2023/08/09 by Varun Suriyanarayana, Suriyanarayana, Varun, Varun Sivashankar +5 · 1 citation
Business, Management and Accounting · Engineering · #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #FOS: Mathematics #Facility Location and Emergency Management #Optimization and Control (math.OC) #Optimization and Packing Problems #Supply Chain and Inventory Management
paper · pdf · doi:10.48550/arxiv.2308.04846
openalex publication_date 2023/08/09 · openalex created_date 2023/08/18 · openalex updated_date 2026/07/28
The joint replenishment problem (JRP) is a classical inventory management problem. We consider a natural generalization with outliers, where we are allowed to reject (that is, not service) a subset of demand points. In this paper, we are motivated by issues of fairness - if we do not serve all of the demands, we wish to ``spread out the pain'' in a balanced way among customers, communities, or any specified market segmentation. One approach is to constrain the rejections allowed, and to have separate bounds for each given customer. In our most general setting, we consider a set of C features, where each demand point has an associated rejection cost for each feature, and we have a given bound on the allowed rejection cost incurred in total for each feature. This generalizes a model of fairness introduced in earlier work on the Colorful k-Center problem in which (analogously) each demand point has a given color, and we bound the number of rejections of each color class. We give the first constant approximation algorithms for the fairness-constrained JRP with a constant number of features; specifically, we give a 2.86-approximation algorithm in this case. Even for the special case in which we bound the total (weighted) number of outliers, this performance guarantee improves upon bounds previously known for this case. Our approach is an LP-based algorithm that splits the instance into two subinstances. One is solved by a novel iterative rounding approach and the other by pipage-based rounding. The standard LP relaxation has an unbounded integrality gap, and hence another key element of our algorithm is to strengthen the relaxation by correctly guessing key attributes of the optimal solution, which are sufficiently concise, so that we can enumerate over all possible guesses in polynomial time - albeit exponential in C, the number of features.