Two-stage production planning for several parallel machines with variable transportation cost

This paper studies a case in which a manufacturer produces a single type of product on multiple parallel machines. The manufacturer has a machine pool available that has a combined production capacity greater than what is required to generate demand. It is assumed that the production rate of machines may be varied in different ranges, which allows the manufacturer to use different cost structures and production capacity of machine to minimize its production costs. Due to the machine maintenance program, each machine has a limit of maximum uninterrupted production time, which is effective in determining the total production cycle. Also for the product transportation from the production buffer stock to the consumption buffer stock, the maximum limit of portable products per transfer is defined, which makes the cost of transporting the goods variable. A mixed integer non-linear programing (MINLP) model is developed to tackle the problem. In this scenario, the manufacturer should decide which machine is to be chosen for to meet a given demand and determine production rate of the selected machine. In addition, this question arises that regarding to the variable transportation cost, how much should the product be shipped to the consumer?To support production and distribution planning in this scenario, a deterministic mathematical model is proposed. Finally, numerical experiments are given and the results are analyzed.

Keywords:

Variable transportation costs , Variable production rates , Two-stage production , Lot sizing