Two techniques for solving nonlinear decreasing demand inventory system with shortage backorders

Astanti, Ririn Diar and Ai, The Jin and Luong, Huynh Trung and Wee, Hui-Ming Two techniques for solving nonlinear decreasing demand inventory system with shortage backorders. In: Jurnal Ilmiah Internasional terindeks SCOPUS, Semester Genap 2013/2014.

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Abstract

This paper studies the effect of two imperfect key production subsystems (KPS) on the optimal number of production cycles where a product is to be manufactured in batches on a production system over a finite planning horizon. During a production run of the product, the two imperfect KPS may shift from an in-control to an out-of control state due to three independent sources of shocks. A shock from source 1, 2, and 3 causes the shift on the first KPS, the second KPS, and both KPS’s, respectively. Each shocks occur at random time U1, U2, and U3 following exponential distribution with mean 1/λ1, 1/λ2, and 1/λ3, respectively. After each individual shocks, consequently, the production system will produced some defective items with different rates. Three different schemes of defectives rates are considered here which are constant, linear increasing function of time, and exponential increasing function of time. For each scheme, a mathematical model describing the situation is developed in order to determine a number of production cycles that minimizes the expected total cost per unit time including setup, inventory carrying, and defective costs. Solution approach of finding optimal solution of the models is provided, together with some numerical examples.

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