Zrinka Lukač

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.

Use of VNS Heuristics for Scheduling of Patients in Hospital

One of the important problems in hospital management is how to schedule the treatments of resident patients in hospital for a given day due to the restrictions imposed by their medical condition as well as restrictions on medical machines and qualified medical personnel availability. Patients are to be subjected to different kinds of treatments, each requiring a medical machine of a certain type as well as a physician being qualified to operate it. This is a highly complex problem not yet adequately addressed in the literature. At present in most hospitals the problem is being solved manually by specialized personnel. However, the resulting schedules are very often inaccurate and inefficient with patients waiting for a long time to be treated and medical personnel often working overtime. In this paper we formulate the model for this problem and develop a simple and efficient method based on Variable Neighbourhood Search for solving it. The heuristics has been tested on real-life as well as on generated instances. Numerical results show that the heuristics proposed outperform commercial software for optimization as well as manual solutions both in quality of solution and in computational time.

Behaviour of F learning automata as multicriteria routing agents in connection oriented networks

The use of intelligent algorithms based on learning automata (LA) has proved to be very efficient for traffic routing control. However, thus far these algorithms have been focused only on unimodal routing problem in connection or packet oriented networks. The problem of multicriteria routing in communication networks is inherently NP-hard. We present a novel heuristic approach to this problem based on the concept of learning automata in fuzzy environments. We call these automata the F type learning automata. Well known learning automata of P, Q and S types are special cases of F type automata. Among others we prove that these automata are nonabsorbing. A general routing scheme enabling implementation of different routing strategies including Best Quality Routing (BQR) and Least Cost Routing (LCR) has been defined and evaluated through simulation results obtained for connection oriented telecommunication network. The behaviour of different t and s norms has been investigated as well.

An alternative approach to solving cost minimization problem with Cobb–Douglas technology

We propose a new method for solving the production cost minimization problem with Cobb–Douglas technology. The method is based on weighted arithmetic–geometric-mean inequality (weighted AM–GM) and it does not use calculus. In comparison to methods which use calculus (like substitution method or the Lagrange multiplier method), our method derives the global minimum costs and unique global minimizer in case of the Cobb–Douglas production function in a new and easier manner. Another benefit of this method is that it derives the exact formula for the optimal level of inputs as well as the formula for minimum costs in general case of

Measuring the Efficiency of the Food Industry in Central and East European Countries by using the Data Envelopment Analysis Approach.

n>2

The measure of savings in the production process

n>2 inputs. Also, it is important to emphasize that our method does not require checking the first and the second order conditions, which is a necessary step in methods using calculus. The result is first derived for the case of two inputs and then generalized for the problem with

Multicriteria dynamic routing in communication networks based on F learning automata

n>2