Modeling and solution algorithm for project scheduling problem considering man-hour under uncertainty

Takumi Kitamura, Takayuki Shiina

Research output: Contribution to journalArticlepeer-review


Projects are often executed under uncertain circumstances and require prior decisions that take uncertainty into account. Among them, the schedule of the initial plan and the plan for additional decisions corresponding to the uncertainties become important. In this study, we developed a mathematical model of a two-stage stochastic programming problem considering time and cost tradeoffs and crushing, which are important in project scheduling. An effective solution using a stochastic integer linear model and a moment matching method was presented for DTCTP-C with random fluctuations. In project management, the duration of a job is determined by the man-hour and the amount of resources required for the job. The duration can be shortened by increasing the amount of additional resources utilized. The cost increases according to the the amount of resources used. This problem is referred to as the Time/Cost Trade-off Problem (TCTP). In this study, the relation between time and cost is represented by an inverse proportional curve. We present a solution to the Stochastic Discrete TCTP-Curve (SDTCTP-C) in which the duration of the job is defined as a random variable. It may also be necessary to study mathematical models that require multiple resources. Future prospects include expanding the model to take into account the amount of resources available at each time period. Furthermore, by reducing the difference between the maximum number of resources used and the minimum number of resources used to the furthest possible extent, it can be said that more realistic scheduling can be performed.

Original languageEnglish
Pages (from-to)37-45
Number of pages9
JournalJournal of Japan Industrial Management Association
Issue number1
Publication statusPublished - 2021


  • Project scheduling
  • Stochastic programming
  • Time/cost trade-off problem

ASJC Scopus subject areas

  • Strategy and Management
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering
  • Applied Mathematics


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