broad range of problem sizes.     

Fleet deployment, network design and hub location of liner shipping companies

A mixed integer linear programming formulation is proposed for the simultaneous design of network and fleet deployment of a deep-sea liner service provider. The underlying network design problem is based on a 4-index (5-index by considering capacity type) formulation of the hub location problem which are known for their tightness. The demand is elastic in the sense that the service provider can accept any fraction of the origin–destination demand. We then propose a primal decomposition method to solve instances of the problem to optimality. Numerical results confirm superiority of our approach in comparison with a general-purpose mixed integer programming solver.     

Hybrid metaheuristic solutions to inventory location routing problem

This paper considers a supply chain network with multiple depots and geographically dispersed customers, each of which faces non-constant demand over a discrete planning horizon. The goal is to determine a set of depots to open, the delivery quantities to customers per period and the sequence in which they are replenished by a vehicle fleet such that the total system-wide cost is minimized. To solve it, first we construct a mixed integer program, and then propose a hybrid metaheuristic consisting of initialization, intensification and post-optimization. Results show that the proposed heuristic is considerably efficient and effective for many classical instances.     

The congested multicommodity network design problem

This paper studies a version of the fixed-charge multicommodity network design problem where in addition to the traditional costs of flow and design, congestion at nodes is explicitly considered. The problem is initially modeled as a nonlinear integer programming formulation and two solution approaches are proposed: (i) a reformulation of the problem as a mixed integer second order cone program to optimally solve the problem for small to medium scale problem instances, and (ii) an evolutionary algorithm using elements of iterated local search and scatter search to provide upper bounds. Extensive computational results on new benchmark problem instances and on real case data are presented.     

A Linear Programming approach for robust network revenue management in the airline industry

The classical revenue management problem consists of allocating a fixed network capacity to different customer classes, so as to maximize revenue. This area has been widely applied in service industries that are characterized by a fixed perishable capacity, such as airlines, cruises, hotels, etc.It is traditionally assumed that demand is uncertain, but can be characterized as a stochastic process (See Talluri and van Ryzin (2005) for a review of the revenue management models). In practice, however, airlines have limited demand information and are unable to fully characterize demand stochastic processes. Robust optimization methods have been proposed to overcome this modeling challenge. Under robust optimization framework, demand is only assumed to lie within a polyhedral uncertainty set (Lan et al. (2008); Perakis and Roels (2010)).In this paper, we consider the multi-fare, network revenue management problem for the case demand information is limited (i.e. the only information available is lower/upper bounds on demand). Under this interval uncertainty, we characterize the robust optimal booking limit policy by use of minimax regret criterion. We present an LP (Linear Programming) solvable mathematical program for the maximum regret so our model is able to solve large-scale problems for practical use. A genetic algorithm is proposed to find the booking limit control to minimize the maximum regret. We provide computational experiments and compare our methods to existing ones. The results demonstrate the effectiveness of our robust approach.     

Designing robust routes for demand-responsive transport systems

In this study, we propose an innovative concept for robust demand-responsive transportation (DRT) systems where vehicles may deviate from the planned route to accept late requests, which are unknown during the planning stage. We propose a new formulation of the problem as a stochastic mixed integer program and describe an efficient heuristic procedure that embeds a tabu search approach in a scheme for merging different scenario solutions. The computational results demonstrate the validity of the heuristic and provide useful managerial insights into DRT systems, thereby showing the value of incorporating uncertainty into the planning process.     

A supporting station model for reliable infrastructure location design under interdependent disruptions

This paper proposes a new modeling method that equivalently transforms interdependent and correlated facility failures in an infrastructure system into only i.i.d. disruptions in a supporting structure. The properties of this structure are examined and a mathematical model is created to solve reliable facility location design problems under correlated facility failure risks. This model is formulated into a compact integer linear program and can be efficiently solved by state-of-the-art solvers. A set of experiments and case studies are conducted to demonstrate the applicability of the proposed model and to draw managerial insights into the optimal system design.     

