Multi-objective optimization with order acceptance for the cumulative job shop scheduling problem in agribusiness

Developing new crop species is crucial for addressing global food challenges and improving agricultural efficiency. In agribusiness, this process involves systematically growing and assessing numerous crop variants under controlled conditions to determine their yield potential and adaptability. Formally, this is a job shop scheduling problem because the crops can be understood as jobs that may have different processing sequences on the resources (e.g., greenhouses). However, since the resources can process several jobs simultaneously, a cumulative job shop problem arises. The primary objective is to maximize the number of accepted jobs from a job pool with given release and due dates. The secondary objective is to minimize delays in job processing, i.e., the jobs’ waiting times, as earlier completion of jobs allows for faster feedback and refinement of future crop variants, ultimately improving the overall testing and development process. In this paper, we formulate this problem as a mixed integer and constraint programming problem. We also show how it can be solved with a flexible hierarchical approach, even for very large problem instances. Comprehensive computational experiments first show that available machine capacity has a greater influence on the objectives than the length of the processing time windows, resulting from the difference between the due and release dates. Secondly, a deviation from the maximum number of accepted jobs disproportionately reduces delays. • We develop a decision support system for a multi-objective agribusiness application. • The problem is established as cumulative job shop scheduling with order acceptance. • We propose new mixed-integer and constraint programming models. • Our flexible hierarchical approach is validated on a large dataset. • We identify impact factors and trade-offs, leading to several managerial insights.