M-Convexity and its applications in operations

Xin Chen, Menglong Li

Research output: Contribution to journalArticlepeer-review


MZ-convexity, one of the main concepts in discrete convex analysis, possesses many salient structural properties and allows for the design of efficient algorithms. In this paper, we establish several new fundamental properties of MZ-convexity and its variant SSQMZ-convexity (semistrictly quasi MZ-convexity). We show that in a parametric maximization model, the optimal solution is nonincreasing in the parameters when the objective function is SSQMZ-concave and the constraint is a box and illustrate when SSQMZ-convexity and MZ-convexity are preserved. A sufficient and necessary characterization of twice continuously differentiable MZ-convex functions is provided. We then use them to analyze two important operations models: a classical multiproduct dynamic stochastic inventory model and a portfolio contract model where a buyer reserves capacities in blocks from multiple competing suppliers. We illustrate that looking from the lens of MZ-convexity allows to simplify the complicated analysis in the literature for each model and extend the results to more general settings.

Original languageEnglish (US)
Pages (from-to)1396-1408
Number of pages13
JournalOperations Research
Issue number5
StatePublished - Sep 1 2021


  • Inventory control
  • M -convexity
  • Nonincreasing optimal solution
  • Portfolio contract
  • SSQM -convexity

ASJC Scopus subject areas

  • Computer Science Applications
  • Management Science and Operations Research


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