Kristina Šorić

Production planning problem with sequence dependent setups as a bilevel programming problem

Abstract Each of n products is to be processed on two machines in order to satisfy known demands in each of T periods. Only one product can be processed on each machine at any given time. Each switch from one item to another requires sequence dependent setup time. The objective is to minimize the total setup time and the sum of the costs of production, storage and setup. We consider the problem as a bilevel mixed 0–1 integer programming problem. The objective of the leader is to assign the products to the machines in order to minimize the total sequence dependent setup time, while the objective of the follower is to minimize the production, storage and setup cost of the machine. We develop a heuristics based on tabu search for solving the problem. At the end, some computational results are presented.

A cutting plane algorithm for a single machine scheduling problem

Abstract Each of N part types (production families or items) is to be processed on a single machine. The part types arrive into the buffer in front of the machine at every unit of time at specified rates. The machine can process a finite number of part types at specified rates, but only one part type can be processed at any given time. Each switch from one type to another requires setup time. The objective is to schedule the part types in the sense that the required demand is met and the average work backlog in the system is minimal. Assuming a finite horizon, we define this problem as mixed 0–1 programming problem. In order to strengthen the formulation, we consider its LP relaxation in an enlarged space of variables. By projecting this polyhedron into the space of the original variables we obtain new valid inequalities for the original problem that are then used as cutting planes in a cutting plane/branch and bound algorithm. At the end we report some computational results that have the objective of empirically estimating the reduction in the integrality gap (the gap between the optimal values of the original problem and its linear programming relaxation). Also, we give and compare the CPU times of the cutting plane/branch and bound algorithm proposed in this paper and the branch and bound algorithm applied directly to the original problem.

The CLWS heuristic for single machine scheduling problem

Abstract A model for real-time control of flexible manufacturing systems is considered. In this model, a machine can process a finite number of part types at specified rates, but only one part type can be processed at any given time. Each switch from one type to another requires setup time. The clear-the-largest-work-after-setup (CLWS) heuristic policy which stabilizes the system in the sense that, in the long run, the required demand is met, has been introduced. That way, a better upper bound on the total work backlog than those available in earlier literature is derived. Computational results for the case of finite horizon show that the error of the heuristic CLWS from the optimal solution is 2.5–3.0% on average. Some computational results that compare the CLWS heuristic to the heuristic available in the earlier literature, for the same problem, are also reported.

Is Operational Research Attractive Enough at Higher Education Institutions in Croatia

In an age where information technology, the Internet, smart phones, mobile applications, interdisciplinarity, big data, business analytics, artificial intelligence, and the fourth industrial revolution have become prevalent, Operational Research (OR) as a scientific and academic discipline is also subject to a specific transformation and evolution. This paper covers the current situation with OR based, on the mentioned trends by analysing OR-related programmes and courses offered at university level, specifically, at higher education institutions (HEIs) in Croatia. Also, aspects of collaboration between HEIs and the business community relating to OR will be studied, as well as the role of the Croatian Operational Research Society (CRORS) as a community that gathers OR researchers and promotes OR as a scientific discipline (Croatian Operational Research Society 2017). Some suggestions to improve the current OR situation at Croatian HEIs, and its impact on economy are also given. The analysis was based on a survey sent to HEIs in Croatia, and subsequently organising a round table discussion and consultations with Croatian employers. The survey questions related to the courses and programmes offered at Croatian HEIs, the number of students attending the courses, recent innovations, collaboration with the business community and plans to make OR even more appealing. The results reveal that the number of OR-related courses is significant, though most are electives, and the lack of OR majors across all higher-education levels in Croatia. In general, OR courses are required to follow terminology trends and utilize more appealing terms such as data analytics and business analytics. Recent and more intensive collaboration with the business community which seeks experts in optimization, analytics, and other OR areas is becoming promising.