A heuristic framework for the bi-objective enhanced index tracking problem

The index tracking problem is the problem of determining a portfolio of assets whose performance replicates, as closely as possible, that of a financial market index chosen as benchmark. In the enhanced index tracking problem the portfolio is expected to outperform the benchmark with minimal additional risk. In this paper, we study the bi-objective enhanced index tracking problem where two competing objectives, i.e., the expected excess return of the portfolio over the benchmark and the tracking error, are taken into consideration. A bi-objective Mixed Integer Linear Programming formulation for the problem is proposed. Computational results on a set of benchmark instances are given, along with a detailed out-of-sample analysis of the performance of the optimal portfolios selected by the proposed model. Then, a heuristic procedure is designed to build an approximation of the set of Pareto optimal solutions. We test the proposed procedure on a reference set of Pareto optimal solutions. Computational results show that the procedure is significantly faster than the exact computation and provides an extremely accurate approximation.     

A New Dynamic Programming Decomposition Method for the Network Revenue Management Problem with Customer Choice Behavior

In this paper, we propose a new dynamic programming decomposition method for the network revenue management problem with customer choice behavior. The fundamental idea behind our dynamic programming decomposition method is to allocate the revenue associated with an itinerary among the different flight legs and to solve a single‐leg revenue management problem for each flight leg in the airline network. The novel aspect of our approach is that it chooses the revenue allocations by solving an auxiliary optimization problem that takes the probabilistic nature of the customer choices into consideration. We compare our approach with two standard benchmark methods. The first benchmark method uses a deterministic linear programming formulation. The second benchmark method is a dynamic programming decomposition idea that is similar to our approach, but it chooses the revenue allocations in an ad hoc manner. We establish that our approach provides an upper bound on the optimal total expected revenue, and this upper bound is tighter than the ones obtained by the two benchmark methods. Computational experiments indicate that our approach provides significant improvements over the performances of the benchmark methods.     

Multi-time scale Markov decision process approach to strategic network growth of reverse supply chains

This paper addresses a complex set of decisions that surround the growth over time of reverse supply chain networks that collect used products for reuse, refurbishment, and/or recycling by processors. The collection network growth problem is decomposed into strategic, tactical and operational problems. This paper focuses on the strategic problem which is to determine how to allocate capital budget resource effectively to grow the network to meet long term collection targets and collection cost constraints. We model the strategic problem as a Markov decision process which can also be posed as multi-time scale Markov decision problem. The recruitment problem in a tactical level appears as a sub-problem for the strategic model. Using dynamic programming, linear programming and Q-Learning approaches, an heuristic is implemented to solve realistically sized problems. A numerical study demonstrates that the heuristic can obtain a good solution for the large-scale problem in reasonable time which is not possible when trying to obtain the optimal solution with the exact DP approach.     

Facility Location: A Robust Optimization Approach

In this research, we apply robust optimization (RO) to the problem of locating facilities in a network facing uncertain demand over multiple periods. We consider a multi‐period fixed‐charge network location problem for which we find (1) the number of facilities, their location and capacities, (2) the production in each period, and (3) allocation of demand to facilities. Using the RO approach we formulate the problem to include alternate levels of uncertainty over the periods. We consider two models of demand uncertainty: demand within a bounded and symmetric multi‐dimensional box, and demand within a multi‐dimensional ellipsoid. We evaluate the potential benefits of applying the RO approach in our setting using an extensive numerical study. We show that the alternate models of uncertainty lead to very different solution network topologies, with the model with box uncertainty set opening fewer, larger facilities. Through sample path testing, we show that both the box and ellipsoidal uncertainty cases can provide small but significant improvements over the solution to the problem when demand is deterministic and set at its nominal value. For changes in several environmental parameters, we explore the effects on the solution performance.     

Multimodal hub location and hub network design

Through observations from real life hub networks, we introduce the multimodal hub location and hub network design problem. We approach the hub location problem from a network design perspective. In addition to the location and allocation decisions, we also study the decision on how the hub networks with different possible transportation modes must be designed. In this multimodal hub location and hub network design problem, we jointly consider transportation costs and travel times, which are studied separately in most hub location problems presented in the literature. We allow different transportation modes between hubs and different types of service time promises between origin–destination pairs while designing the hub network in the multimodal problem. We first propose a linear mixed integer programming model for this problem and then derive variants of the problem that might arise in certain applications. The models are enhanced via a set of effective valid inequalities and an efficient heuristic is developed. Computational analyses are presented on the various instances from the Turkish network and CAB data set.     

