An Integer Black-Box Optimization Model for Repairable Spare Parts Management

Introduction

Modern organizations are fully dependent on readily available spare parts to maximize operational capability in case of failures. Managing repairable inventories - which are spares normally characterized by high market value - represents an important managerial domain for improving operational readiness and reducing life-cycle costs for equipment (Yerpude et al., 2019). As a component downtime can be very costly, inventories are required to keep the stock-out time as low as possible. Nevertheless, an excessive number of spare parts may generate not negligible holding costs. Spare parts shall thus be thoroughly optimized to balance high system availability requirements and low cost of allocation (Sleptchenko et al., 2018).

Repairable items are usually managed following a one-for-one replenishment policy, where the part is ordered after each substitution in lots of one. This situation is usually represented as a (S-1, S) policy where S is the optimum number of items in the inventory, and S-1 is the re-order level, i.e. the number of items below which activates the need for a re-ordering. This latter remains meaningful for parts characterized by high inventory cost and low demand, where the economic order quantity tends to a size of one (Diaz and Fu, 1997). In case of failure, the defective part is removed from the equipment and substituted with a functioning one. In the meantime, the original defective part is sent to a maintenance facility to be repaired.

Traditionally, inventory is balanced following an item-approach process, i.e. inventory levels for each item are set independently (Wong et al., 2006), failing to give a holistic optimization (Tripathi and Misra, 2012). The assignment of over-simplified constraints and requirements at the item level becomes increasingly less adequate for the needs of the so-called HA-HCLDS (High Availability, High Cost and Low Demand Systems) (Costantino et al., 2018), which represent the focus of the current manuscript. Starting from the original contribution of Sherbrooke (1968), it is possible to set items’ stock levels jointly, adopting a systemic optimization, as for the so-called system-approach. The system-approach allows a holistic perspective on the system, being fed by systemic variables (e.g., total inventory budget, overall system’s availability), and supporting the identification of system-wide parameters (e.g., the budget required for an overall service level, the effect of a stock reduction on the overall system service level).

The dominant system-approach model for repairable items is the Multi-Echelon Technique for Recoverable Item Control (METRIC), which relies on Palm’s theorem (Sherbrooke, 1968). Since the METRIC aims to respect a systemic perspective, it has to take into account a large number of variables, e.g. for each item at each local warehouse, the demand rate, the on-site repairing time, the turn-around-time, the reparability level. The approach should be also subjected to constraints related to holding costs, and availability requirements. The corresponding algorithmic computational complexity – which is non-linearly increasing with the number of items - forces the analysts to develop and adopt approximated optimization solutions.

Traditionally, METRIC approaches adopt heuristics based on the so-called marginal allocation algorithm, as initially proposed by (Sherbrooke, 1968). The marginal allocation generates acceptable stock level solutions in a limited time interval, counting on the incremental benefits related to the combinatorial placement of an additional item in stock.

After reviewing the literature on optimization algorithms for the METRIC, this paper explores possible enhancements for the marginal allocation heuristics in order to define an alternative optimization algorithm for solving the system-approach model for repairable items. The main contribution of this paper consists thus of advancing the existing literature on operational research for multi-item inventory systems through an enhanced time-effective optimization algorithm. More specifically, the METRIC-based model aims at defining the stock level for a single site that allows minimizing the holding costs whilst satisfying availability constraints.