Multi-Product Newsvendor Problem with Customer-Driven Demand Substitution: A Stochastic Integer Program Perspective

2018 ◽  
Author(s):  
Jie Zhang ◽  
Weijun Xie ◽  
Subhash Sarin
Keyword(s):  
Integer Program ◽  
Newsvendor Problem ◽  
Demand Substitution ◽  
Stochastic Integer Program

Multiproduct Newsvendor Problem with Customer-Driven Demand Substitution: A Stochastic Integer Program Perspective

2020 ◽  
Author(s):  
Jie Zhang ◽  
Weijun Xie ◽  
Subhash C. Sarin
Keyword(s):  
Necessary Optimality Conditions ◽  
Integer Program ◽  
Newsvendor Problem ◽  
Sensitivity Analyses ◽  
Quadratic Program ◽  
Optimal Order ◽  
Demand Substitution ◽  
Performance Guarantees ◽  
Optimal Value ◽  
Stochastic Integer Program

This paper studies a multiproduct newsvendor problem with customer-driven demand substitution, where each product, once run out of stock, can be proportionally substituted by the others. This problem has been widely studied in the literature; however, because of nonconvexity and intractability, only limited analytical properties have been reported and no efficient approaches have been proposed. This paper first completely characterizes the optimal order policy when the demand is known and reformulates this nonconvex problem as a binary quadratic program. When the demand is random, we formulate the problem as a two-stage stochastic integer program, derive several necessary optimality conditions, prove the submodularity of the profit function, and also develop polynomial-time approximation algorithms and show their performance guarantees. We further propose a tight upper bound via nonanticipativity dual, which is proven to be very close to the optimal value and can yield a good-quality feasible solution under a mild condition. Our numerical investigation demonstrates effectiveness of the proposed algorithms. Moreover, several useful findings and managerial insights are revealed from a series of sensitivity analyses.

scholarly journals A Stochastic Integer Program with Dual Network Structure and Its Application to the Ground-Holding Problem

2003 ◽  
Vol 51 (1) ◽  
pp. 167-171 ◽  
Author(s):  
Michael O. Ball ◽  
Robert Hoffman ◽  
Amedeo R. Odoni ◽  
Ryan Rifkin
Keyword(s):  
Network Structure ◽  
Integer Program ◽  
Stochastic Integer Program

Capacitated strategic assortment planning under explicit demand substitution

2021 ◽  
Author(s):  
Nagihan Çömez-Dolgan ◽  
Nilgun Fescioglu-Unver ◽  
Ecem Cephe ◽  
Alper Şen
Keyword(s):  
Assortment Planning ◽  
Demand Substitution

scholarly journals Lane Allocation Optimization in Container Seaport Gate System Considering Carbon Emissions

2021 ◽  
Vol 13 (7) ◽  
pp. 3628
Author(s):  
Zhihong Jin ◽  
Xin Lin ◽  
Linlin Zang ◽  
Weiwei Liu ◽  
Xisheng Xiao
Keyword(s):  
Branch And Bound ◽  
Carbon Emissions ◽  
Integer Program ◽  
Arrival Times ◽  
Proposed Model ◽  
Gate System ◽  
Appointment System ◽  
Truck Appointment System ◽  
Gate Congestion ◽  
Allocation Decisions

Long queues of arrival trucks are a common problem in seaports, and thus, carbon emissions generated from trucks in the queue cause environmental pollution. In order to relieve gate congestion and reduce carbon emissions, this paper proposes a lane allocation framework combining the truck appointment system (TAS) for four types of trucks. Based on the distribution of arrival times obtained from the TAS, lane allocation decisions in each appointment period are determined in order to minimize the total cost, including the operation cost and carbon emissions cost. The resultant optimization model is a non-linear fractional integer program. This model was firstly transformed to an equivalent integer program with bilinear constraints. Then, an improved branch-and-bound algorithm was designed, which includes further transforming the program into a linear program using the McCormick approximation method and iteratively generating a tighter outer approximation along the branch-and-bound procedure. Numerical studies confirmed the validity of the proposed model and algorithm, while demonstrating that the lane allocation decisions could significantly reduce carbon emissions and operation costs.

scholarly journals Scanning integer points with lex-inequalities: a finite cutting plane algorithm for integer programming with linear objective

4OR ◽  
2020 ◽  
Author(s):  
Michele Conforti ◽  
Marianna De Santis ◽  
Marco Di Summa ◽  
Francesco Rinaldi
Keyword(s):  
Integer Point ◽  
Cutting Plane ◽  
Integer Program ◽  
Compact Set ◽  
Cutting Plane Method ◽  
Integer Points ◽  
Gomory Cuts ◽  
The Family ◽  
Split Cuts ◽  
Number Of Iterations

AbstractWe consider the integer points in a unimodular cone K ordered by a lexicographic rule defined by a lattice basis. To each integer point x in K we associate a family of inequalities (lex-inequalities) that define the convex hull of the integer points in K that are not lexicographically smaller than x. The family of lex-inequalities contains the Chvátal–Gomory cuts, but does not contain and is not contained in the family of split cuts. This provides a finite cutting plane method to solve the integer program $$\min \{cx: x\in S\cap \mathbb {Z}^n\}$$ min { c x : x ∈ S ∩ Z n } , where $$S\subset \mathbb {R}^n$$ S ⊂ R n is a compact set and $$c\in \mathbb {Z}^n$$ c ∈ Z n . We analyze the number of iterations of our algorithm.

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