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The purpose of this study is, firstly, to examine capital structure optimization and secondly, to provide a framework for determining the optimal capital structure from the aspect of capital cost and corporate value. The results of our work provide an innovative model for arriving at a company’s optimal capital structure based on the estimation of the effective cost of capital and the determination of the shares of new equity and long-term debt that will both minimize the overall cost of capital and maximize its value. The model can be applied for quantitative estimates of optimal capital structure. This paper contributes to the literature by applying mathematical modeling and mathematical theory of optimization to solve the problem of capital structure optimization, and by providing a framework for determining optimal capital structure. The scientific contribution of this research is development of a model of optimal capital structure from the aspect of capital cost and corporate value, and new equations for calculating the effective costs of long-term financing sources. This model provides explicit advice on optimal long-term debt and equity level and can be applied to produce a firm-specific recommendation about optimal capital structure that a given company should use.

U članku su navedena tri problema koji se rješavaju modeliranjem linearnom funkcijom pomoću računala. Navedeni problemi se mogu razviti u nastavne scenarije, jer posjeduju otvorenost i istraživački potencijal u skladu s teorijom Realističnog matematičkog obrazovanja.

We are living in the digital world. Are universities actually ready to educate the future experts? Are we ready to teach our students for the future globalized competitive labor market for the jobs that today don’t exist? Zagreb School of Economics and Management started the new four year undergraduate program Business Mathematics and Economics for challenging this issue. The main point is in educating the experts who will fill the gap between business practice and the developing digital technologies and STEM. We are teaching business mathematics through case studies, real data and optimization algorithms. How do we do it? In this work we will present some case studies from our university practice where we use the technology for more dynamic mathematics class.

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.

This paper studies the problem of interdependence between central bank and commercial bank goals. The basic central bank task is to achieve and to maintain price stability. Croatian external debt has been increasing for years and so the activities of the Croatian National Bank are designed to correct this situation. In order to stop the further increase of the external debt, the Croatian National Bank uses several monetary policy instruments, among which is the marginal reserve requirement. On the other hand, the goal of commercial banks is to maximise profits. Banks take loans from abroad at a lower interest rate and invest this money in Croatia at a higher interest rate, thus fulfilling their goal. In order to obtain the desired effects of the marginal reserve requirement, its optimal percentage value should be determined. This problem is modelled as a bi-level mixed 0-1 programming problem. The objective of the leader (Croatian National Bank) is to minimize the increase in household loans by setting different percentages of the reserve requirements for loans extended to households and for those granted to enterprises. The objective of the followers (banks) is to maximize profits. In order to solve this NP-hard problem a heuristic is proposed. In order to verify the model, the paper ends with simulations and the presentation of computational results.

Rad promatra problem međuovisnosti ciljeva centralne i poslovnih banaka. Osnovni je cilj Hrvatske narodne banke postizanje i održavanje stabilnosti cijena. Zbog višegodišnjeg problema visokog udjela inozemnog duga u BDP-u, aktivnosti centralne banke uvelike su orijentirane na destimuliranje porasta zaduživanja poslovnih banaka u inozemstvu. U cilju sprječavanja daljnjeg rasta inozemnog duga poslovnih banaka, Hrvatska narodna banka koristi nekoliko instrumenata monetarne politike, među kojima se posebno izdvaja granična obvezna pričuva. S druge strane, cilj poslovnih banaka je ostvarenje što veće dobiti. Pri tom se one zadužuju u inozemstvu po nižoj, a sredstva plasiraju u vidu kredita na domaćem tržištu po višoj kamatnoj stopi i tako ostvaruju svoj cilj. Da bi granična obvezna pričuva postigla željene efekte, potrebno je odrediti optimalni postotak izdvajanja. U tu je svrhu razvijen matematički model dvorazinskog mješovitog 0-1 programiranja. Cilj voditelja (u ovom slučaju HNB-a) je određivanjem različitih postotaka pričuve minimizirati porast kreditnih plasmana stanovništvu od strane poslovnih banaka, a cilj sljedbenika (poslovnih banaka) je maksimizacija dobiti. S matematičke je strane problem NP-težak i stoga se za njegovo rješavanje koristi heuristika. Na kraju su izvršene simulacije radi verifikacije modela i izloženi rezultati numeričkih izračuna.

Each of N items (products) is to be processed on two machines in order to satisfy known demands in each of T periods. Only one item can be processed on each machine at any given time. Each switch from one item to another requires sequence dependent setup time. The object is to minimize the total set up time and the sum of the costs of production, backlog, storage and set up. In order to obtain the solution, we divide the above problem into two subproblems by introducing the hierarchy into the model. Because of this, we model the problem as a bilevel mixed 0-1 integer programming problem. The object of the leader is to assign the items to the machines in order to minimize the total setup time, while the object of the follower is to minimize the production, backlog, 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 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.

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.

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 different setup times.A better upper bound on the total work backlog than those available in literature is derived by introducing 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.Studying whether the CLWS scheduling policy induces convergence to a stationary state, some precedence relations between part types are reported with the computational results.

In this paper, we analyze how different search strategies (namely, the breadth-first, the depth-first and the best-first) influence the execution speed of the parallel branch-and-cut algorithm for solving the capacitated vehicle routing problem. We report anomalous behavior observed as a part of the experimental evaluation of the algorithm and relate to it known theoretical results on anomalies in parallel and on efficiency of search strategies in sequential branch-and-bound algorithms.

After the downfall of the socialist planned economy and with the beginning of transition towards market economy there has been an increasing interest in foreign direct investments (FDI) in transitional countries. This interest is shown by both parties &#8211 ; ; ; multinational economies as investors and transitional countries as host countries. This work starts from the thesis that these companies have to investigate the attractiveness of individual transitional countries for potential investments by using multicriterial analysis.