A periodic review model under stochastic demand and stochastic occurrence of defectives

Date of Publication


Document Type

Master's Thesis

Degree Name

Master of Science in Industrial Engineering

Subject Categories

Industrial Engineering


Gokongwei College of Engineering


Industrial Engineering

Thesis Adviser

Edgar De Castro

Defense Panel Chair

Jesus Capulong

Defense Panel Member

Rolando Ramon Diaz
Antonio Medina


In a typical production system, whether it is technologically advanced or not, manufacturing operations are often imperfect so there output may contain defective items. The presence of defective items lead to the reduction in the original optimal order quantity which would, in turn, either trigger shortages or cause the ordering of raw materials to take place more frequently. In effect, the total quantity available for sale would be less and potential customers may be lost. Few authors have considered the simultaneous effect of demand variability and occurrence of defectives in a single period model. Further, all available literature on single period models are unconstrained. This study formulated a TWO-PERIOD OPTIMAL PRODUCTION PLAN which considers the simultaneous effect of stochastic demand and stochastic occurrence of defectives. Moreover, the inventory model that was developed includes a capacity constraint. This study includes set-up cost, production cost, salvage value, holding cost and backorder cost in the objective function. Convexity of the model was tested using the Unconstrained Optimization Technique and the Liebnitz' Rule. A numerical example was presented using the derived model. Both the demand pattern and the occurrence of defectives were assumed to be uniformly distributed. The Jacobian Transformation and Convolution Method were used to determine the density function of the product and sum of two uniform distributions, respectively.

Abstract Format






Accession Number


Shelf Location

Archives, The Learning Commons, 12F Henry Sy Sr. Hall

Physical Description

[172] leaves


Stochastic processes; Materials management; Mathematical models

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