A novel modeling approach for the fleet deployment problem within a short-term planning horizon

This paper is concerned with model development for a short-term fleet deployment problem of liner shipping operations. We first present a mixed integer nonlinear programming model in which the optimal vessel speeds for different vessel types on different routes are interpreted as their realistic optimal travel times. We then linearize the proposed nonlinear model and obtain a mixed integer linear programming (MILP) model that can be efficiently solved by a standard mixed integer programming solver such as CPLEX. The MILP model determines the optimal route service frequency pattern and take into account the time window constraints of shipping services. Finally, we report our numerical results and performance of CPLEX on randomly generated instances.     

A Green Vehicle Routing Problem

A Green Vehicle Routing Problem (G-VRP) is formulated and solution techniques are developed to aid organizations with alternative fuel-powered vehicle fleets in overcoming difficulties that exist as a result of limited vehicle driving range in conjunction with limited refueling infrastructure. The G-VRP is formulated as a mixed integer linear program. Two construction heuristics, the Modified Clarke and Wright Savings heuristic and the Density-Based Clustering Algorithm, and a customized improvement technique, are developed. Results of numerical experiments show that the heuristics perform well. Moreover, problem feasibility depends on customer and station location configurations. Implications of technology adoption on operations are discussed.     

A robust mathematical model and heuristic algorithms for integrated aircraft routing and scheduling,with consideration of fleet assignment problem

One of the most important airline's products is to determine the aircraft routing and scheduling and fleet assignment. The key input data of this problem is the traffic forecasting and allocation that forecasts traffic on each flight leg. The complexity of this problem is to define the connecting flights when passengers should change the aircraft to reach the final destination. Moreover, as there exists various types of uncertainties during the flights, finding a solution which is able to absorb these uncertainties is invaluable. In this paper, a new robust mixed integer mathematical model for the integrated aircraft routing and scheduling, with consideration of fleet assignment problem is proposed. Then to find good solutions for large-scale problems in a rational amount of time, a heuristic algorithm based on the Simulated Annealing (SA) is introduced. In addition, some examples are randomly generated and the proposed heuristic algorithm is validated by comparing the results with the optimum solutions. The effects of robust vs non-robust solutions are examined, and finally, a hybrid algorithm is generated which results in more effective solution in comparison with SA, and Particle Swarm Optimization (PSO).     

Shift designs for freight handling personnel at air cargo terminals

This paper presents an integrated mixed integer linear programming (MILP) model for determining manpower requirements and related personnel shift designs for the build-up and break-down of the unit load devices (ULDs) at the air cargo terminal to minimize manpower costs. To utilize the manpower resources efficiently, we implement a new mechanism for demand leveling. In addition, we consider the qualification hierarchy between build-up and break-down workers. A case study based on the real-life data shows that the model is useful for manpower planning at air cargo terminals and the integrated approach is far superior to a traditional two-stage approach.     

Stochastic optimization of sustainable hybrid generation bioethanol supply chains

This paper focuses on designing a hybrid generation bioethanol supply chain (HGBSC) that will account for economic, environmental and social aspects of sustainability under various uncertainties. A stochastic mixed integer linear programming model is proposed to design an optimal HGBSC. A case study set in the state of North Dakota in the United States is used as an application of the proposed model. The results suggest that the designs of optimal HGBSC change when different sustainability standards are applied. In addition, sensitivity analysis is conducted to provide deeper understanding of the proposed model.     

Modeling downstream petroleum supply chain: The importance of multi-mode transportation to strategic planning

This paper proposes a deterministic mixed integer linear programming (MILP) model for downstream petroleum supply chain (PSC) network to determine the optimal distribution center (DC) locations, capacities, transportation modes, and transfer volumes. The model minimizes multi-echelon multi-product cost along the refineries, distribution centers, transportation modes and demand nodes. The relationship between strategic planning and multimodal transportation is further elucidated. A case study was considered with real data from the U.S. petroleum industry and transportation networks within Geographic Information System (GIS). A scenario analysis is also conducted to demonstrate the impact of key parameters on PSC decisions and total cost.     

