Demand Modeling in the Presence of Unobserved Lost Sales

2020 ◽  
Author(s):  
Shivaram Subramanian ◽  
Pavithra Harsha
Keyword(s):  
Large Scale ◽  
Partial Information ◽  
Optimal Parameter ◽  
Arrival Rate ◽  
Mixed Integer ◽  
Mixed Integer Program ◽  
Optimization Approach ◽  
Estimation Model ◽  
Solution Quality ◽  
Demand Models

We present an integrated optimization approach to parameter estimation for discrete choice demand models where data for one or more choice alternatives are censored. We employ a mixed-integer program (MIP) to jointly determine the prediction parameters associated with the customer arrival rate and their substitutive choices. This integrated approach enables us to recover proven, (near-) optimal parameter values with respect to the chosen loss-minimization (LM) objective function, thereby overcoming a limitation of prior multistart heuristic approaches that terminate without providing precise information on the solution quality. The imputations are done endogenously in the MIP by estimating optimal values for the probabilities of the unobserved choices being selected. Under mild assumptions, we prove that the approach is asymptotically consistent. For large LM instances, we derive a nonconvex-contvex alternating heuristic that can be used to obtain quick, near-optimal solutions. Partial information, user acceptance criteria, model selection, and regularization techniques can be incorporated to enhance practical efficacy. We test the LM model on simulated and real data and present results for a variety of demand-prediction scenarios: single-item, multi-item, time-varying arrival rate, large-scale instances, and a dual-layer estimation model extension that learns the unobserved market shares of competitors. This paper was accepted by Yinyu Ye, optimization.

A Novel Approach for Two-Stage UAV Path Planning in Pipeline Network Inspection

2020 ◽  
Author(s):  
Rui Qiu ◽  
Yongtu Liang
Keyword(s):  
Path Planning ◽  
Large Scale ◽  
Flight Path ◽  
Mixed Integer ◽  
Optimization Approach ◽  
Two Stage ◽  
Calculation Time ◽  
Pipeline Network ◽  
Second Stage ◽  
Computational Performance

Abstract Currently, unmanned aerial vehicle (UAV) provides the possibility of comprehensive coverage and multi-dimensional visualization of pipeline monitoring. Encouraged by industry policy, research on UAV path planning in pipeline network inspection has emerged. The difficulties of this issue lie in strict operational requirements, variable flight missions, as well as unified optimization for UAV deployment and real-time path planning. Meanwhile, the intricate structure and large scale of the pipeline network further complicate this issue. At present, there is still room to improve the practicality and applicability of the mathematical model and solution strategy. Aiming at this problem, this paper proposes a novel two-stage optimization approach for UAV path planning in pipeline network inspection. The first stage is conventional pre-flight planning, where the requirement for optimality is higher than calculation time. Therefore, a mixed integer linear programming (MILP) model is established and solved by the commercial solver to obtain the optimal UAV number, take-off location and detailed flight path. The second stage is re-planning during the flight, taking into account frequent pipeline accidents (e.g. leaks and cracks). In this stage, the flight path must be timely rescheduled to identify specific hazardous locations. Thus, the requirement for calculation time is higher than optimality and the genetic algorithm is used for solution to satisfy the timeliness of decision-making. Finally, the proposed method is applied to the UAV inspection of a branched oil and gas transmission pipeline network with 36 nodes and the results are analyzed in detail in terms of computational performance. In the first stage, compared to manpower inspection, the total cost and time of UAV inspection is decreased by 54% and 56% respectively. In the second stage, it takes less than 1 minute to obtain a suboptimal solution, verifying the applicability and superiority of the method.

scholarly journals A GRASP Approach for Solving Large-Scale Electric Bus Scheduling Problems

Energies ◽  
2021 ◽  
Vol 14 (20) ◽  
pp. 6610
Author(s):  
Raka Jovanovic ◽  
Islam Safak Bayram ◽  
Sertac Bayhan ◽  
Stefan Voß
Keyword(s):  
Public Transport ◽  
High Speed ◽  
Large Scale ◽  
Integer Program ◽  
Mixed Integer ◽  
Transport Systems ◽  
Mixed Integer Program ◽  
Scheduling Problems ◽  
Electric Bus ◽  
Battery Capacity

