Abstract
This chapter begins with an introduction to the book’s scope and preliminary concepts applied throughout the book. We then present a set of basic, foundational, and classical models from the operations planning literature that serve as the underpinning of the work presented throughout the book. These models include the economic order quantity (EOQ), the newsvendor problem, the economic lot-sizing problem (ELSP), the knapsack problem (KP), the generalized assignment problem (GAP), and the facility location problem (FLP). The main results presented later in this book generalize these classical models to account for a planner’s ability to influence demands, which have traditionally served as fixed parameters in these foundational models.
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Notes
- 1.
The notation
implies that some constant K exists such that as T increases, the number of steps required to solve the problem is bounded by KT
2. - 2.
More specifically, non-increasing marginal costs imply C t +H t ≥C t+1 for t=1,…,T−1, i.e., given that orders are placed in periods s and t with s>t, then satisfying a unit of demand in period s or later is at least as cheap when using production in period s as it is when using production in period t.
- 3.
In the language of complexity theory, the recognition version of an optimization problem with a maximization objective asks the question “Does a feasible solution exist with objective function value at least equal to K for some constant K?” Thus, the recognition version of the problem always has a yes/no answer (see [6]).
- 4.
We assume uniqueness of R j /D j ratios, as items with identical values may be combined into one item in the continuous version of the problem.
implies that some constant K exists such that as T increases, the number of steps required to solve the problem is bounded by KT
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© 2012 Joseph Geunes
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Geunes, J. (2012). Scope of Problem Coverage and Introduction. In: Demand Flexibility in Supply Chain Planning. SpringerBriefs in Optimization. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9347-2_1
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