Modeling and optimizing the integrated problem of closed-loop supply chain network design and disassembly line balancing

This paper describes an integrated model that jointly optimizes the strategic and tactical decisions of a closed-loop supply chain (CLSC). The strategic level decisions relate to the amounts of goods flowing on the forward and reverse chains. The tactical level decisions concern balancing disassembly lines in the reverse chain. The objective is to minimize costs of transportation, purchasing, refurbishing, and operating the disassembly workstations. A nonlinear mixed integer programming formulation is described for the problem. Numerical examples are presented using the proposed model.     

Heuristics for quay crane scheduling at indented berth

This paper discusses the quay crane scheduling problem at indented berth, an extension to the current quay crane scheduling problem in the field of container terminal operation. A mixed integer programming model by considering the unique features of the quay crane scheduling problem at indented berth is formulated. For solution, decomposition heuristic framework is developed and enhanced by Tabu search. To evaluate the performance of the proposed heuristic framework, a comprehensive numerical test is carried out and its results show the good quality of the proposed heuristic framework.     

Reliable emergency service facility location under facility disruption,en-route congestion and in-facility queuing

The planning of emergency service facility location, especially for those expecting high demand and severe conditions, requires consideration of victims’ en-route travel, in-facility service quality, and reliability of these service facilities themselves. This paper first presents a scenario-based stochastic mixed-integer non-linear program (MINLP) model that integrates facility disruption risks, en-route traffic congestion and in-facility queuing delay into an integrated facility location problem. We derive lower and upper bounds to this highly complex problem by approximating the expected total system costs across the normal and all probabilistic facility disruption scenarios. This allows us to develop a more tractable approximate MINLP formulation and a Lagrangian Relaxation (LR) based solution approach. The relaxed sub-problem for location and service allocation decisions is further reformulated into a second-order conic program. Numerical experiments show that the approximate model and LR solution approach are capable of overcoming the computational difficulties associated with the problem. Interesting findings and managerial insights are obtained from a series of sensitivity analyses, e.g., regarding the importance of considering in-facility queuing in location design, and the significance of resource pooling on the optimal facility deployment.     

The multi-period service territory design problem – An introduction,a model and a heuristic approach

In service territory design applications, a field service workforce is responsible for providing recurring services at their customers’ sites. We introduce the associated planning problem, which consists of two subproblems: In the partitioning subproblem, customers must be grouped into service territories. In the scheduling subproblem, customer visits must be scheduled throughout the multi-period planning horizon. The emphasis of this paper is put on the scheduling subproblem. We propose a mixed integer programming model for this subproblem and present a location-allocation heuristic. The results of extensive experiments on real-world instances show that the proposed heuristic produces high-quality solutions.     

A three-level supply chain network design model with risk-pooling and lead times

This paper considers a single-sourcing network design problem for a three-level supply chain consisting of suppliers, distribution centers (DC’s) and retailers, where risk-pooling strategy and DC-to-supplier dependent lead times are considered. The objective is to determine the number and locations of suppliers and DC’s, the assignment of each location-fixed DC to a supplier and that of each retailer to a DC, which minimizes the system-wide location, transportation, and inventory costs. The problem is formulated as a nonlinear integer programming model, for which a two-phase heuristic solution algorithm is derived based on the Lagrangian relaxation approach. Numerical experiments show that the proposed heuristic is effective and also efficient.     

Empty container management for intermodal transportation networks

We present a computational analysis of the effect of planning horizon length on empty container management for intermodal transportation networks. The analysis is based on an integer program that seeks to minimize total costs related to moving empty containers, subject to meeting requirements for moving loaded containers. A case study of potential container-on-barge operations within the Mississippi River basin illustrates the effects of planning horizon length on mode selection. A longer planning horizon can encourage the use of inexpensive, slow transportation modes, such as barge. The impact depends on the number and location of container storage pools.     

Optimal cargo container loading plans under stochastic demands for air express carriers

In this research, we develop a stochastic-demand cargo container loading plan model with the objective of minimizing the total operating cost, subject to the related operating constraints. The model is formulated as a nonlinear mixed integer program that is characterized as NP-hard. We employ a problem linearization technique, coupled with a mathematical programming solver, to develop a solution method. To preliminarily evaluate the model and the solution method, we perform a case study using data from an international air express carrier. The results show that the model and the solution method could be useful for air express carriers.