Penalizing passenger’s transfer time in computing airlines revenue

Airline strategic alliances result in a form of cooperation where firms can access the resources of others network members in order to create added value for their passengers. The shortcoming of this process is that each member of the network makes individual revenue management decisions to maximize its own income, resulting in a sub-optimal income for the network members.To deal with this problem, this paper suggests a resource allocation based on a transfer pricing mechanism, to cooperatively divide the revenue of a passenger between network members. The method penalizes the total time that a passenger takes for reaching the final destination. The model takes into consideration that the profit is independent of the number of available seats (with a maximum determined for each airline). The method computes the optimal transfer pricing and, at the same time, optimizes the quantity of seats (the booking limits). The solution results in a strong Nash equilibrium, which incorporate both the transfer prices and booking limits. We describe the transfer pricing process using an ergodic, finite and continuous-time Markov game model for multiple players. The revenue of each airline in the supply chain will depend on the number of flight transfers and the transit time of the passenger at the airports: the longer the time to the final destination, the lower the price. We compute a collaborative equilibrium point, useful for understanding the resulting revenue of each member of the network. For solving the game, we employ an iterative method based on a proximal approach that involves time penalization. In our final contribution, we present results from a numerical example, which validates the proposed Markov game model and measures the benefits of the transfer pricing resource allocation.     

Pricing,Allocation, and Overbooking in Dynamic Service Network Competition When Demand Is Uncertain

We study the problem of combined pricing, resource allocation, and overbooking by service providers involved in dynamic noncooperative oligopolistic competition on a network that represents the relationships of the providers to one another and to their customers when service demand is uncertain. We propose, analyze, and compute solutions for a model that is more general than other models reported in the revenue management literature to date. In particular, previous models typically consider only three or four of five key revenue management features that we have purposely built into our model: (1) pricing, (2) resource allocation, (3) dynamic competition, (4) an explicit network, and (5) uncertain demand. Illustrative realizations of the abstract problem we study are those of airline revenue management and service provision by companies facing resource constraints. Under fairly general regularity conditions, we prove existence and uniqueness of a pure strategy Nash equilibrium for dynamic oligopolistic service network competition described by our model. We also show, for an appropriate notion of regularity, that competition leads to the underpricing of network services, a finding numerically illustrated by an example of intermediate size. Our proposed algorithm can be implemented using well‐known off‐the‐shelf commercial software.     

Reliable Supply Chain Network Design

Risk management in supply chains has been receiving increased attention in the past few years. In this article, we present formulations for the strategic supply chain network design problem with dual objectives, which usually conflict with each other: minimizing cost and maximizing reliability. Quantifying the total reliability of a network design is not as straightforward as total cost calculation. We use reliability indices and develop analytical formulations that model the impact of upstream supply chain on individual entities’ reliability to quantify the total reliability of a network. The resulting multiobjective nonlinear model is solved using a novel hybrid algorithm that utilizes a genetic algorithm for network design and linear programming for network flow optimization. We demonstrate the application of our approach through illustrative examples in establishing tradeoffs between cost and reliability in network design and present managerial implications.     

A flexible model for the pricing of perishable assets

We present a flexible and versatile model which addresses the problem of assigning optimal prices to assets whose value becomes zero after a fixed expiry date. (Such assets include the important example of seats on airline flights.) Our model is broad in scope, in particular encompassing the ability to deal with arrivals of customers in groups. It is highly adaptable and can be adjusted to deal with a very extensive set of circumstances.Our approach to the problem is based on elementary and intuitively appealing ideas. We model the arrival of customers (or groups of customers) according to an inhomogeneous Poisson process. We incorporate into the model time dependent price sensitivity (which may also be described as “time dependent elasticity of demand”). In this setting the solution to the asset pricing problem is achieved by setting up coupled systems of differential equations which are readily amenable to numerical solution via (for instance) a vectorised Runge-Kutta procedure. An attractive feature of our approach is that it unifies the treatment of discrete and continuous prices for the assets.     

Using branch-and-price approach to solve the directed network design problem with relays

We present node-arc and arc-path formulations, and develop a branch-and-price approach for the directed network design problem with relays (DNDR). The DNDR problem can be used to model many network design problems in transportation, service, and telecommunication system, where relay points are necessary. The DNDR problem consists of introducing a subset of arcs and locating relays on a subset of nodes such that in the resulting network, the total cost (arc cost plus relay cost) is minimized, and there exists a directed path linking the origin and destination of each commodity, in which the distances between the origin and the first relay, any two consecutive relays, and the last relay and the destination do not exceed a predefined distance limit. With the node-arc formulation, we can directly solve small DNDR instances using mixed integer programming solver. With the arc-path formulation, we design a branch-and-price approach, which is a variant of branch-and-bound with bounds provided by solving linear programs using column generation at each node of the branch-and-bound tree. We design two methods to efficiently price out columns and present computational results on a set of 290 generated instances. Results demonstrate that our proposed branch-and-price approach is a computationally efficient procedure for solving the DNDR problem.     

