An extended EMQ model for a failure prone machine with general lifetime distribution

Abstract This paper presents an EMQ model which determines an optimal lot size in a failure prone machine. It is assumed that time between failures of a machine is generally distributed, and a machine is repaired instantaneously when it fails. Depending on various types of failure rate function of a machine, it is discussed how to determine an EMQ and prove its uniqueness. Variations of an EMQ depending on repair cost are also examined. Through numerical experiments, extensive investigations are carried out on the effects of repair cost and setup cost to an EMQ as well as average cost, and some interesting behaviors are observed.

[1]  Sheldon M. Ross,et al.  Stochastic Processes , 2018, Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics.

[2]  רבקה פריאור,et al.  גמלאות נפגעי עבודה, 1989 , 1991 .

[3]  Meir J. Rosenblatt,et al.  Economic Production Cycles with Imperfect Production Processes , 1986 .

[4]  Evan L. Porteus.  Investing in Reduced Setups in the EOQ Model , 1985 .

[5]  Arnoldo C. Hax,et al.  Production and inventory management , 1983 .

[6]  Dimitri Kececioglu,et al.  Reliability engineering handbook , 1991 .

[7]  Liliane Pintelon,et al.  Production Batching with Machine Breakdowns and Safety Stocks , 1992, Oper. Res..

[8]  Richard E. Barlow,et al.  Statistical Theory of Reliability and Life Testing: Probability Models , 1976 .

[9]  דבי עובדיה,et al.  קו חירום לנשים מוכות , 1991 .

[10]  U. Hjorth.  A Reliability Distribution With Increasing, Decreasing, Constant and Bathtub-Shaped Failure Rates , 1980 .

[11]  Graham K. Rand,et al.  Decision Systems for Inventory Management and Production Planning , 1979 .

[12]  Meir J. Rosenblatt,et al.  Simultaneous determination of production cycle and inspection schedules in a production system , 1987 .

[13]  P. Billington.  The classic economic production quantity model with setup cost as a function of capital expenditure , 1987 .

[14]  אסתר טולידנו,et al.  מקבלי דמי אבטלה בשנת 1990 , 1991 .

[15]  Meir J. Rosenblatt,et al.  A Production and Maintenance Planning Model with Restoration Cost Dependent on Detection Delay , 1989 .

[16]  Evan L. Porteus.  Optimal Lot Sizing, Process Quality Improvement and Setup Cost Reduction , 1986, Oper. Res..

[17]  Hau L. Lee,et al.  Lot sizing to reduce capacity utilization in a production process with defective items, process corrections, and rework , 1992 .

[18]  יעקב צדקה,et al.  משפחתונים לקשישים בטבריה , 1991 .

[19]  Chang Hyun Kim,et al.  An extended optimal lot sizing model with an unreliable machine , 1997 .

[20]  M. A. Rahim.  JOINT DETERMINATION OF PRODUCTION QUANTITY, INSPECTION SCHEDULE, AND CONTROL CHART DESIGN , 1994 .

[21]  A. Seidmann,et al.  Production lot sizing with machine breakdowns , 1992 .