Continuous-time scheduling of production, distribution and sales in photovoltaic supply chains with declining prices

Supply chain networks in the photovoltaic sector were faced with a rapid decline in prices during the past few years, which is predicted to go on in the following years. These circumstances force related companies to coordinate production, distribution and transportation planning of all their network sites thoroughly. Moreover, continuous-time scheduling of processes is required to determine times of sales exactly within a multi-day planning horizon. Applying this type of scheduling is possible due to assessable price trends and existing framework agreements with wholesalers, and even necessary due to its impact on the realized sales prices, and thus, the network profit. For this reason, we develop a mixed-integer linear programming model that meets the requirements of fully-integrated photovoltaic supply chains that cover processing of raw materials, manufacturing of intermediate and finished products in two alternative methods, and selling them on international markets. The multi-product approach enables to connect supply chain stages with different product maturities. The modeling is motivated by a real-life case of a global photovoltaic group headquartered in Germany. As it was not possible to optimize this problem with high-performance software and hardware within 3 months, we tested several relax-and-fix decomposition methods. By selecting those algorithms that were able to generate high-quality solutions within acceptable computation times of less than half a day, a satisfying solution was found. The appropriateness of the selected algorithms is additionally demonstrated by analyzing randomly generated scenarios in a numerical study.