An optimal (S-1, S) inventory control policy for multi-indentured aircraft engine spare parts

This paper presents a mathematical model for determining optimal stock levels of a three-level indentured aircraft engine comprising modules and components. The mathematical model follows an (S-1, S) inventory control policy typically used for high cost, low demand repairable items. A (S-1, S) policy means that the reorder point is S-1, quantity of order is 1 and stock level is a decision variable to be determined. The application of this model is targeted at air transport companies that own these spares, with the aim of reducing their costs of spares. The system operates as follows: Engines down for maintenance are removed from the aircraft and refitted with serviceable ones. These engines are stripped into modules and further into components. Faulty components are assessed for reparability before they are either sent for repair or scrapped. Scrapped components are purchased on a one-for-one basis. Once the serviceable components are returned, they are assembled back to modules and engines, completing the engine maintenance resupply time. Modules and components also have their individual resupply times. For modules, it starts when the module has been stripped from the engine to when it is reassembled from components. Likewise for components, it starts when the component has been stripped from the module to when it has returned from repair or purchase. Engine and module resupply times may be extended due to delays caused by stock-outs of their associated modules and components and this incurs heavy penalty costs. Hence, the optimization process seeks to minimize the occurrence of stock-outs. A number of assumptions are made in the formulation. Among them are that demands occur independently and randomly, following a stationary Poisson process. The number of units in the resupply system is given by Palm’s theorem. Also, demand for an engine is caused by the failure of one component in one module only. Repair and storage facilities have infinite capacity and all engines, modules and components are unique and mutually exclusive. A computationally efficient differential evolution algorithm is employed in the optimization process due to the large number of stock level variables to be estimated. Results of interest are the optimal stock levels, expected backorders, holding, penalty and total cost. A preliminary result is generated for a given engine type having the following parameters: a demand of 1 engine per week, penalty cost per non-operational engine grounded per day of $5,000, average probability of component repair among all components of 0.7 and fill rate of 0.95. Variations of results with changing parameters are tabulated, plotted and discussed. Some interesting trends to note are: As the penalty cost per non-operational engine grounded per day becomes large, it shadows the changes in stock levels caused by an increasing fill rate. The expected backorders of engines and penalty cost are independent of the probability of component repair. Demand is the most critical factor affecting stock levels, followed by probability of component repair. Several extensions to the model were highlighted in order to relax the assumptions made. Firstly, fluctuating demand rates with time can be considered by employing a negative binomial distribution to model Poisson demand processes whose means drift with time. A further study with Bayesian analysis can be used to determine the changes in the mean. Secondly, with reference to the component reliability “bathtub” curve, failure rate increases as the component ages. The binomial distribution can be used in place of the Poisson due to the ease of parameter estimation. Thirdly, modules with common components can have their demands aggregated to form a common stock pool, which results in a smaller stock level than when considered separately. Fourthly, when the failure of a module is due to two or more associated component failures, demand for each component has to be individually estimated by Bayesian analysis or James-stein estimation by way of a separate study. Finally, regardless of the distribution of repair times, the model is still applicable following Palm’s theorem. Some areas for further research include demand prediction studies for multiple failures and fluctuating means, provisions in the formulation for storage and/or repair capacity constraints, and incorporating the effects redundancy on stock levels. Beyond the model, a stocking policy for aircraft expendables which form the majority of the engine components can be separately developed. Also, using simulation rather than a mathematical model provides a more intuitive approach to long-term stock planning with unsteady parameter data.Bachelor of Engineering (Mechanical Engineering