Affiliations: [a]
Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, West Bengal, India
| [b]
Department of Mathematics, Sidho-Kanho-Birsha University, Purulia, West Bengal, India
Correspondence:
[*]
Corresponding author. Manoranjan De, Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore-721102, West Bengal, India. Tel.: +91 8016155728; E-mail: [email protected].
Abstract: Imperfect economic production lot size (EPL) models are considered over different types of uncertain finite time horizons with stock-dependent demand, reliability dependent defective rate and random out-of-control state. Generally in EPL models, defective production starts after the passage of some time from production commencement. So occurrence of defective production is random and imposed here through a chance constraint. Reliability of a machinery system affects on the defective rate and production cost to produce an item. Here unit production cost depends on reliability and production rate and part of it is taken against the environment protection cost. Both linear and non-linear production dependent forms of quality are considered. The problems are formulated as total cost minimization problems with crisp, random, fuzzy, fuzzy-random, rough and fuzzy-rough constraints and solved using generalized reduced gradient method (GRG). Several special cases are derived and numerical experiments are performed to illustrate the general and particular models.
Keywords: Imperfect production, random defective rate, stock-dependent demand, chance constraints, reliability, uncertain time horizon
