Optimal production and admission control for a stochastic SOM system with demands for product and PSS

Abstract

In decades, many traditional manufacturing firms are making the transition from products manufacturers to the providers of product-service systems (PSSs). The new business mode to support this transition is termed service-oriented manufacturing (SOM) paradigm by researchers and practitioners. In this paper, we address the problem of optimal control for a SOM system in which one factory manufactures products in the first stage and then one service centre realises PSSs by adding some product-based services on the products in the second stage. There are two-class external demands: demands for products and PSSs. The PSSs orders have higher priority and are fully accepted whereas the product orders can either be accepted or rejected. The optimal dynamic admission control of the product orders and the optimal dynamic production control of products are examined simultaneously. We first model the system in the context of a simple production-inventory-queue system and formulate the optimal integrated control problem as a continuous Markov decision process in which the objective is to maximise the profit of the firm. Then we characterise the optimal integrated dynamic control by two state-dependent threshold functions. The monotonicity of two optimal control curves verifies that, to achieve an effective management for the SOM system, the controls of manufacturing subsystem and service subsystem in the SOM system must be coo. We also illustrate the impacts of the revenues of both product orders and PSS orders on the optimal policy numerically. It is interesting that the optimal control policy is independent of the revenue of PSS order.