Optimal service parts contract with multiple response times and on-site spare parts

This study examines user outsourcing of spare parts management to vendors through a service contract. The user’s selection of a fixed-price service parts contract is formulated as a stochastic integer programming model that decides multiple response times and on-site spare parts, while considering component breakdown with uncertain failure rates. We analytically derive the optimality conditions for the continuous case and subsequently design an efficient algorithm. Numerical illustrations and analyses are conducted to evaluate decisions under various scenarios. Our analysis shows that when both failure rate and expedited contract cost are high, coupled with low part cost, users would prefer the purchase of spare parts for all components to expedited contracts. A fixed-price expedited contract has a lower marginal cost with respect to failure rate than a fixed-price next day contract and a usage-based contract. We also examine inventory behaviour for a single part, multiple types of parts, and multiple groups of parts. It is shown that there is a cost-saving pooling effect in spare parts for identical items, which significantly raises the likelihood of having on-site stored parts. The problem becomes more complex for multiple items, reflecting bundling effects between items for a given contract.