Multi Echelon Techniques in Optimal Inventory Modeling of Systems with Repairable Items

Presented by Nuriye Kaptanlar

14/05/2003

Repairable Spares Optimization

• What is Spares Optimization?

- At the core of supply chain management

- Aimed at determining the best* answers to

- How many spares should we buy?

- Where should we put them?

* Best is satisfying a performance goal for the lowest cost.

Why to hold spare inventory?

• In general - To attain a certain level of end-item (i.e. aircraft)

availability, in order to be able to continue the daily operations.

• Since spare parts are too expensive, -the reduction in the amount of inventory kept for

them while achieving the desired operational availability would cause significant savings

-managing spare parts’ inventory effectively would enable to achieve a higher operational availability with the same amount of investment.

What has been done?

• Has been researched since late 60s• MODMETRIC United States Air Force Logistics

Command • Manugistics, I2, TFD• The software Vari-METRIC• Turkish Air Force Project:

- SAP R/3 + APO + Vari-METRIC- to achieve desired operational availability

levels of different aircraft types

Characterization

• Operational versus support sites• Single versus multiple echelons• Divergent versus convergent systems• Acyclic versus cyclic models• Condemnations allowed versus conservative

systems• Deterministic versus stochastic demand• Item based versus multi indenture structure

Base Stock

ServiceableServiceable UnserviceableUnserviceable

In-house Repair

Weapon System

Depot Repair

METRIC

Fleet

Military Supply Points

METRIC Assumptions

• Demand for each item ~ Compound Poisson• Demand is stationary over the prediction period• Demand on where repair is to be accomplished

depends on the complexity of the repair only.• Lateral resupply is ignored• System is conservative (no condemnation)

METRIC is used for

• Optimization:• Determining optimal base-depot stock levels for each item

• Redistribution:• Allocating the stock between the bases and depot

• Evaluation:• Providing an assessment of the performance and

investment cost for the system of any allocation between the bases and depot.

Literature

• Review papers- Nahmias (1981) - Demmy and Presutti (1981) - Diaz and Fu (1995) - Guide and Srivastava (1997) - Kennedy, Patterson and Fredendall (2002)

• Classification according to:- solution methodologies proposed - mathematical models used (continuous, periodic review

and queuing models) - stochasticity of demand

Literature ‘ed

• Sherbrooke (1971) -option of minimizing the expected number of non-

operable aircrafts -approximation

• Simon (1971)-completely recoverable-completely consumable-partially recoverable items -with some rate of condemnation -deterministic shipment and repair times -Poisson demand process at the depot

MODMETRIC

• Muckstadt (1978-79) - multi-indenture - the optimal stock levels for

- LRUs- SRUs

- minimize E(backorders for LRUs) subject to budget constraint for investment- Lagrangian Optimization

Drawback: limited to level echelon and two indenture case & complex

Vari-METRIC

• Graves (1985)

- two-parameter negative binomial distribution to fit the distribution of backorders at the bases

- considers the depot as a K-server service center resulting in dependent replenishment lead-times (different in METRIC) ~ an item at the depot could seize the service station directly if the server is idle and if the server is busy, the item should wait in the queue for the end of the repair of the preceding items.

DynaMETRIC

• Pyke (1990)

- Deals with non-stationary demand conditions

- Simulation based approximate approach

- two general observations:

(i) repair center’s utilization rate should not exceed 0.8,

(ii) a decrease in transportation times result in utmost benefit

Aproximations

• Kim et al. (1996) - min the system costs s.t. fill rate - single indenture & have a finite population- allow repairs at both echelons - no inventory is kept at the depot level- significant computational speed

• Cheung and Hausman (1993, 1995) - partial replenishments are not allowed for the multiple

failures - cannibalization is included - the upper and lower bounds for the average number of

backorders at the bases

Aproximations ‘ed

• Diaz and Fu (1997) – limited repair capacities

– analyze the effects of limited capacity for numerous repair distributions

References

• Cheung, K.L., and Hausman, W.H., (1993), “A multi-echelon inventory model with multiple failures” Naval Research Logistics, Vol.40, pp.593-602.

• Cheung, K.L., and Hausman, W.H., (1995), “Multiple failures in a multi-item spares inventory model” IIE Transactions, Vol.27, pp.171-180. 

• Demmy, S.W., and Presutti, V.J., (1981), “ Multi-echelon inventory theory in the Ait Force Logistics Command” In: Schwartz, L.B. (Ed.), Multi-Level Inventory Control Systems: Theory and Practice, North Holland Publishing Company, New York, NY, pp. 279-297. 

• Diaz, A., and Fu, M.C., (1995), “Multi-echelon models for repairable items: a review” Working Paper, University of Maryland.

• Diaz, A., and Fu, M.C., (1997), “Models for multi-echelon repairable item inventory systems with limited repair capacity” European Journal of Operational Research, Vol.97, Issue 3, pp. 480-492.

• Graves, S.C., (1985), “A multi-echelon inventory model for a repairable item with one-for-one replenishment,” Management Science, Vol.31, pp.1247-1256.

• Guide, V.D.R., and Srivastava, R., (1997), “Repairable inventory theory: models and applications,” European Journal of Operational Research, 102, pp.1-20.

•  Kennedy, W.J., Patterson, J.W., and Fredendall L.D., (2002) “An overview of recent literature on spare parts inventories” International Journal of Production Economics, 76, pp. 201-215.

• Kim, J., Shin, K., and Yu, H., (1996), “Optimal algorithm to determine the spare inventory level for a repairable-item inventory system,” Computers and Operations Research, Vol.23, pp.289-297.

• Muckstadt, J.A., (1978), “Some approximations in multi-item, multi-echelon inventory systems for recoverable items,” Naval Research Logistics Quarterly, Vol.25, pp.377-394.

• Muckstadt, J.A., (1979), “A three-echelon, multi-item model for recoverable items,” Naval Research Logistics Quarterly, Vol.26, pp.199-221.

• Nahmias, S., (1981), “Managing repairable item inventory systems: A review.,” In: Schwarz, L.B., (Ed.), Multi-Level Inventory Control Systems: Theory and Practice. North Holland Publishing Company, New York, NY, pp.253-277.

• Pyke, D.F., (1990), “Priority repair and dispatch policies for repairable-item logistics system,” Naval Research Logistics, Vol.37, pp.1-30.

• Sherbrooke, C.C., (1968), ”METRIC: A Multi-Echelon Technique for Recoverable Item Control,” Operations Research, 16, pp. 122-141.

• Sherbrooke, C.C., (1971), ”An evaluator for the number of operationally ready aircraft in a multi-item supply system,” Operations Research, 19, pp. 618-635.

•  Sherbrooke, C.C., (1992), “Multi-echelon inventory systems with lateral supply,” Naval Research Logistics, Vol.39, pp.29-40.

•  Simon, R.M., (1971), “Stationary properties of a two-echelon inventory model for low demand items,” Operations Research, 19, pp.761-773.

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