This research deals with a lean supply chain system where the production
facilities operate under a just-in-time (JIT) environment, and the facilities consist of a raw
material supplier, a manufacturer with multi-work-stage, and multiple buyers where
inventories of raw materials, work-in-process (WIP), and finished products are involved
respectively. This work considers that the raw materials are multi-ordered supplying to
the 1st work-stage to reduce the inventory carrying cost, the finished products have a
demand pattern that changes linearly with time that can simulate the demands of shortlife
cycle products in the market, an optimal set of production rates selection for each
work-stage by incorporating the production capacity constraints to reduce the production
cost.
The mathematical formulation of the problem is categorized as a mixed integer
non-linear programming problem which is solved to find optimum raw material
procurement rate, a set of optimal production rate at each work-stage, optimum finished
product shipment, optimum Kanban number and its capacity at each Kanban stage, and
the minimum system inventory cost. The objective function of the total inventory cost
developed in this research is a higher-order exponential function with respect to the
decision variables (raw material procurement rate and production rate at each work-stage)
for which the closed form solutions are cumbersome. Therefore, Algorithm I is developed
to find the optimal relaxed solutions of raw material procurement rate and production rate
at each stage, and minimum total inventory related cost including raw materials, WIP and
finished products of the production system, then Algorithm II (Branch & Bound
Technique) is used to provide near-optimal integer solutions of the problem. Numerical
examples are presented to demonstrate the solution techniques. Sensitivity analysis is
performed to show the effects of the parameters on the total inventory cost model. Future
research direction is suggested for further improvement of the existing results.
The production and supply chain management play a significant role for the
necessary amount of materials and parts that arrive at the proper time and place. The
model developed here can help a manager quickly respond to consumers’ needs,
determine the right policies to setup the operational layout of production rate of each
stage, raw material ordering rate, Kanban configuration at each stage, finish product
delivery frequently and manage a production system operation efficiently.