Formulation Matters: Reciprocating Integer Programming for Birchbox Product Assortment

2021 ◽  
Vol 51 (5) ◽  
pp. 347-360
Author(s):  
Irvin Lustig ◽  
Patricia Randall ◽  
Robert Randall
Keyword(s):  
Integer Programming ◽  
Integer Program ◽  
Mixed Integer ◽  
Mixed Integer Program ◽  
Programming Formulation ◽  
Programming Technique ◽  
Monthly Basis ◽  
Customer Base ◽  
Product Assortment ◽  
Business Requirements

Birchbox created a mixed-integer programming formulation to determine the products that it will send to its subscribers in individual boxes on a monthly basis. The goal of this formulation is to produce a set of different box configurations that are then assigned to customers to meet the diverse needs of its varied customer base. As Birchbox’s business grew, the mixed-integer program was taking days to solve, and experimenting with different business requirements to determine the best set of configurations became impossible. Therefore, Princeton Consultants created the Reciprocating Integer Programming technique to reduce these solution times, thus decreasing them to typically under 20 minutes. This has dramatically changed the way that Birchbox can run its subscription business.

Improving Sports Media’s Crystal Ball for National Basketball Association Playoff Elimination

2020 ◽  
Author(s):  
Mark A. Husted ◽  
Eli V. Olinick ◽  
Alexandra M. Newman
Keyword(s):  
Integer Programming ◽  
Mixed Integer Programming ◽  
Integer Program ◽  
National Basketball Association ◽  
Mixed Integer ◽  
Mixed Integer Program ◽  
Crystal Ball ◽  
Winning Percentage ◽  
Mip Models ◽  
Do So

The National Basketball Association (NBA) is divided into two conferences, each of which comprises 15 teams. At the end of the regular season, the top eight teams from each conference, based on winning percentage, compete in the playoffs. Mixed-integer-programming (MIP) models determine when a team has guaranteed its position in the playoffs (clinched) or, conversely, when it has been eliminated before the completion of the regular season. Our models incorporate a series of complex two-way tiebreaking criteria used by the NBA to determine how many more games are needed either to clinch or to avoid elimination. We compare the time at which a given team has clinched or been eliminated, in terms of the number of games played in the season to date, as posted in the NBA official standings, against results from our mixed-integer program. For the 2017–2018 season, when our models outperform those of the NBA, they do so by an average of 4.1 games. We also describe a scenario in which the NBA erroneously reported that the Boston Celtics had clinched a playoff spot and, conversely, show that the Golden State Warriors had clinched a playoff spot before the official announcement by the NBA.

A stochastic mixed integer program to model spatial wildfire behavior and suppression placement decisions with uncertain weather

2016 ◽  
Vol 46 (2) ◽  
pp. 234-248 ◽  
Author(s):  
Erin J. Belval ◽  
Yu Wei ◽  
Michael Bevers
Keyword(s):  
Wildland Fire ◽  
Fire Behavior ◽  
Integer Program ◽  
Mixed Integer ◽  
Mixed Integer Program ◽  
Weather Forecasts ◽  
Placement Decisions ◽  
Weather Events ◽  
Weather Changes ◽  
Nonanticipativity Constraints

Wildfire behavior is a complex and stochastic phenomenon that can present unique tactical management challenges. This paper investigates a multistage stochastic mixed integer program with full recourse to model spatially explicit fire behavior and to select suppression locations for a wildland fire. Simplified suppression decisions take the form of “suppression nodes”, which are placed on a raster landscape for multiple decision stages. Weather scenarios are used to represent a distribution of probable changes in fire behavior in response to random weather changes, modeled using probabilistic weather trees. Multistage suppression decisions and fire behavior respond to these weather events and to each other. Nonanticipativity constraints ensure that suppression decisions account for uncertainty in weather forecasts. Test cases for this model provide examples of fire behavior interacting with suppression to achieve a minimum expected area impacted by fire and suppression.

A Note on a Conceptual Framework for Dynamic Location—Allocation Analysis

1976 ◽  
Vol 8 (4) ◽  
pp. 443-446
Author(s):  
W G Truscott
Keyword(s):  
Conceptual Framework ◽  
Integer Program ◽  
Original Version ◽  
Mixed Integer ◽  
Mixed Integer Program ◽  
Location Allocation ◽  
Dynamic Location

This note examines a previously published model for dynamic location—allocation analysis. The usefulness of this model is enhanced by reformulating the problem as an operational zero-one, mixed-integer program while retaining the intent of the original version.

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.

Mixed Integer Programming Formulation for the Energy-Efficient Train Timetables Problem

2017 ◽  
pp. 65-86
Author(s):  
Rodrigo Alexander Castro Campos ◽  
Sergio Luis Pérez Pérez ◽  
Gualberto Vazquez Casas ◽  
Francisco Javier Zaragoza Martínez
Keyword(s):  
Integer Programming ◽  
Mixed Integer Programming ◽  
Energy Efficient ◽  
Mixed Integer ◽  
Programming Formulation ◽  
Integer Programming Formulation

Multi-Objective Territory Design for Sales Managers of a Direct Sales Company

2019 ◽  
pp. 160-178 ◽  
Author(s):  
Elias Olivares-Benitez ◽  
Pilar Novo Ibarra ◽  
Samuel Nucamendi-Guillén ◽  
Omar G. Rojas
Keyword(s):  
Integer Program ◽  
National Average ◽  
Mixed Integer ◽  
Mixed Integer Program ◽  
Sales Managers ◽  
Territory Design ◽  
Direct Sales ◽  
Sales Company ◽  
A Company

This chapter presents a case study to organize the sales territories for a company with 11 sales managers to be assigned to 111 sales coverage units in Mexico. The assignment problem is modeled as a mathematical program with two objective functions. One objective minimizes the maximum distance traveled by the manager, and the other objective minimizes the variation of the sales growth goals with respect to the national average. To solve the bi-objective non-linear mixed-integer program, a weights method is selected. Some instances are solved using commercial software with long computational times. Also, a heuristic and a metaheuristic based on simulated annealing were developed. The design of the heuristic generates good solutions for the distance objective. The metaheuristic produces better results than the heuristic, with a better balance between the objectives. The heuristic and the metaheuristic are capable of providing good results with short computational times.

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