Price changing and inventory sharing in supply chain management

The main task of supply chain management is to balance efficiency and effectiveness. Numerous operational management strategies are used to make a supply chain efficient, one such is inventory management. In this paper, we will consider a particular part of a supply chain consisting comprising a manufacturer and a retailer with the goal of minimizing associated inventory costs. We will focus on an inventory of final products determined as the difference between supply and demand and are expressed as a function of price, inflation rate and change in inflation rate resulting in the possible speculations. The manufacturer’s inventory cost is a function of these same variables, with the retailer’s inventory cost having the same function in addition to the margin. The problem is formulated as a dynamic game to share the speculation problem. The optimization problems to be solved are optimal control theory problems with objective functions in the form of integral functional with the integrand depending on the state function and its first and second derivative

A Mathematical Model and Programme Support for Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policy

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

CREATION OF OPTIMAL PERFORMANCE OF AN INVESTMENT PROJECT

The selection of an investment project is formulated as a multi-criteria decision-making problem. This paper presents a case in which the decision-maker uses nine criteria or rather attributes (Net Present Value, Internal Rate of Return, Payback Period, Accounting Rate of Return, Cumulative Cash Flows, Return on Investment, Net Profit Margin, Interest Coverage Ratio and Current Ratio). Individual utility functions are constructed for each attribute separately, as well as a global utility function representing a weighted sum of individual utility functions. For every attribute a finite set of ordered pairs or utility points is determined, taking into account the decision-maker’s assessment. The given points are then approximated by the utility function. Finally, according to the decision-maker’s assessment the optimization problem is solved with the purpose of achieving an optimal performance for each project. By way of negotiation the performances on offer approach the optimal performance of the project with the purpose of realising an agreement between the decision-maker and the investor

PERFORMANCE OF THE CROATIAN INSURANCE COMPANIES - MULTICRITERIAL APPROACH

This paper will perform a multi-criteria analysis of the insurance sector in the Republic of Croatia. The analysis is performed based on five indicators for the eight largest insurance companies in Croatia. The multicriteria business performance is calculated with use of a score, the weighted sum of relative values of indicators. The score is obtained by calculating weights as a solution of a goal programming problem. The goal of a specific insurance company is to increase the value of an indicator in comparison to it’s value a year before. Hence, some insurance companies have more goals that they wish to obtain. The results reveal that the Croatian insurance sector has given the highest priority to return on investment and return on equity for 2011

PERFORMANCE OF THE CROATIAN INSURANCE COMPANIES - MULTICRITERIAL APPROACH

This paper will perform a multi-criteria analysis of the insurance sector in the Republic of Croatia. The analysis is performed based on five indicators for the eight largest insurance companies in Croatia. The multicriteria business performance is calculated with use of a score, the weighted sum of relative values of indicators. The score is obtained by calculating weights as a solution of a goal programming problem. The goal of a specific insurance company is to increase the value of an indicator in comparison to it’s value a year before. Hence, some insurance companies have more goals that they wish to obtain. The results reveal that the Croatian insurance sector has given the highest priority to return on investment and return on equity for 2011

Matematički model i programska podrška za određivanje vrijednosti granične obvezne pričuve kao instrumenta monetarne politike

U radu se promatra problem međuovisnosti ciljeva središnje banke 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 središnje banke uvelike su usmjerene na destimuliranje rasta zaduživanja poslovnih banaka u inozemstvu. Radi sprječavanja daljnjeg rasta inozemnog duga poslovnih banaka, HNB se koristi s nekoliko instrumenata monetarne politike, među kojima se posebno izdvaja granična obvezna pričuva. Nasuprot tome, cilj poslovnih banaka je ostvarenje što veće dobiti. Pritom se one zadužuju u inozemstvu po nižoj, a sredstva plasiraju u obliku kredita na domaćem tržištu po višoj kamatnoj stopi i tako ostvaruju svoj cilj. Da bi granična obvezna pričuva imala željene učinke, potrebno je odrediti optimalni postotak izdvajanja. Za to je razvijen matematički model dvorazinskoga mješovitog 0-1 programiranja. Cilj voditelja (u ovom primjeru HNB-a) jest određivanjem različitih postotaka pričuve minimizirati porast kreditnih plasmana stanovništvu od poslovnih banaka, a cilj sljedbenika (poslovnih banaka) jest maksimizacija dobiti. S matematičke je strane to NP-težak problem i stoga se za njegovo rješavanje primjenjuje heuristika. Na kraju su provedene simulacije radi verifikacije modela i izloženi rezultati numeričkih izračuna

A Mathematical Model and Programme Support for Determination of the Values of the Marginal Reserve Requirement as Instrument of Monetary Policy

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

Production Planning Problem with Sequence Dependent Setups,

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 multi-criteria analysis of the banking system in the Republic of Croatia

This paper analysis business strategies of banks by solving a goal programming model using a multi-criteria decision making approach. Multi-criteria business performance is represented as the weighted sum of selected indicators, and the weights or importance of the indicators are a solution of the corresponding problem of goal programming. The ten biggest commercial banks (according to size of balance sheet assets) in the Republic of Croatia were chosen. For an analysis of the operations of the ten banks, three groups of indicators were chosen – profitability, security/risk and liquidity – which were calculated from the banks’ financial reports for the year 2010

A MATHEMATICAL MODEL AND DECISION SUPPORT SYSTEM FOR DETERMINATION OF THE VALUES OF THE MARGINAL RESERVE REQUIREMENT AS INSTRUMENT OF MONETARY POLICY

Abstract 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 249-278 (2007) Key words: monetary policy instruments, commercial banks credit activity, marginal reserve requirement, bi-level mixed 0-1 programming problem, NP-hard problem, heuristi