Production planning and scheduling in multi-stage batch production environment

Abstract

We address the problem of jointly determining production planning and scheduling decisions in a complex multi-stage, multi-product, multi-machine, and batch-production environment. Large numbers of process and discrete parts manufacturing industries are characterized by increasing product variety, low product volumes, demand variability and reduced strategic planning cycle. Multi-stage batch-processing industries like chemicals, food, glass, pharmaceuticals, tire, etc. are some examples that face this environment. Lack of efficient production planning and scheduling decisions in this environment often results in high inventory costs and low capacity utilization. In this research, we consider the production environment that produces intermediate products, by-products and finished goods at a production stage. By-products are recycled to recover reusable raw materials. Inputs to a production stage are raw materials, intermediate products and raw materials. Complexities in the production process arise due to the desired coordination of various production stages and the recycling process. We consider flexible production resources where equipments are shared amongst products. This often leads to conflict in the capacity requirements at an aggregate level and at the detailed scheduling level. The environment is characterized by dynamic and deterministic demands of finished goods over a finite planning horizon, high set-up times, transfer lot sizes and perishability of products. The decisions in the problem are to determine the production quantities and inventory levels of products, aggregate capacity of the resources required and to derive detailed schedules at minimum cost. We determine production planning and scheduling decisions through a sequence of mathematical models. First, we develop a mixed-integer programming (MIP) model to determine production quantities of products in each time period of the planning horizon. The objective of the model is to minimize inventory and set-up costs of intermediate products and finished goods, inventory costs of by-products and reusable raw materials, and cost of fresh raw materials. This model also determines the aggregate capacity of the resources required to implement the production plan. We develop a variant of the planning model for jointly planning sales and production. This model has additional market constraints of lower and upper bounds on the demand. Next, we develop an MIP scheduling model to execute the aggregate sales and productions plans obtained from the planning model. The scheduling model derives detailed equipment wise schedules of products. The objective of the scheduling model is to minimize earliness and tardiness (E/T) penalties. We use branch and bound procedure to solve the production-planning problem. Demand of finished goods for each period over the planning horizon is an input to the model. The planning model is implemented on a rolling horizon basis. We consider flowshop setting for the finished goods in the production environment. The due dates of finished goods are based on the customers orders. We report some new results for scheduling decisions in a permutation flowshop with E/T penalties about a common due date. This class of problems can be sub-divided into three groups-one, where the common due date is such that all jobs are necessarily tardy; the second, where the due date is such that the problem is unrestricted; and third is a group of problems where the due date is between the above two. The models developed are tested on data for a chemical company in India. The results of cost minimization model in a particular instance indicated savings of 61.20 percent in inventory costs of intermediate products, 38.46 percent in set-up costs, 8.58 percent in inventory cost by-products and reusable raw materials, and 20.50 percent in fresh raw material costs over the actual production plan followed by the company. The results of the contribution maximization model indicate 42.54 percent increase in contribution. We also perform sensitivity analysis on results of the production planning and scheduling problem. The contribution flowshop setting for the finished goods in the production planning and scheduling problem. Traditional models on multi-stage production planning and scheduling are primarily based on assembly and fabrication types of product structures and do not consider the issues involved in recycling process. Scheduling theory with E/T penalties is largely limited to single machine environment. We expect that models developed in this research would from basis for production planning and scheduling decisions in multi-stage, multi-machine batch processing systems. The sensitivity analysis of the models would provide an opportunity to the managers to evaluate the alternate production plans and to respond to the problem complexities in a better way.