Electrifying public bus transportation is a critical step in reaching net-zero goals. In this paper, the focus is on the problem of optimal scheduling of an electric bus (EB) fleet to cover a public transport timetable. The problem is modelled using a mixed integer program (MIP) in which the charging time of an EB is pertinent to the battery’s state-of-charge level. To be able to solve large problem instances corresponding to real-world applications of the model, a metaheuristic approach is investigated. To be more precise, a greedy randomized adaptive search procedure (GRASP) algorithm is developed and its performance is evaluated against optimal solutions acquired using the MIP. The GRASP algorithm is used for case studies on several public transport systems having various properties and sizes. The analysis focuses on the relation between EB ranges (battery capacity) and required charging rates (in kW) on the size of the fleet needed to cover a public transport timetable. The results of the conducted computational experiments indicate that an increase in infrastructure investment through high speed chargers can significantly decrease the size of the necessary fleets. The results also show that high speed chargers have a more significant impact than an increase in battery sizes of the EBs.

scholarly journals Supply Chain Optimization by Mixed Integer Program for Manufacturer and Retailer System of Poultry firm in Bangladesh

2016 ◽  
Vol 34 ◽  
pp. 75-87
Author(s):  
Mohammad Khairul Islam ◽  
Mohammed Forhad Uddin ◽  
Md M Alam
Keyword(s):  
Large Scale ◽  
Raw Materials ◽  
Integer Program ◽  
Mixed Integer ◽  
Mixed Integer Program ◽  
Selling Price ◽  
Supply Chain Optimization ◽  
Self Employment ◽  
Gdp Growth Rate ◽  
The Cost

In this study, we formulate mixed integer program for manufacturer and retailer system of poultry firm in Bangladesh that is one of the most promising sectors to increase Gross Domestic Product (GDP) growth rate plus equitable distribution through arranging food security as well as ensuring self-employment, creating purchasing power and reducing poverty at a large scale. From the survey, it has observed that the selling price of eggs and chicken fluctuate depending on the natural calamities. We have made a question survey on some poultry firm in the district of Mymensingh and Gazipur. This paper maximized the profit and minimizes the cost. The formulated mixed integer program has solved by branch and bound algorithm using A Mathematical Programming Language (AMPL). It has observed that the profit and selling price have very good relationship with production cost and raw materials cost but no significant relation with fixed cost.GANIT J. Bangladesh Math. Soc.Vol. 34 (2014) 75-87

Analysis of Optimal Unit Numbers and Sizes for Microturbine Cogeneration Systems

2004 ◽  
Author(s):  
Satoshi Gamou ◽  
Koichi Ito ◽  
Ryohei Yokoyama
Keyword(s):  
Energy Demand ◽  
Large Scale ◽  
Maximum Energy ◽  
Mixed Integer ◽  
Small Scale ◽  
Optimization Approach ◽  
Operational Strategies ◽  
Energy Demands ◽  
Exhaust Heat ◽  
Annual Total

The relationships between unit numbers and capacities to be installed for microturbine cogeneration systems are analyzed from an economic viewpoint. In analyzing, an optimization approach is adopted. Namely, unit numbers and capacities are determined together with maximum contract demands of utilities such as electricity and natural gas so as to minimize the annual total cost in consideration of annual operational strategies corresponding to seasonal and hourly energy demand requirements. This optimization problem is formulated as a large-scale mixed-integer linear programming one. The suboptimal solution of this problem is obtained efficiently by solving several small-scale subproblems. Through numerical studies carried out on systems installed in hotels by changing the electrical generating/exhaust heat recovery efficiencies, the initial capital cost of the microturbine cogeneration unit and maximum energy demands as parameters, the influence of the parameters on the optimal numbers and capacities of the microturbine cogeneration units is clarified.

scholarly journals Partitioning and solving large-scale tactical harvest scheduling problems for industrial plantation forests

2020 ◽  
Vol 50 (8) ◽  
pp. 811-818
Author(s):  
Pedro Bellavenutte ◽  
Woodam Chung ◽  
Luis Diaz-Balteiro
Keyword(s):  
Large Scale ◽  
Optimization Procedure ◽  
Mixed Integer ◽  
Forest Planning ◽  
Planning Problem ◽  
Optimization Approach ◽  
Scheduling Problems ◽  
Harvest Scheduling ◽  
Plantation Forests ◽  
Industrial Plantation

