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  • 1
    Electronic Resource
    Electronic Resource
    A mathematical programming system for preference and compatibility maximized menu planning and scheduling (1978)
    Springer
    Mathematical programming 15 (1978), S. 63-76 
    Details
    ISSN: 1436-4646
    Keywords: Menu Planning ; Separation Scheduling ; Menu Scheduling ; Decomposition ; Non-linear Programming ; Binary Knapsack Problem ; Lagrangian Relaxation ; Transportation Problem ; Branch and Bound
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper, the analytical representation of food preference is used in a separable non-linear program to yield the serving frequencies of menu items for a finite time horizon. The frequencies obtained in this way insure cost and nutritional control. Subsequently, the scheduling problem dealing with item assignments to meals and days is formulated as an integer program consisting of several transportation problems linked by weekly nutritional constraints. This problem is solved using a branch and bound algorithm which employs Lagrangian relaxation to obtain bounds and to decide on branching strategy.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01609000
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Improved penalty calculations for a mixed integer branch-and-bound algorithm (1974)
    Springer
    Mathematical programming 6 (1974), S. 212-223 
    Details
    ISSN: 1436-4646
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper presents an extension of Tomlin's penalties for the branch-and-bound linear mixed integer programming algorithm of Beale and Small. Penalties which are uniformly stronger are obtained by jointly conditioning on a basic variable and the non-basic variable yielding the Tomlin penalty. It is shown that this penalty can be computed with a little additional arithmetic and some extra bookkeeping. The improvement is easy to incorporate for the normal case as well as when the variables are grouped into ordered sets with generalized upper bounds. Computational experience bears out the usefulness of the extra effort for predominantly integer problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580237
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    Paper (German National Licenses)
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