Application of Quasi-Integer Programming to the Solution of Menu Planning Problems with Variable Portion Size.
Abstract
The paper presents the application of a modified mixed integer programming algorithm to plan menus in which the portion size of the menu items can vary over a specified positive range. Previous mathematical programming formulations of menu planning problems have either required the variables representing menu items to be bivalent, or have dropped the integer requirement completely. This latter case gives rise to a feed mix problem, and the former to a zero-one programming problem. In many instances, a more realistic formulation would require that if an item is offered, its portion size must be between a specified upper and lower bound. Although this paper addresses itself solely to menu planning, it is readily seen that real world problems in capital budgeting may be tractable with a similar formulation. It will be shown how any branch-and-bound mixed integer programming algorithm of the type proposed by Beale and Small can be modified to solve the discontinuous programming problem discussed here. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1973
- Accession Number
- AD0769229
Entities
People
- Prabhakant Sinha
- Ronald D. Armstrong
Organizations
- University of Massachusetts Amherst