Spatially explicit, tactical forest planning is a necessary but challenging task in the management of plantation forests. It involves harvest scheduling and planning for road access and log transportation over time and space. This combinatorial problem can be formulated into the fixed-charge transportation problem (FCTP), in which the sum of fixed and variable costs is minimized while meeting harvest volume requirements and allowing necessary road maintenance and log hauling activities. The problem can be solved using general optimization methods such as mixed-integer linear programming (MILP), but the computational efficiency of the MILP-based approach quickly drops as the size and complexity of the problem increases. We developed a new optimization procedure that partitions the large planning problem into smaller subproblems. We applied a hybrid optimization approach using both MILP and heuristic rules to efficiently solve the large FCTP that otherwise may not be solvable using traditional methods. We applied our approach to an industrial plantation forest in Brazil. Our applications demonstrate the performance of the new optimization procedure and the benefit of solving large forest planning problems that integrate harvest scheduling with road access and transportation.

On the preventive management of sediment-related sewer blockages: a combined maintenance and routing optimization approach

2016 ◽  
Vol 74 (2) ◽  
pp. 302-308 ◽  
Author(s):  
John E. Fontecha ◽  
Raha Akhavan-Tabatabaei ◽  
Daniel Duque ◽  
Andrés L. Medaglia ◽  
María N. Torres ◽  
...  
Keyword(s):  
Cost Savings ◽  
Integer Program ◽  
Mixed Integer ◽  
Mixed Integer Program ◽  
Optimal Time ◽  
Optimization Approach ◽  
Planning And Scheduling ◽  
Routing Optimization ◽  
Dump Trucks ◽  
Geographically Distributed

In this work we tackle the problem of planning and scheduling preventive maintenance (PM) of sediment-related sewer blockages in a set of geographically distributed sites that are subject to non-deterministic failures. To solve the problem, we extend a combined maintenance and routing (CMR) optimization approach which is a procedure based on two components: (a) first a maintenance model is used to determine the optimal time to perform PM operations for each site and second (b) a mixed integer program-based split procedure is proposed to route a set of crews (e.g., sewer cleaners, vehicles equipped with winches or rods and dump trucks) in order to perform PM operations at a near-optimal minimum expected cost. We applied the proposed CMR optimization approach to two (out of five) operative zones in the city of Bogotá (Colombia), where more than 100 maintenance operations per zone must be scheduled on a weekly basis. Comparing the CMR against the current maintenance plan, we obtained more than 50% of cost savings in 90% of the sites.

scholarly journals A General Cooperative Optimization Approach for Distributing Service Points in Mobility Applications

Algorithms ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 232
Author(s):  
Thomas Jatschka ◽  
Günther R. Raidl ◽  
Tobias Rodemann
Keyword(s):  
Objective Function ◽  
Matrix Factorization ◽  
Large Scale ◽  
User Interaction ◽  
User Preferences ◽  
Mixed Integer ◽  
Optimization Approach ◽  
Mixed Integer Linear Program ◽  
User Interactions ◽  
The Matrix

This article presents a cooperative optimization approach (COA) for distributing service points for mobility applications, which generalizes and refines a previously proposed method. COA is an iterative framework for optimizing service point locations, combining an optimization component with user interaction on a large scale and a machine learning component that learns user needs and provides the objective function for the optimization. The previously proposed COA was designed for mobility applications in which single service points are sufficient for satisfying individual user demand. This framework is generalized here for applications in which the satisfaction of demand relies on the existence of two or more suitably located service stations, such as in the case of bike/car sharing systems. A new matrix factorization model is used as surrogate objective function for the optimization, allowing us to learn and exploit similar preferences among users w.r.t. service point locations. Based on this surrogate objective function, a mixed integer linear program is solved to generate an optimized solution to the problem w.r.t. the currently known user information. User interaction, refinement of the matrix factorization, and optimization are iterated. An experimental evaluation analyzes the performance of COA with special consideration of the number of user interactions required to find near optimal solutions. The algorithm is tested on artificial instances, as well as instances derived from real-world taxi data from Manhattan. Results show that the approach can effectively solve instances with hundreds of potential service point locations and thousands of users, while keeping the user interactions reasonably low. A bound on the number of user interactions required to obtain full knowledge of user preferences is derived, and results show that with 50% of performed user interactions the solutions generated by COA feature optimality gaps of only 1.45% on average.

scholarly journals Quantile Inverse Optimization: Improving Stability in Inverse Linear Programming

