Bin packing with “Largest In Bottom” constraint: tighter bounds and generalizations

The (online) bin packing problem with LIB constraint is stated as follows: The items arrive one by one, and must be packed into unit capacity bins, but a bigger item cannot be packed into a bin which already contains a smaller item. The number of used bins has to be minimized as usually. We show that the absolute performance bound of algorithm First Fit is not worse than 2+1/6≈2.1666 for the problem, improving the previous best upper bound 2.5. Moreover, if the item sizes do not exceed 1/d, then we improve the previous best result 2+1/d to 2+1/d(d+2), for any d≥2. (Both previously best results are due to Epstein, Nav. Res. Logist. 56(8):780–786, 2009.) Furthermore, we define a problem with the generalized LIB constraint, where some incoming items cannot be packed into the bins of some already packed items. The (in)compatibility of the incoming item with the items already packed becomes known only at the arrival of the actual item, and is given by an undirected graph (and, as usual in case of online graph problems, we can see only that part of the graph what already arrived). We show that 3 is an upper bound for this general problem if some natural transitivity constraint is satisfied.     

Books reviews

Peter M. Blau and Marshall W. Meyer, Bureaucracy in Modern Society (3rd. ed). New York, Random House, 1987.

Gareth Morgan, Images of Organization, Beverly Hills, Sage Publications, 1986.

Malvyn Dubrovsky (ed.) Technological Change and Workers’ Movements. Explorations in the World Economy: Publications of the Fernand Braudel Center. Vol.4: Beverly Hills, Sage Publications, 1985.

Helmut Klages, Gerhard Franz, and Willi Herbert, Sozialpsychologie der Wohlfahrtgesellschaft. Zur Dynamik von Wertorientirungen, Einstellungen und Ansprüchen (Social Psychology of the Welfare State. On Dynamics of Value Orientations, Attitudes and Claims). Frankfurt ‐ New York, Campus Verlag, 1987.

Gunter Endruweit, Eduard Gauler, Wolfgang H.Stähle, and Bernhard Wilpert, eds. Handbuch der Arbeitbeziehungen. Deutschland‐Oesterreich‐Schweiz. (Handbook of Work Relations: FRG, Austria and Switzerland). Berlin ‐ New York, Walter de Gruyter, 1985.

Gerhard Lenski and Jean Lenski, Human Societies. An Introduction to Macrosociology, 5th ed., New York, McGraw‐Hill, 1987.

Stephen K.Sanderson, Macrosociology. An Introduction to Human Societies. New York, Harper and Row, 1988.

Wojciech Gasparski and Tadeusz Pszczolowski, eds. Praxiological Studies. Polish Contributions to the Science of Efficient Action. Warsaw‐Dordrecht, PWN and D.Reidel, 1983.

James S. Coleman, Individual Interests and Collective Action. Selected Essays. Cambridge, Cambridge University Press, 1986.

Darreil Steffensmeier, The Fence: In the Shadow of Two Worlds. Totowa, Rowman and Littlefield Publishers, 1986, pp. 295.

Max Kaase (ed.) Politische Wissenschaft und Politische Ordnung. Analysen zu Theorie und Empirie demokratischer Regierungsweise. Festschrift zum 65. Geburstag von Rudolf Wildenmann. Opladen, Westdeutscher Verlag, 1986.

Volker Meja, Dieter Misgeld, and Nico Stehr eds. Modern German Sociology. New York, Columbia University Press, 1987.

Feliks Gross, Ideologies, Goals and Values, Greenwood Press, 1985.     

Recruitment and the Role of Employment Services in Bulgarian Industry

ABSTRACT: This article is based on two surveys of Bulgarian manufacturing enterprises completed by the International Labour Organization in 1992 The surveys covering both state and private sector firms in this transition economy undergoing severe structural change collected a wealth of data on labour and employment practices at the micro level The authors examine recruitment and vacancy rates in the industrial sector managerial recruitment preferences on the basis of age gender and educational back ground and the recruitment methods used by managements in hiring workers The role of the national employment services in labour allocation is also analyzed revealing different recruitment strategies between state and private sector firms