Integrating Social Network Effects in the Share‐Of‐Choice Problem

Accounting for social network effects in marketing strategies has become an important issue. Taking a step back, we seek to incorporate and analyze social network effects on new product development and then propose a model to engineer product diffusion over a social network. We build upon the share‐of‐choice (SOC) problem, which is a strategic combinatorial optimization problem used commonly as one of the methods to analyze conjoint analysis data by marketers in order to identify a product with largest market share, and show how to incorporate social network effects in the SOC problem. We construct a genetic algorithm to solve this computationally challenging (NP‐Hard) problem and show that ignoring social network effects in the design phase results in a significantly lower market share for a product. In this setting, we introduce the secondary operational problem of determining the least expensive way of influencing individuals and strengthening product diffusion over a social network. This secondary problem is of independent interest, as it addresses contagion models and the issue of intervening in diffusion over a social network, which are of significant interest in marketing and epidemiological settings.     

A shelf-space optimization model when demand is stochastic and space-elastic

The more customer demand is impulse-driven, the more it is space-dependent and the more it is subject to variation. We investigate the corresponding problem of retail shelf-space planning when demand is stochastic and sensitive to the number and position of facings. We develop a model to maximize a retailer׳s profit by selecting the number of facings and their shelf position under the assumption of limited space. The model is particularly applicable to promotional or temporary products.We develop the first optimization model and solution approach that takes stochastic demand into account, since the current literature applies deterministic models for shelf-space planning. By the means of an innovative modeling approach for the case with space- and positioning effects and the conversion of our problem into a mixed-integer problem, we obtain optimal results within very short run times for large-scale instances relevant in practice. Furthermore, we develop a solution approach to account for cross-space elasticity, and solve it using an own heuristic, which efficiently yields near-optimal results. We demonstrate that correctly considering space elasticity and demand variation is essential. The corresponding impacts on profits and solution structures become even more significant when space elasticity and stochastic demand interact, resulting in up to 5% higher profits and up to 80% differences in solution structures, if both effects are correctly accounted for. We develop an efficient modeling approach, compare the model results with approaches applied in practice and derive rules-of-thumb for planners.     

优化设施服务的网络调整费用均衡问题研究

在物流网络中,当服务设施(配送中心、大型超市等)建立后,由于设施服务水平、市场需求等因素发生变化,需要调整物流网络中各个环节的配送时间来优化设施的服务能力。调整优化的过程中既要考虑需求目标、运行费用的同时也需要考虑调整的成本。本文针对该问题,提出了优化设施服务的物流网络调整费用均衡模型,并针对单个设施的树形配送网络结构,通过辅助网络将该问题转化为最小费用流问题,给出了多项式算法。最后,文中给出了算例以及两种费用的均衡分析。     

多目标物流网络优化模型的研究

针对物流网络规划中需要考虑多个目标的问题,以配流中心存储容量及使用率为约束,建立了基于总费用及最大单程距离(费用)最小的双目标数学模型,给出了优化模型的求解方法,为决策者提供多种可供选择的优化方案。     

Planning of a decentralized distribution network using bilevel optimization

This paper proposes a bilevel optimization problem to model the planning of a distribution network that allows us to take into account how decisions made at the distribution stage of the supply chain can affect and be affected by decisions made at the manufacturing stage. Usually, the distribution network design problem decides on the opening of depots and the distribution from the depots to customers only and pays no attention to the manufacturing process itself. By way of example, the paper discusses the implications of formulating a bilevel model to integrate distribution and manufacturing, maintaining the hierarchy existing in the decision process. The resulting model is a bilevel mixed integer optimization problem. Hence, only small instances can be optimally solved in an acceptable computing time. In order to be able to solve the optimization model for realistic large systems, a metaheuristic approach based on evolutionary algorithms is developed. The algorithm combines the use of an evolutionary algorithm to control the supply of depots with optimization techniques to determine the delivery from depots to customers and the supply from manufacturing plants to depots. A computational experiment is carried out to assess the efficiency and robustness of the algorithm.     