2021 ◽  
Author(s):  
Zahed Shahmoradi ◽  
Taewoo Lee
Keyword(s):  
Linear Programming ◽  
Large Scale ◽  
Robust Regression ◽  
Model Fitting ◽  
Exact Algorithm ◽  
Integer Program ◽  
Inverse Optimization ◽  
Mixed Integer ◽  
Mixed Integer Program ◽  
The Impact

Although inverse linear programming (LP) has received increasing attention as a technique to identify an LP that can reproduce observed decisions that are originally from a complex system, the performance of the linear objective function inferred by existing inverse LP methods is often highly sensitive to noise, errors, and uncertainty in the underlying decision data. Inspired by robust regression techniques that mitigate the impact of noisy data on the model fitting, in “Quantile Inverse Optimization: Improving Stability in Inverse Linear Programming,” Shahmoradi and Lee propose a notion of stability in inverse LP and develop an inverse optimization model that identities objective functions that are stable against data imperfection. Although such a stability consideration renders the inverse model a large-scale mixed-integer program, the authors analyze the connection between the model and well-known biclique problems and propose an efficient exact algorithm as well as heuristics.

scholarly journals Fuzzy Reliability Optimization for 2-Hub Center Problem with Cluster-Based Policy and Application in Cross-Border Supply Chain Network Design Using TS Algorithm

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Chenyi Yan ◽  
Xifu Wang ◽  
Kai Yang
Keyword(s):  
Supply Chain ◽  
Large Scale ◽  
Mixed Integer ◽  
Optimization Approach ◽  
Reliability Optimization ◽  
Supply Chain Network ◽  
Center Problem ◽  
Fuzzy Reliability ◽  
Hub Location Problem ◽  
Cross Border

As information and communication technology evolves and expands, business and markets are linked to form a complex international network, thus generating plenty of cross-border trading activities in the supply chain network. Through the observations from a typical cross-border supply chain network, this paper introduces the fuzzy reliability-oriented 2-hub center problem with cluster-based policy, which is a special case of the well-studied hub location problem (HLP). This problem differs from the classical HLP in the sense that (i) the hub-and-spoke (H&S) network is grouped into two clusters in advance based on their cross-border geographic features, and (ii) a fuzzy reliability optimization approach based on the possibility measure is developed. The proposed problem is first modeled through a mixed-integer nonlinear programming (MINLP) formulation that maximizes the reliability of the entire cross-border supply chain network. Then, some linearization techniques are implemented to derive a linear model, which can be efficiently solved by exact algorithms run by CPLEX for only small instances. To counteract the difficulty for solving the proposed problem in realistic-sized instances, a tabu search (TS) algorithm with two types of move operators (called “Swap I” and “Swap II”) is further developed. Finally, a series of numerical experiments based on the Turkish network and randomly generated large-scale datasets are set up to verify the applicability of the proposed model as well as the superiority of the TS algorithm compared to the CPLEX.

scholarly journals Shortest-Path Optimization of Ship Diesel Engine Disassembly and Assembly Based on AND/OR Network

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Deng-Zhi Chen ◽  
Chen Wei ◽  
Guo-Ling Jia ◽  
Zhi-Hua Hu
Keyword(s):  
Diesel Engine ◽  
Shortest Path ◽  
Large Scale ◽  
Random Search ◽  
Computing Time ◽  
Graph Model ◽  
Mixed Integer ◽  
Mixed Integer Linear Program ◽  
Optimal Sequence ◽  
Solution Quality

Ship diesel engine disassembly and assembly (SDEDA) is essential for ship inspection and maintenance and navigation safety. The SDEDA consists of various machinery parts and operations. It is crucial to develop a system of SDEDA operations to improve the efficiency of disassembly and assembly (D&A). Considering the “AND” and “OR” relations (modeled as links) among the D&A operations (modeled as nodes), an “AND/OR” network is developed to extend a specialized graph model for the D&A sequencing problem in the context of education and training. Then, we devised a mixed-integer linear program (MILP) to optimize the SDEDA sequence based on the AND/OR network. Considering the flow balance in the AND/OR network, we developed exact algorithms and random search algorithms using breadth-first, branch cut and depth-first strategies to minimize the cost of the shortest path that represents an optimal sequence of D&A operations. To the best of our knowledge, it is the first try to formulate the D&A operations by an extended network model. Numerical experiments show that the proposed algorithms are practical for solving large-scale instances with more than 2000 D&A operations. The breadth-first shortest-path algorithm outperforms the MILP solver from the perspective of solution quality and computing time, and all developed algorithms are competitive in terms of computing time.

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