• Optimal control policies in a hybrid MTS/MTO production system equipped with multiple machines capable of MTS and MTO production by a setup operation were investigated.
• Switching machines between MTS and MTO production incurs a setup period and cost. The optimal control problem was formulated as a discrete-time Markov decision process.  
• Numerical experiments provided the following findings: (1) switching of machines is effective, (2) switching of one machine is sufficient, and (3) dedicating some machines to MTS or MTO is acceptable.  

We studied optimal control policies for a production system composed of multiple hybrid machines that can handle both make-to-stock (MTS) production and make-to-order (MTO) production. In MTS production, products are produced and stocked in advance, and demand is satisfied from stock. On the other hand, in MTO production, production is started after a job order from a customer arrives and the produced product is delivered to the customer. Each machine can produce MTS or MTO products based on the specified production mode. When it becomes necessary to produce the other type of product, a setup operation is required, resulting in time loss and cost. In this study, the optimization problem was modeled as a discrete-time Markov decision process, and the optimal control policies that minimize the average cost per period were obtained under the random arrival of orders for MTS and MTO products. The average cost comprised MTS inventory, number of waiting jobs of MTO, lost sales of MTS and MTO, and setup costs. 

From the numerical experiment, it was clarified that (1) it is adequate to switch the mode of machines to MTS or MTO according to the conditions, (2) it is sufficient to examine whether or not to switch one machine even if it is possible to switch several machines at one time, and (3) it is worth examining to fix the operation mode of some hybrid machines to MTS or MTO. 

Many manufacturing companies deal with both MTS and MTO productions, and they are required to operate their limited resources efficiently. Our study provides suggestions for investigating optimal control policies in these companies.

Reference
 Yutaro Sato, Hiroyuki Maeda, Ryusei Toshima, Keisuke Nagasawa, Katsumi Morikawa, Katsuhiko Takahashi, "Switching decisions in a hybrid MTS/MTO production system comprising multiple machines considering setup," International Journal of Production Economics, Vol. 263, 2023, 108877. DOI:10.1016/j.ijpe.2023.108877