April - June 2007 - Kasetsart University

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From the statistical tests, the qualities of
solutions found from both methods were not
significantly different for test problem sets 1, 2
and 3. However, Algorithm 2 became superior to
the pattern search for larger problem sets. Notice
on the test results, the total cost obtained from the
pattern search could be as poor as 68% deviating
from the MINLP lower bounds in large problem
instances, while those from Algorithm 2 would not
be worse than 20% from the lower bounds.
Algorithm 2 was hence the most efficient method
for solving this safety stock determination
problem, in terms of both solution quality and
computation time.
DISCUSSION
It had been shown in the previous section
that Algorithm 2, which was based on a basic NLP
theorem, could provide high quality solutions in
short computation times for the safety stock level
determination problem in the considered two-stage
manufacturing system. The algorithm utilized only
a set of simple decision rules, in contrast to the
pattern search heuristic, which required the users
to comprehend its mechanisms. The decision rules
for finding optimum safety stocks also matched
the common managerial logics that when the
opportunity cost was high, the safety stocks should
be held to prevent the product deficiency, but they
should not be stocked when the inventory costs
were high. Moreover, the search heuristic such as
pattern search would terminate the search after
some stopping criteria had been satisfied.
Therefore, in some cases, it might not thoroughly
search the solution space for the solutions.
CONCLUSION
In this research, two algorithms for
determining safety stocks in a two-stage
manufacturing system were proposed by analyzing
the derivatives of cost function and the cost
Kasetsart J. (Nat. Sci.) 41(2)
comparisons. The algorithms were found to work
very efficiently on the test problems. They could
provide high-quality solutions for every test
instance in less than 1 second. The deviations from
the known integer solutions or the lower bounds
were less than 3% on average. The algorithms also
outperformed the pattern search algorithm, which
was presented in the previous research.
ACKNOWLEDGEMENT
This project was funded by faculty of
Agro-Industry, Kasetsart University. The author
gratefully acknowledges this support.
LITURATURE CITED
Inderfurth, K. and S. Minner. 1998. Safety Stocks
in Multi-Stage Inventory Systems under
Different Service Measures. Eur. J. Oper.
Res. 106: 57-73.
Krupp, J.A.G. 1997. Safety Stock Management.
Prod. Inventory Manag. J. 38(3): 11-18.
Kolda, T.G., R.M. Lewis and V. Torczon. 2003.
Optimization by Direct Search: New
Perspectives on Some Classical and Modern
Methods. Siam Rev. 45(3): 385–482
Maia, L.O.A. and R.Y. Qassim. 1999. Minimum
Cost Safety Stocks for Frequent Delivery
Manufacturing. Int. J. Prod. Econ. 62: 233-
236.
Marsden, J.E. and A. Tromba. 1981. Vector
Calculus. 2 nd ed. W.H. Freeman. San
Francisco. 591 p.
Montgomery, D.C. and G.C. Runger. 2004.
Applied Statistics and Probability for
Engineers, 3 rd ed. John Wiley & Sons. New
Jersey. 706 p.
Silver, E.A., D.F. Pyke and R. Peterson. 1998.
Inventory Management and Production
Planning and Scheduling. 3 rd ed. John Wiley
& Sons. New Jersey. 754 p.
Siribanluoewut, Y. 2006. Determining Safety