A strategic model of job arrivals to a single machine with earliness and tardiness penalties

Amihai Glazer, Refael Hassin, Liron Ravner

Research output: Contribution to journalArticlepeer-review


We consider a game of decentralized timing of jobs to a single server (machine) with a penalty for deviation from a due date, and no delay costs. The jobs’ sizes are homogeneous and deterministic. Each job belongs to a single decision maker, a customer, who aims to arrive at a time that minimizes his(her) deviation penalty. If multiple customers arrive at the same time, then their order of service is determined by a uniform random draw. We show that if the cost function has a weighted absolute deviation form, then any Nash equilibrium is pure and symmetric, that is, all customers arrive together. Furthermore, we show that there exist multiple, in fact a continuum, of equilibrium arrival times, and provide necessary and sufficient conditions for the socially optimal arrival time to be an equilibrium. The base model is solved explicitly, but the prevalence of a pure symmetric equilibrium is shown to be robust to several relaxations of the assumptions: restricted server availability, inclusion of small waiting costs, stochastic job sizes, randomly sized population, heterogeneous due dates, and nonlinear deviation penalties.

Original languageEnglish
Pages (from-to)265-278
Number of pages14
JournalIISE Transactions
Issue number4
StatePublished - 3 Apr 2018
Externally publishedYes

Bibliographical note

Publisher Copyright:
Copyright © 2018 “IISE”.


  • Queue arrival time game
  • decentralized scheduling
  • equilibrium sequencing
  • single machine sequencing

ASJC Scopus subject areas

  • Industrial and Manufacturing Engineering


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