100:
202:, which argues that the costs of carrying inventory have typically been underestimated, including both the direct, obvious costs of storage space and insurance, but also the harder-to-measure costs of increased variables and complexity, and thus decreased flexibility, for the business enterprise.
156:
One issue is infrequent large orders vs. frequent small orders. Large orders will increase the amount of inventory on hand, which is costly, but may benefit from volume discounts. Frequent orders are costly to process, and the resulting small inventory levels may increase the probability of
189:
aspects of food preparation and presentation, and so it is rational to buy and store somewhat more to reduce the chances of running out of key ingredients. The situation often comes down to two key questions: confidence in the merchandise selling, and the benefits accruing if it does?
470:
is allowed to go negative, corresponding to back-ordered items, will depend on the specific situation; if allowed there will usually be a penalty for back orders. The store has costs that are related to the number of items in store and the number of items ordered:
181:: if the items are not on the shelves, they cannot be sold. And the wholesale market is not perfect; there can be considerable delays, particularly with the most popular toys. So, the entrepreneur or business manager will buy speculatively. Another example is a
197:
inventory often accumulates between two departments because the consuming and the producing department do not coordinate their work. With improved coordination this buffer inventory could be eliminated. This leads to the whole philosophy of
172:
A second issue is related to changes in demand (predictable or random) for the product. For example, having the needed merchandise on hand in order to make sales during the appropriate buying season(s). A classic example is a
185:
store. If there is a six-week, or more, delay for customers to receive merchandise, some sales will be lost. A further example is a restaurant, where a considerable percentage of the sales are the
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is the problem faced by a firm that must decide how much to order in each time period to meet demand for its products. The problem can be modeled using mathematical techniques of
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Simchi-Levi, David, Xin Chen, and Julien Bramel. The Logic of
Logistics: Theory, Algorithms, and Applications for Logistics Management, 2nd ed. New York: Springer Verlag, 2004.
438:
722:
635:
468:
309:
282:
255:
329:
228:
994:
Kenneth J. Arrow, Samuel Karlin, and
Herbert E. Scarf: Studies in the Mathematical Theory of Inventory and Production, Stanford University Press, 1958
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Silver, Edward A., David F. Pyke, and Rein
Peterson. Inventory Management and Production Planning and Scheduling, 3rd ed. Hoboken, NJ: Wiley, 1998.
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A third issue comes from the view that inventory also serves the function of decoupling two separate operations. For example,
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1078:, in series: International Series in Operations Research and Management Science, Springer, New York, NY, 2010. (253 pages -
920:
844:
1061:, in series International Series in Operations Research & Management Science, Springer, NY, NY, 2005.(310 pages -
930:
882:
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Snyder, Lawrence V. Fundamentals of Supply Chain Theory, 2nd ed. Hoboken, NJ: John Wiley & Sons, Inc, 2019.
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Tempelmeier, Horst. Inventory
Management in Supply Networks, 3rd. Edition, Norderstedt (Books on Demand) 2011,
794:
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125:
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Porteus, Evan L. Foundations of
Stochastic Inventory Theory. Stanford, CA: Stanford University Press, 2002.
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Although the number of models described in the literature is immense, the following is a list of classics:
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35:
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Thomson M. Whitin, G. Hadley, Analysis of
Inventory Systems, Englewood Cliffs: Prentice-Hall 1963
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410:
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Many university courses in inventory theory use one or more of the following current textbooks:
724:), upper bounds on inventory and so on. Inventory models can be based on different assumptions:
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Many other features can be added to the model, including multiple products (denoted
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The mathematical approach is typically formulated as follows: a store has, at time
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59:
31:
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Rossi, Roberto. Inventory
Analytics. Cambridge, UK: Open Book Publishers, 2021.
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Zipkin, Paul H. Foundations of
Inventory Management. Boston: McGraw Hill, 2000.
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Zipkin Paul H., Foundations of
Inventory Management, Boston: McGraw Hill, 2000,
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50:: it studies the decisions faced by firms and the military in connection with
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165:. In principle all these factors can be calculated mathematically and the
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128:. Statements consisting only of original research should be removed.
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allocation and so on and provides the mathematical foundation for
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theory of inventory and production) is the sub-specialty within
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Axsaeter, Sven. Inventory
Control. Norwell, MA: Kluwer, 2000.
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Inventory and Supply Chain Management with Forecast Updates
86:. The study of such models is part of inventory theory.
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Beyer, D., Cheng, F., Sethi, S.P., and Taksar, M.I.,
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Demand is random, only one replenishment: classical
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986:on inventory theory publishing current research.
843:Constant fill rate for the part being produced:
836:Infinite fill rate for the part being produced:
331:follows a given probability distribution. Thus:
42:that is concerned with the design of production/
887:Several products produced on the same machine:
990:Classic books that established the field are:
257:items in stock. It then orders (and receives)
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862:Demand is random, continuous replenishment:
881:Demand varies deterministically over time:
874:Demand varies deterministically over time:
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399:{\displaystyle x_{k+1}=x_{k}+u_{k}-w_{k}}
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144:Learn how and when to remove this message
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600:{\displaystyle c_{k}=p(x_{k})+h(u_{k})}
536:. Often this will be in additive form:
1055:Sethi, S.P., Yan, H., and Zhang, H.,
684:{\displaystyle \sum _{k=0}^{T}c_{k}.}
7:
850:Orders placed at regular intervals:
637:in an optimal way, i.e. to minimize
529:{\displaystyle c_{k}=c(x_{k},u_{k})}
790:: infinite, deterministic or random
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1075:Markovian Demand Inventory Models
793:Presence or absence of quantity
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889:Economic lot scheduling problem
778:: finite versus infinite (T=+∞)
969:, 3rd ed. Waveland Press, 2011
840:model, a.k.a. Wilson EOQ Model
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124:the claims made and adding
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610:The store wants to select
72:inventory control problem
18:Inventory control problem
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852:fixed time period model
838:Economic order quantity
781:Presence or absence of
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965:W. Hopp, M. Spearman,
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878:or Wagner-Whitin model
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30:(or more formally the
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901:Inventory control
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324:{\displaystyle w}
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107:This section
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60:supply chains
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52:manufacturing
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776:Time horizon
732:: constant,
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209:
200:Just In Time
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32:mathematical
27:
26:
870:(Q,r) model
187:value-added
56:warehousing
937:References
799:Imperfect
765:continuous
738:stochastic
728:Nature of
134:March 2016
118:improve it
64:spare part
795:discounts
770:Lead time
649:∑
425:≥
384:−
183:furniture
179:Christmas
175:toy store
163:customers
159:stockouts
122:verifying
68:logistics
44:inventory
1124:Category
895:See also
818:Location
812:Products
806:Capacity
761:discrete
755:Flow of
747:variable
443:Whether
801:quality
763:versus
749:versus
177:before
169:found.
167:optimum
116:Please
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1103:
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1019:
1009:
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730:demand
90:Issues
70:. The
847:model
751:fixed
743:Costs
48:costs
1111:ISBN
1101:ISBN
1091:ISBN
1080:ISBN
1063:ISBN
1047:ISBN
1037:ISBN
1027:ISBN
1017:ISBN
1007:ISBN
951:ISBN
757:time
82:and
38:and
120:by
1126::
759::
745::
230:,
78:,
62:,
58:,
54:,
1086:)
1069:)
710:k
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679:.
674:k
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582:(
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560:(
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498:(
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358:=
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319:w
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266:u
243:k
239:x
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147:)
141:(
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132:(
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20:)
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