Abstract
This paper investigates the effect of permissible delay in payments on ordering policies in a periodic review (s, S) inventory model with stochastic demand. A new mathematical model is developed, which is an extension to that of Veinott and Wagner (Mngt Sci 1965; 11: 525) who applied renewal theory and stationary probabilistic analysis to determine the equivalent average cost per review period. The performance of the model is validated using a custom-built simulation programme. In addition, two distribution-free heuristic methods of reasonable accuracy develop approximate optimal policies for practical purposes based only on the mean and the standard deviation of the demand. Numerical examples are presented with results discussed.
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Acknowledgements
We are grateful to the two referees for their constructive comments and suggestions. BS Maddah thanks his current academic advisor, Dr Ebru Bish of Virginia Tech, for her support and encouragement while this work was being revised.
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Appendices
Appendix B: The SPAM of Schneider and Ringuest38
Evaluate λ τ , σ τ , and D p as in Appendix A.
Find
where
The value of q above is determined according to the values of c using a rational approximation as follows:
If c<0.5, set w=(ln (1/c 2))0.5. Otherwise, set w=c, and then compute q by
where if c<0.5, then
If c⩾0.5, then
Find
where
The value of g above is found based on w=(ln (25/v 2))0.5 where v=(1−γ)μ/σ τ .
where
Finally, the ‘optimal’ policy is obtained as follows:
if D p /λ>1.5, then the ‘optimal’ policy is ŝ=s p and Ŝ=s p +D p .
Otherwise, the optimal policy is ŝ=min(s p , S 0) and Ŝ=min(s p +D p , S 0 ).
Appendix A: The RPAM of Ehrhardt and Mosier34
Let λ and σ be the mean and standard deviation of the demand per review period. Find the following
and
If D p /λ>1.5, then the ‘optimal’ policy is ŝ=s p and Ŝ=s p +D p .
Otherwise, the optimal policy is ŝ=min (s p , S 0) and Ŝ=min (s+D p , S 0), where
with Φ−1(·) being the inverse cumulative density function of the standard Normal distribution. The values of Φ−1(·) function are usually tabulated. Silver et al 25 (pp 735–736) provide an accurate rational approximation for this function, which is suited for spreadsheets applications.
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Maddah, B., Jaber, M. & Abboud, N. Periodic review (s, S) inventory model with permissible delay in payments. J Oper Res Soc 55, 147–159 (2004). https://doi.org/10.1057/palgrave.jors.2601675
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DOI: https://doi.org/10.1057/palgrave.jors.2601675