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.     

Stochastic resource allocation for containerized cargo transportation networks when capacities are uncertain

We consider the stochastic resource allocation problem for containerized cargo transportation with uncertain capacities and network effects, in which a freight operator needs to allocate a certain amount of capacity to each product to maximize the expected profit. We formulate the problem as a constrained stochastic programming model and provide theoretical results that completely characterize the optimal solution to the model under a special case. Under a general case, we build an approximation model of the problem and propose a sampling based algorithm to solve the approximation model. A number of numerical experiments are offered to test the algorithm.     

A hybrid decomposition algorithm for designing a multi-modal transportation network under biomass supply uncertainty

This study presents a two-stage stochastic programming model for the design and management of a biomass co-firing supply chain network under feedstock supply uncertainty. To represent a more realistic case, we generate scenarios from prediction errors of the historical and forecasted biomass supply availabilities. We solve the model using a hybrid decomposition algorithm that combines Sample average approximation with an enhanced Progressive hedging algorithm. The proposed algorithm is validated via a real-world case study using data from Mississippi and Alabama. Computational results indicate that the proposed algorithm is capable of producing high quality solutions in a reasonable amount of time.     

Dynamic network design for reverse logistics operations under uncertainty

The design of reverse logistics network has attracted growing attention with the stringent pressures from environmental and social requirements. In general, decisions about reverse logistics network configurations are made on a long-term basis and factors influencing such reverse logistics network design may also vary over time. This paper proposes dynamic location and allocation models to cope with such issues. A two-stage stochastic programming model is further developed by which a deterministic model for multiperiod reverse logistics network design can be extended to account for the uncertainties. A solution approach integrating a recently proposed sampling method with a heuristic algorithm is also proposed in this research. A numerical experiment is presented to demonstrate the significance of the developed stochastic model as well as the efficiency of the proposed solution method.     

A stochastic programming winner determination model for truckload procurement under shipment uncertainty

We propose a two-stage stochastic integer programming model for the winner determination problem (WDP) in combinatorial auctions to hedge the shipper’s risk under shipment uncertainty. The shipper allows bids on combinations of lanes and solves the WDP to determine which carriers are to be awarded lanes. In addition, many other important comprehensive business side constraints are included in the model. We demonstrate the value of the stochastic solution over one obtained by a deterministic model based on using average shipment volumes. Computational results are given that indicate that moderately sized realistic instances can be solved by commercial branch and bound solvers in reasonable time.     

Marrying supply chain sustainability and resilience: A match made in heaven

Sustainable supply chain management has become an integral part of corporate strategy for virtually every industry. However, little is understood about the broader impacts of sustainability practices on the capacity of the supply chain to tolerate disruptions. This article aims to explore the sustainability–resilience relationship at the supply chain design level. A multi-objective optimization model featuring a sustainability performance scoring method and a stochastic fuzzy goal programming approach is developed that can be used to perform a dynamic sustainability tradeoff analysis and design a “resiliently sustainable” supply chain. Important managerial and practical insights are obtained from an empirical case study.     

Robust schedule design for liner shipping services

This paper examines the design of liner ship route schedules that can hedge against the uncertainties in port operations, which include the uncertain wait time due to port congestion and uncertain container handling time. The designed schedule is robust in that uncertainties in port operations and schedule recovery by fast steaming are captured endogenously. This problem is formulated as a mixed-integer nonlinear stochastic programming model. A solution algorithm which incorporates a sample average approximation method, linearization techniques, and a decomposition scheme, is proposed. Extensive numerical experiments demonstrate that the algorithm obtains near-optimal solutions with the stochastic optimality gap less 1.5% within reasonable time.     

Sustainable hub location under mixed uncertainty

This paper addresses a novel sustainable hub location problem (SHLP) in which two new environmental-based cost functions accounting for air and noise pollution of vehicles are incorporated. To cope with uncertain data incorporated in the model, a mixed possibilistic–stochastic programming approach is proposed to construct the crisp counterpart. A simulated annealing (SA) and an imperialist competitive algorithm (ICA) with a new solution representation are developed to solve real-sized instances whose performances are compared with a proposed lower bound. Finally, some computational experiments are provided to demonstrate the effectiveness of the proposed model and solution approaches.     

Robust schedule design for liner shipping services

This paper examines the design of liner ship route schedules that can hedge against the uncertainties in port operations, which include the uncertain wait time due to port congestion and uncertain container handling time. The designed schedule is robust in that uncertainties in port operations and schedule recovery by fast steaming are captured endogenously. This problem is formulated as a mixed-integer nonlinear stochastic programming model. A solution algorithm which incorporates a sample average approximation method, linearization techniques, and a decomposition scheme, is proposed. Extensive numerical experiments demonstrate that the algorithm obtains near-optimal solutions with the stochastic optimality gap less 1.5% within reasonable time.     

