In this presentation we address the planning and scheduling of a real-world process for manufacturing tinted glass in a single-stage multi-product process with two continuous lines. The goal of this work is the development of a decision making tool to support supply chain decisions at the level of short and medium term scheduling, and also strategic decisions such as product portfolio composition. The core element of this tool is a Mixed-Integer Linear Programming (MILP) model involving production planning and scheduling decisions. An important feature of this model is the integration of the consumption, production and storage of waste glass (cullet) with the production schedule. This tool has been used by the supply chain group in PPG Glass to address strategic decisions.
The scheduling of multiproduct continuous processes in the processing industries has not received as much attention as batch scheduling. However, multi-product continuous lines are common in the paper, glass, steel, and specialty chemicals industries, and their optimal scheduling has been studied by some authors. Sahinidis and Grossmann (1991) addressed the optimal scheduling of continuous parallel lines with a cyclical operation and constant demand. Latter Pinto and Grossmann (1994) extended the former work considering multiple production stages. In both works the problems were formulated as Mixed-Integer NonLinear Programming (MINLP) models using slots to represent the time activities, and specific solution methods were proposed. Cooke and Rohdler (2006) studied the scheduling of a multi-product continuous reactor for manufacturing polymers with different grades, with also constant demand. These authors propose a MINLP lot-size model based on an extended basic period approach, and a specific decomposition algorithm with three levels. An interesting feature of their model is the integration of the optimal scheduling with safety stocks calculation under demand and production uncertainty. Miegeville (2005) developed a customized MILP lot-sizing model for the scheduling of tinted glass production. The model involves the aggregation of products into families and different levels of time resolution, in order to handle the hierarchical production scheduling and inventory control. At the planning level, Liu and Papageorgiou (2008) proposed a TSP based MILP model for continuous lines, while Erdirik-Dogan and Grossmann (2008) have addressed the integration of planning and scheduling using a bi-level decomposition algorithm, involving a TSP based MILP model in the upper level, and a continuous time slot based model in the lower level.
The model proposed in this work was developed based on the continuous time slot MILP model proposed by Erdirik-Dogan and Grossmann (2008). Recently, Lima et al. (2011) have extended the model of Erdirik-Dogan and Grossmann by including the following features: a) carry-over changeovers across the due dates; b) minimum run lengths across the due dates; c) a rigorous aggregation of the products based on the type of changeovers; d) definition of minimum inventory levels at the end of the time horizon; and e) some specific constraints for glass production. Meanwhile, the model was further developed to capture the cullet operations integrated with the production, which represent real constraints of operation, and have a significant economic value. These constraints were not addressed by Miegeville (2005) in his glass production planning model.
From the process point of view, we address the optimal scheduling of the production of specialty glass characterized by different colors. The color of each glass depends on the color of the substrate and the color of a coating if added. The changeover from one substrate to another substrate implies a transition time in the order of days, while the changeover from a specific substrate color to a product with the same substrate with a coating requires a comparatively short changeover. During changeovers, the process produces cullet at the same conditions (energy, raw materials, and production rate). The process scheduling is restricted by: 1) sequence-dependent changeovers between a subset of the products and no changeovers between another subset of products; 2) impositions on the sequence of production and production times between products without changeovers; 3) minimum run lengths due to process control and stability; and 4) by a complex compatibility and recycling profile of cullet. The market demand for each product is not constant during the time horizon, and therefore we do not consider a cyclic operation.Each product has a minimum requirement for cullet feed to the process in order to achieve glass quality standards, and to minimize energy costs. An interesting feature is the bidirectional relation between the scheduling, and the cullet generated and consumed, since a given sequence of production will generate specific amounts of cullet, but also the quality and quantity of cullet available in storage can restrict the products to be produced. The cullet is generated due to the process yield and during the transitions, creating two major types of cullet, transition cullet and product cullet. The recycling of cullet is characterized by a compatibility matrix between cullet recycled and product to produce, and by specific rates of cullet consumption as a function of the production run. The cullet recycling is modeled using mass balances for the transition cullet and product cullet that is produced and consumed, and inventory balances, since there is a maximum storage capacity. Cullet generated over the storage capacity has to be sold. These balances are applied at the end of each slot because the dilution cullet generated in slot l of a specific changeover may be used for a different product in slot l+1.
In this work we consider two parallel production lines operating in parallel. One line produces most of the products, while the other produces only a subset of products plus a dedicated product. Two valid assumptions in this process are the following: 1) both lines will not produce the same product in the same time period; and 2) one production line does not consume cullet from produced during changeovers. These two features of the process prevent the need to synchronize the start and end of the slots of both lines to account for the simultaneous consumption of the same type of cullet. Therefore, the balances for the cullet consumption and generation are made over each slot, and synchronized at the end of each the time period.
To solve the current MILP models, the hybrid rolling horizon strategy described in the Lima et al. (2011) is used. However, in order to cope with the increased size of the models, the time horizons for the scheduling model and planning model have been reduced to 3 and 6 months, respectively. Different case studies are presented to demonstrate a) the impact of considering the cullet model in the scheduling in terms of number of transitions and length of the production runs; b) the impact of different final inventory level conditions or constraints at the end of the planning horizon. Variations of the rolling horizon algorithms, and different inventory features are compared in terms of the size of the models, and computational efficiency in terms of integrality gaps and CPU time.
The model developed is the core of a software tool, where the MILP model developed in GAMS is integrated with a spreadsheet software for data input and display the results. This model has already been used to study strategic decisions at the level of product portfolio composition.
Cooke, D.L., Rohleder T.R., (2006). Inventory evaluation and product slate management in large-scale continuous process industries. Journal of Operations Management. 24, 235-249.
Erdirik-Dogan, M., Grossmann, I.E., (2008) Simultaneous planning and scheduling of single-stage multi-product continuous plants with parallel lines, Computers and Chemical Engineering, 32, 11, 2664-2683.
Lima, R.M., Grossmann, I.E., Jiao, Y. (2011) Long-term scheduling of a single-unit multi-product continuous process to manufacture high performance glass. Computers and Chemical Engineering. 35 (2011) 554–574
Liu, S., Pinto, J. M., & Papageorgiou, L. G. (2008). TSP-based MILP model for medium term planning of single-stage continuous multiproduct plants. Industrial & Engineering Chemistry Research, 47(20), 7733–7743.
Miegeville N. (2005), Supply chain optimization in the process industry: Methods and case study of the glass industry. PhD thesis. École Centrale Paris
Pinto, J.M., Grossmann, I.E. (1994), Optimal cyclic scheduling of multistage continuous multiproduct plants. Computers and chemical Engineering, 18(9), 797-816.
Sahinidis, N.V., Grossmann, I.E., (1991), MINLP model for cyclic multiproduct scheduling on continuous parallel lines. Computers and Chemical Engineering. 15 (2), 85-103.