Determining Expected Value and Variance of Demand for Safety Stock Level under Random Parameters

Abstract

The patients demand is vital in healthcare area. Thus, to determine safety stock level is also significant. But, determining safety stock level in inventory systems based on stochastic lead-time is a much smaller section of literature especially in healthcare area. Therefore, this study aimed to contribute to the literature in this area. This study is investigated for calculating the expected value and variance of demand for determining safety stock level under random parameters (the number of arrivals, transferal rates between levels and length of stays). The lead-time required when supplying medical material in the hospital is also random. A case study is presented using with the real data obtained from Neonatal Intensive Care Unit which has a complex inventory system because of the random parameters and transferal probabilities between levels.

Keywords

• Expected Value,Healthcare Systems,Neonatal Intensive Care Unit,Random Parameters,Safety Stock Level

References

1. [1] Louly, MA. and Dolgui, A. (2009). Calculating safety stocks for assembly systems with random component procurement lead times: A branch and bound algorithm. European Journal of Operation Research 199: 723- 731.
2. [2] Silver, EA. and Zufferey, N. (2005). Inventory control of raw materials under stochastic and seasonal lead times. International Journal of Production Research 43: 5161- 5179.
3. [3] Kelle, P. and Silver, EA. (1990). Safety stock reduction by order splitting. Naval Research Logistics 37: 725- 743.
4. [4] Lambrecht, MR. and Vandaele, NJ. (1996). A general approximation for the single product lot sizing model with queuing delays. European Journal of Operation Research 95: 73- 88.
5. [5] Hung, YF. and Chang, CH. (1999). Determining safe-ty stocks for production planning in uncertain manufac-turing. International Journal of Production Economics 58: 199- 208.
6. [6] Alstrom, P. (2001). Numerical computation of inven-tory policies, based on the EOQ/ value for order-point systems. International Journal of Production Economics 71: 235- 245.
7. [7] Persona, A., Catena, M., Ferrari, E. and Manzini, R. (2003). Quantitative models for evaluating safety stocks in case of modular products. In : 17th International Con-ference on Production Research (ICPR 17th), 3-7 August 2003, Blacksburg, Virginia, USA.
8. [8] Persona, A., Battini, D., Manzini, R. and Pareschi, A. (2007). Optimal safety stock levels of subessemblies and manufacturing components. International Journal of Production Economics 110: 147- 159.

9. [9] Desmet, B., Aghezzaf, EH. and Vanmaele, H. (2010). A normal approximation model for safety stock optimiza-tion in a two echelon distribuation system. Journal of the Operational Research Society 61 (1): 156- 163.
10. [10] Krajewski, LJ.. and Ritzman, LP. (1996). Operations Management: Strategy and Analysis. Addison-Wesley Publishing Company: New York.
11. [11] Kowalski, JC. (1998). CEO’s and CFO’s Express Con-cern about Materials Management. Healthcare Financial Management 56- 60.
12. [12] Feller, W. (1971). An Introduction to Probability Theory and its Applications. J Wiley: New York.
13. [13] Ross, SM. Applied Probability Models with Optimi-zation Applications. Dover Publications: New York, 1992.
14. [14] Tijms, HC. A First Course in Stochastic Models. John Wiley and Sons Ltd: England, 2003.
15. [15] Akcan, S. and Kokangul, A. A new approximation for inventory control system with decision variable lead-time and stochastic demand. International Journal of Industrial Engineering 2013; 20 (3-4): 262-272.
16. [16] Kokangul, A, Ozkan, A., Akcan, S., Ozcan, K. and Narli, M. Statistical Analysis of Patients’ Characteristics in Neonatal Intensive Care Units. Journal of Medical Systems 2010; 34 (4): 471-478.