Blood platelet production: Optimization by dynamic programming and simulation

Abstract Blood platelets are precious, as voluntarily supplied by donors, and highly perishable, with limited lifetimes of 5–7 days. Demand is highly variable and uncertain. A practical production and inventory rule is strived for that minimizes shortages and spill. The demand and production are periodic, as varying over the seven days of the week. Demand for ‘young’ platelets (oncology and hematology) and demand for platelets of ‘any’ age up to the maximal shelf life (traumatology and general surgery) are distinguished. A combined Markov dynamic programming (MDP) and simulation approach is presented and applied to a real life case of a Dutch blood bank. By down-sizing the dimension and applying this combined approach it is shown that order-up-to type replenishment rules that perform quite well can be found. Particularly, a double-level order-up-to rule, so-called 2D rule, is derived, with one level corresponding to ‘young’ platelets and one to the total inventory. This rule is easy to implement and is shown to be ‘nearly optimal’. This approach and the double order-up-to rule seem to be new. The results are most suitable for sensitivity analyses such as with respect to shortages and production costs for blood platelet inventory management.

[1]  William P. Pierskalla,et al.  Optimal Issuing Policies for Perishable Inventory , 1972 .

[2]  Russell R. Barton,et al.  Proceedings of the 2000 winter simulation conference , 2000 .

[3]  John B. Jennings,et al.  Blood Bank Inventory Control , 1973 .

[4]  Steven Nahmias,et al.  Perishable Inventory Theory: A Review , 1982, Oper. Res..

[5]  Liming Liu,et al.  A discrete‐time model for perishable inventory systems , 1999, Ann. Oper. Res..

[6]  Steven Nahmias,et al.  Optimal Ordering Policies for Perishable Inventory - II , 1975, Oper. Res..

[7]  Jan van der Wal,et al.  Blood Platelet Production: a multi-type perishable inventory problem , 2004, OR.

[8]  van Zyl,et al.  Inventory control for perishable commodities , 1963 .

[9]  Steven Nahmias,et al.  Optimal ordering policies for a product that perishes in two periods subject to stochastic demand , 1973 .

[10]  Mark S. Daskin,et al.  Case study in platelet inventory management , 1997 .

[11]  E Brodheim,et al.  A computer planning model for blood platelet production and distribution. , 1991, Computer methods and programs in biomedicine.

[12]  Rolf A. Deininger,et al.  Generalization of White's Method of Successive Approximations to Periodic Markovian Decision Processes , 1972, Oper. Res..

[13]  Lee W. Schruben,et al.  A survey of simulation optimization techniques and procedures , 2000, 2000 Winter Simulation Conference Proceedings (Cat. No.00CH37165).

[14]  Steven Nahmias,et al.  Higher-Order Approximations for the Perishable-Inventory Problem , 1977, Oper. Res..

[15]  Brant E. Fries,et al.  Optimal Ordering Policy for a Perishable Commodity with Fixed Lifetime , 1975, Oper. Res..

[16]  Shmuel Gal,et al.  A Markovian Model for a Perishable Product Inventory , 1977 .

[17]  Ijbf Ivo Adan,et al.  Fitting Discrete Distributions on the First Two Moments , 1995, Probability in the Engineering and Informational Sciences.

[18]  R E Ledman,et al.  Platelet production planning to ensure availability while minimizing outdating , 1984, Transfusion.

[19]  John N. Tsitsiklis,et al.  Neuro-Dynamic Programming , 1996, Encyclopedia of Machine Learning.

[20]  Morris A. Cohen.  Analysis of Single Critical Number Ordering Policies for Perishable Inventories , 1976, Oper. Res..

[21]  G. Prastacos.  Blood Inventory Management: An Overview of Theory and Practice , 1984 .

[22]  A J Katz,et al.  Simulation Analysis of Platelet Production and Inventory Management , 1983, Vox sanguinis.

[23]  W P Pierskalla,et al.  Management Policies for a Regional Blood Bank , 2003, Transfusion.

[24]  Betsy S. Greenberg,et al.  Two-Stage Perishable Inventory Models , 1993 .

[25]  Steven Nahmias,et al.  S-1, S Policies for Perishable Inventory , 1985 .

[26]  Amedeo R. Odoni,et al.  On Finding the Maximal Gain for Markov Decision Processes , 1969, Oper. Res..

[27]  S. K. Goyal,et al.  Recent trends in modeling of deteriorating inventory , 2001, Eur. J. Oper. Res..