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2012 | OriginalPaper | Buchkapitel

1. Scope of Problem Coverage and Introduction

verfasst von : Joseph Geunes

Erschienen in: Demand Flexibility in Supply Chain Planning

Verlag: Springer New York

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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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Fußnoten
1
The notation https://static-content.springer.com/image/chp%3A10.1007%2F978-1-4419-9347-2_1/MediaObjects/978-1-4419-9347-2_1_Fig9b_HTML.gif 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.
 
Literatur
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Zurück zum Zitat Federgruen A, Tzur M (1991) A Simple Forward Algorithm to Solve General Dynamic Lot Sizing Models with n Periods in or Time. Management Science 37(8):909–925 MATHCrossRef Federgruen A, Tzur M (1991) A Simple Forward Algorithm to Solve General Dynamic Lot Sizing Models with n Periods in https://static-content.springer.com/image/chp%3A10.1007%2F978-1-4419-9347-2_1/MediaObjects/978-1-4419-9347-2_1_Fig26b_HTML.gif or https://static-content.springer.com/image/chp%3A10.1007%2F978-1-4419-9347-2_1/MediaObjects/978-1-4419-9347-2_1_Fig27b_HTML.gif Time. Management Science 37(8):909–925 MATHCrossRef
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Zurück zum Zitat Frieze A, Clarke M (1984) Approximation Algorithms for the m-Dimensional 0–1 Knapsack Problem: Worst-Case and Probabilistic Analyses. European Journal of Operational Research 15(1):100–109 MathSciNetMATHCrossRef Frieze A, Clarke M (1984) Approximation Algorithms for the m-Dimensional 0–1 Knapsack Problem: Worst-Case and Probabilistic Analyses. European Journal of Operational Research 15(1):100–109 MathSciNetMATHCrossRef
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Zurück zum Zitat Garey M, Johnson D (1979) Computers and Intractability. W.H. Freeman and Company, New York MATH Garey M, Johnson D (1979) Computers and Intractability. W.H. Freeman and Company, New York MATH
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Zurück zum Zitat Harris F (1913) How Many Parts to Make at Once. Factory Magazine Management 10:135–136, 152 Harris F (1913) How Many Parts to Make at Once. Factory Magazine Management 10:135–136, 152
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Zurück zum Zitat Silver E, Pyke D, Peterson R (1998) Inventory Management and Production Planning and Scheduling, 3rd edn. Wiley, New York Silver E, Pyke D, Peterson R (1998) Inventory Management and Production Planning and Scheduling, 3rd edn. Wiley, New York
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Zurück zum Zitat Wagelmans A, van Hoesel S, Kolen A (1992) Economic Lot Sizing: An Algorithm That Runs in Linear Time in the Wagner-Whitin Case. Operations Research 40(S1):S145–S156 CrossRef Wagelmans A, van Hoesel S, Kolen A (1992) Economic Lot Sizing: An https://static-content.springer.com/image/chp%3A10.1007%2F978-1-4419-9347-2_1/MediaObjects/978-1-4419-9347-2_1_Fig29b_HTML.gif Algorithm That Runs in Linear Time in the Wagner-Whitin Case. Operations Research 40(S1):S145–S156 CrossRef
Metadaten
Titel
Scope of Problem Coverage and Introduction
verfasst von
Joseph Geunes
Copyright-Jahr
2012
Verlag
Springer New York
DOI
https://doi.org/10.1007/978-1-4419-9347-2_1