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Optimal machine capacity expansions with nested limitations under stochastic demand
Author(s) -
Çakanyıldırım Metin,
Roundy Robin O.,
Wood Samuel C.
Publication year - 2004
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/nav.10112
Subject(s) - computer science , production (economics) , purchasing , resource (disambiguation) , service (business) , upper and lower bounds , product (mathematics) , holding cost , space (punctuation) , mathematical optimization , mathematics , operations management , economics , computer network , mathematical analysis , geometry , economy , macroeconomics , operating system
This paper studies capacity expansions for a production facility that faces uncertain customer demand for a single product family. The capacity of the facility is modeled in three tiers, as follows. The first tier consists of a set of upper bounds on production that correspond to different resource types (e.g., machine types, categories of manpower, etc.). These upper bounds are augmented in increments of fixed size (e.g., by purchasing machines of standard types). There is a second‐tier resource that constrains the first‐tier bounds (e.g., clean room floor space). The third‐tier resource bounds the availability of the second‐tier resource (e.g., the total floor space enclosed by the building, land, etc.). The second and third‐tier resources are expanded at various times in various amounts. The cost of capacity expansion at each tier has both fixed and proportional elements. The lost sales cost is used as a measure for the level of customer service. The paper presents a polynomial time algorithm (FIFEX) to minimize the total cost by computing optimal expansion times and amounts for all three types of capacity jointly. It accommodates positive lead times for each type. Demand is assumed to be nondecreasing in a “weak” sense. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.