یک روش برنامه ریزی خطی تصادفی برای بهینه سازی بخش خدمات

Service Parts Stock Management is a part of the service process to ensure that right spare parts are in the warehouse at the right place and time, with respect to a customer demand. Customer satisfaction can be measured through the First Fill Rate Value (FFRV). The FFRV optimization is an inventory planning problem, which can be formalized through a stochastic linear programming problem and evaluated for different spare parts or sets of them, considering production and cost constraints. In this paper the problem and the details of the proposed approach will be discussed and assessed through some experimental data.

Service Parts Management is one of the main components of strategic service logistics, requiring a complex decision making process [1], that companies use to ensure that right spare parts and resources are at the right place at the right time. From a producer point of view spare parts are considered uneconomical since they involve logistical and economical requirements; they might never be used and the cost of inventory on hand is not negligible [2] and [3]. However, without spare parts on hand, a company's customer satisfaction levels could drop, since the customers has to wait for long time before their products can be fixed. The company's trade-off is between spare parts inventory and resources to achieve optimal customer satisfaction levels with minimal costs. As suggested by Ref. [4], fill rate is a simple but effective measure of inventory availability and customer satisfaction can be related to the First Fill Rate Value (FFRV). In particular, FFRV is a measure of fulfilment quality, corresponding to the ratio between the order items satisfied by the available inventory and the total number of received order items. FFRV can be evaluated for different spare parts or sets of them [5], taking into account production and cost constraints. In this paper we propose a solution to this inventory optimization by approaching it through the definition and the solution of a stochastic linear programming problem (SLPP). This planning involves quantities and variables associated with a sequence of time intervals (called time buckets) composing the planning horizon. In the proposed approach the quality constraints are based on a piecewise linear regression of FFRV identified by means of the analysis of historical data. The focus of the work presented in this paper is to develop and experiment an optimization model that is appropriate for facing the inventory planning problem, i.e., that is able to suitably set the safety factors taking into account costs and levels of service. The problem will be solved with a scenario-generation method, firstly formally defining the considered Inventory Stock Mix Optimization Problem (ISMOP) and then introducing the details of the proposed approach. The effectiveness of procedure will be evaluated by presenting some experimental results.

The spare parts optimization problem is crucial for customer oriented manufacturing industry. The FFRV is a possible measure to evaluate the quality of the planned inventory. This paper formalizes the optimization problem providing a stochastic linear programming approach and converting it in a deterministic linear problem. A convex piecewise linear estimation of the FFR, by using a quadratic regression model, has been adopted to model the real analyzed industrial context. Finally, a test over 2704 spare parts aggregated in three different families has been performed to show the effectiveness of the proposed approach with respect to stocking costs savings.