Carrying capacity procurement of rail and shipping services for automobile delivery with uncertain demand

The determination of the optimal carrying capacity procurement of rail and shipping services in the automobile intermodal network with unique characteristics is essential to save automobile delivery cost. In this research we develop a two-stage stochastic programming model for the tactical-level decision problem arising in the special automobile intermodal network. Furthermore, we improve the sample average approximation algorithmic procedure to solve the model. We apply the model and solution method to a case study associated with the Shanghai Automobile Industry Corporation. We believe that this study deals with an emerging new research topic with practical significance for the automobile industry.     

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.     

Dynamic supply chain network design with capacity planning and multi-period pricing

This paper addresses a new problem in designing and planning a multi-echelon and multi-product supply chain network over a multi-period horizon in which customer zones have price-sensitive demands. Based on price-demand relationships, a generic method is presented to obtain price levels for products and then, a mixed-integer linear programming model is developed. Due to the problem intractability, a simulated annealing algorithm that uses some developed linear relaxation-based heuristics for capacity planning and pricing is presented. Numerical results demonstrate the significance of the model as well as the efficiency of the solution algorithm and linear relaxation-based heuristics.     

Robust optimization for fleet planning under uncertainty

We create a formulation and a solution procedure for fleet sizing under uncertainty in future demands and operating conditions. The formulation focuses on robust optimization, using a partial moment measure of risk. This risk measure is incorporated into the expected recourse function of a two-stage stochastic programming formulation, and stochastic decomposition is used as a solution procedure. A numerical example illustrates the importance of including uncertainty in the fleet sizing problem formulation, and the nature of the fundamental tradeoff between acquiring more vehicles and accepting the risk of potentially high costs if insufficient resources are available.     

A three-stage stochastic facility routing model for disaster response planning

This paper presents a three-stage mixed-integer stochastic programming model for disaster response planning, considering the opening of local distribution facilities, initial allocation of supplies, and last mile distribution of aid. The vehicles available for transportation, the state of the infrastructure and the demand of the potential beneficiaries are considered as stochastic elements. Extensive computational testing performed on realistic instances shows that the solutions produced by the stochastic programming model are significantly better than those produced by a deterministic expected value approach.     

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.     

An approximate algorithm for the two-dimensional air cargo revenue management problem

For the air cargo revenue management problem, this study developed a solution algorithm based on approximating the expected revenue function in the dynamic programming (DP) model while taking into account the stochastic volume and weight of shipments. In order to alleviate the computational load, the approximation was achieved by computing only a limited number of points in the DP state space. In the simulation experiment, the developed algorithm was compared with a recent heuristic algorithm based on de-coupling the relationship between weight and volume. It was found that the approach of this study can generate higher revenue than the de-coupling control for most of the cases.     

Stochastic optimization models for the airport gate assignment problem

Uncertainties inherent in the airport traffic may lead to the unavailability of gates for accommodating scheduled flights. Incorporating random disruptions is crucial in constructing effective flight-gate assignments. We consider the gate assignment problem under uncertainty in flight arrival and departure times and develop stochastic programming models incorporating robustness measures based on the number of conflicting flights, idle and buffer times. The proposed models are formulated as large-scale mixed-integer programming problems and tabu search algorithms are implemented to obtain assignments of reasonable quality. We conduct a computational study to analyze the proposed alternate models and show the effectiveness of the solution methods.     

A deterministic mathematical model to support temporal and spatial decisions of the soybean supply chain

A novel deterministic mathematical model is presented as part of research into a stochastic optimization model for the soybean supply chain in Brazil. The model was conceived as a tool to aid in the decision-making of any trader involved in this highly complex market. The model is intended to be applied to decisions related to tactical planning over a time span of one year. The major spatial and temporal components of the soybean complex, including transportation mode decisions, are incorporated into the model. The mathematical model is described in detail. Several stochastic parameters are used with fixed values in the deterministic model to construct various scenarios. These parameters are the purchase and sale prices of the grain on the market, the crop failure rate and the volumes of demand. The model was tested using data from a large trade in Brazil with consistent results.     

Optimizing road network daily maintenance operations with stochastic service and travel times

This paper studies optimization methods for a routing problem encountered in daily maintenance operations of a road network. Stochastic service and travel times on road segments are considered. The problem is formulated as a variation of the capacitated arc routing problem (CARP). A chance-constrained programming model is firstly developed and solved by a branch-and-cut algorithm. A stochastic programming model with recourse is also proposed to take into account the recourse costs in case of route failure. The problem is solved by an adaptive large neighborhood search algorithm. The computational experiments demonstrate the effectiveness of the algorithm.     

Lead time aggregation: A three-echelon supply chain model

In this paper, destructive effects of upstream aggregated stochastic lead times on the supply chain (SC) performance are analyzed. For this purpose, a three-echelon SC consisting of one producer, one distributor, and one retailer is modeled. Both the producer and distributor face stochastic lead times, which can be also aggregated to create a long unpredictable lead time. In order to scale down shortages at the retailer site, an incentive scheme is proposed to convince the upstream members to increase their reorder points. Applying the coordinated model considerably increases the total profit earned by the whole SC as well as all SC members.