An Arborescent Network Formulation and Dual Ascent Based Procedure for the Two-Stage Multi-Item Dynamic Demand Lotsize Problem

Traditional approaches for modeling and solving dynamic demand lotsize problems are based on Zangwill's single-source network and dynamic programming algorithms. In this paper, we propose an arborescent fixed-charge network (ARBNET) programming model and dual ascent based branch-and-bound procedure for the two-stage multi-item dynamic demand lotsize problem. Computational results show that the new approach is significantly more efficient than earlier solution strategies. The largest set of problems that could be solved using dynamic programming contained 4 end items and 12 time periods, and required 475.38 CPU seconds per problem. The dual ascent algorithms averaged .06 CPU seconds for this problem set, and problems with 30 end items and 24 time periods were solved in 85.65 CPU seconds. Similar results verify the superiority of the new approach for handling backlogged demand. An additional advantage of the algorithm is the availability of a feasible solution, with a known worst-case optimality gap, throughout the problem-solving process.     

A Model for the Transportation of Hazardous Waste*

Many decision problems, such as the transportation of hazardous waste, can be modeled by networks. However, due to the imprecise nature of much of the information decision makers have available, it is sometimes difficult to determine a best approach to the problem. To alleviate this problem, a network model that combines both precise and imprecise information is presented for the transportation of hazardous waste. The properties of the network model are investigated and solution procedures are presented.     

A Dynamic Disaggregation Approach to Approximate Linear Programs for Network Revenue Management

The linear programming approach to approximate dynamic programming has received considerable attention in the recent network revenue management (RM) literature. A major challenge of the approach lies in solving the resulting approximate linear programs (ALPs), which often have a huge number of constraints and/or variables. Starting from a recently developed compact affine ALP for network RM, we develop a novel dynamic disaggregation algorithm to solve the problem, which combines column and constraint generation and exploits the structure of the underlying problem. We show that the formulation can be further tightened by considering structural properties satisfied by an optimal solution. We prove that the sum of dynamic bid‐prices across resources is concave over time. We also give a counterexample to demonstrate that the dynamic bid‐prices of individual resources are not concave in general. Numerical experiments demonstrate that dynamic disaggregation is often orders of magnitude faster than existing algorithms in the literature for problem instances with and without choice. In addition, adding the concavity constraints can further speed up the algorithm, often by an order of magnitude, for problem instances with choice.     

A sustainable supply chain network considering lot sizing with quantity discounts under disruption risks: centralized and decentralized models

This study proposes a framework for the main parties of a sustainable supply chain network considering lot-sizing impact with quantity discounts under disruption risk among the first studies. The proposed problem differs from most studies considering supplier selection and order allocation in this area. First, regarding the concept of the triple bottom line, total cost, environmental emissions, and job opportunities are considered to cover the criteria of sustainability. Second, the application of this supply chain network is transformer production. Third, applying an economic order quantity model lets our model have a smart inventory plan to control the uncertainties. Most significantly, we present both centralized and decentralized optimization models to cope with the considered problem. The proposed centralized model focuses on pricing and inventory decisions of a supply chain network with a focus on supplier selection and order allocation parts. This model is formulated by a scenario-based stochastic mixed-integer non-linear programming approach. Our second model focuses on the competition of suppliers based on the price of products with regard to sustainability. In this regard, a Stackelberg game model is developed. Based on this comparison, we can see that the sum of the costs for both levels is lower than the cost without the bi-level approach. However, the computational time for the bi-level approach is more than for the centralized model. This means that the proposed optimization model can better solve our problem to achieve a better solution than the centralized optimization model. However, obtaining this better answer also requires more processing time. To address both optimization models, a hybrid bio-inspired metaheuristic as the hybrid of imperialist competitive algorithm (ICA) and particle swarm optimization (PSO) is utilized. The proposed algorithm is compared with its individuals. All employed optimizers have been tuned by the Taguchi method and validated by an exact solver in small sizes. Numerical results show that striking similarities are observed between the results of the algorithms, but the standard deviations of PSO and ICA–PSO show better behavior. Furthermore, while PSO consumes less time among the metaheuristics, the proposed hybrid metaheuristic named ICA–PSO shows more time computations in all small instances. Finally, the provided results confirm the efficiency and the performance of the proposed framework and the proposed hybrid metaheuristic algorithm.

     

Optimal design of supply chain networks under uncertain transient demand variations

We consider a detailed mathematical formulation for the problem of designing supply chain networks comprising multiproduct production facilities with shared production resources, warehouses, distribution centers and customer zones and operating under time varying demand uncertainty. Uncertainty is captured in terms of a number of likely scenarios possible to materialize during the lifetime of the network. The problem is formulated as a mixed-integer linear programming problem and solved to global optimality using standard branch-and-bound techniques. A case study concerned with the establishment of Europe-wide supply chain is used to illustrate the applicability and efficiency of the proposed approach. The results obtained provide a good indication of the value of having a model that takes into account the complex interactions that exist in such networks and the effect of inventory levels to the design and operation.