Heuristic Production and Sale Policy for a Two-Product-Type Manufacturing System With Downward Substitution

In this paper, we study a manufacturing system with downward substitution in sales, i.e., selling superior products as inferior ones when the demand for the latter cannot be met immediately, in order to reduce the backlog cost. However, downward substitution in sales also causes profit loss. Therefore, controlling a manufacturing system with downward substitution in sales in order to minimize total production cost is a problem worthy of investigation. In this paper, we focus on the production and sale control problem for a two-product-type manufacturing system with downward substitution in sales and time-delay between the releasing of raw materials and the output of final goods. The system is decomposed into two subsystems. In the first subsystem, the state variables are total production surpluses (i.e., the sum of work-in-process and final goods surpluses), and a hedging point policy with a new structure is constructed to control the raw material releasing rates of the two product-types. In the second subsystem, the state variables are the final goods surpluses, and a new switching curve policy is constructed to control the downward substitution rate in sales. Numerical experiments show that downward substitution in sales contributes to the reduction of total production cost, especially when the time-delay is large.

I. Introduction

In the hard disk drive (HDD) industry, the following phenomenon often happens [1]: multiple types of HDDs with different capacities can be assembled in a production line, and the assembly processes of different types of HDDs are almost the same. The types of final goods are determined by the types of raw materials that are released into the production line. The final goods are going to meet the demands from the market. However, the demands are uncertain. If the demand cannot be met immediately, it has to be backlogged, which brings extra cost much greater than the inventory cost. To reduce the backlog cost, if the demands of a type of HDD with smaller capacity (e.g., 400 GB) cannot be met immediately, and we have the inventory of another type of HDD with larger capacity (e.g., 500 GB), then we can sell some HDDs with larger capacity to the customers in place of the HDDs with smaller capacity at a lower price. Of course, that will lead to profit loss. However, if the reduction of backlog cost is greater than the profit loss, it is worthy of doing like this. This phenomenon of selling superior products as inferior ones is called downward substitution, which is a type of product substitution.