Newsvendor problem - Revision history

Wc593 at 11:36, 21 December 2020

2020-12-21T11:36:48Z

← Older revision		Revision as of 07:36, 21 December 2020
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	Authors: Morgan McCormick (mm3237), Brittany Yesner (by286), Daniel Aronson (da523), John Bednarek (jwb389)		Authors: Morgan McCormick (mm3237), Brittany Yesner (by286), Daniel Aronson (da523), John Bednarek (jwb389) (SysEn 5800 Fall 2020)

	== Introduction ==		== Introduction ==

Da523: /* Description */

2020-12-13T22:18:24Z

Description

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	== Description ==		== Description ==
	The newsvendor model is a model used to determine the optimal inventory levels in operations management and applied economic applications. The assumptions for this problem usually include fixed prices and uncertain demands for perishable products with limited availability. In this model, any unit of demand, ''R'', over the current inventory level, ~~''n''~~, is identified as a lost sale.		The newsvendor model is a model used to determine the optimal inventory levels in operations management and applied economic applications. The assumptions for this problem usually include fixed prices and uncertain demands for perishable products with limited availability. In this model, any unit of demand, ''R'', over the current inventory level, x, is identified as a lost sale.

	== Formulation ==		== Formulation ==
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	=== Personal Investments ===		=== Personal Investments ===
	The tradeoff between tying funds up in a stock against holding cash reserves follows the model of the newsvendor problem because putting too much much of your money in stocks could lead to having to sell stocks undervalue to free up cash ~~whole~~ holding too much money in cash reserves could lead to money that is under performing. The newsvendor problem can help investors find an optimal way to allow to minimize risk while allowing enough opportunity to create a large gain. With recent trends of market volatility, evaluating cash positions and market exposure has become ever more important.<ref name=":2">Birge, J. and Louveaux, F. Introduction to Stochastic Programming, Springer, 2011.</ref>		The tradeoff between tying funds up in a stock against holding cash reserves follows the model of the newsvendor problem because putting too much much of your money in stocks could lead to having to sell stocks undervalue to free up cash while holding too much money in cash reserves could lead to money that is under performing. The newsvendor problem can help investors find an optimal way to allow to minimize risk while allowing enough opportunity to create a large gain. With recent trends of market volatility, evaluating cash positions and market exposure has become ever more important.<ref name=":2">Birge, J. and Louveaux, F. Introduction to Stochastic Programming, Springer, 2011.</ref>

	=== Emergency Resources ===		=== Emergency Resources ===
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	=== Manufacturing ===		=== Manufacturing ===
	The amount of units of a good to manufacture follows the model of the newsvendor problem because while overproduction would always meet demand, production costs increase and storage costs are introduced for the excess inventory. Manufacturers and wholesalers often rely on razor thin margins. By understanding how to limit excess storage and money that it ~~put~~ out into the materials themselves the business can find an accurate way of maximizing the cash flow. Inventory is often one of the crippling factors of a business. Businesses often can save money on individual units by producing larger quantities, but this ultimately eats away at having a strong cash position to address the concerns of a changing market.<ref name=":2" />		The amount of units of a good to manufacture follows the model of the newsvendor problem because while overproduction would always meet demand, production costs increase and storage costs are introduced for the excess inventory. Manufacturers and wholesalers often rely on razor thin margins. By understanding how to limit excess storage and money that it puts out into the materials themselves the business can find an accurate way of maximizing the cash flow. Inventory is often one of the crippling factors of a business. Businesses often can save money on individual units by producing larger quantities, but this ultimately eats away at having a strong cash position to address the concerns of a changing market.<ref name=":2" />

	=== Real Estate ===		=== Real Estate ===

Mm3237: /* Numerical Example */

2020-12-13T17:08:50Z

Numerical Example

Show changes

Jwb389 at 16:53, 13 December 2020

2020-12-13T16:53:59Z

← Older revision		Revision as of 12:53, 13 December 2020
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	To formulate a standard newsvendor problem to determine profit, the function is <math display="inline">E[profit] = E[s * min(x, R)] - wx </math> . In the formulation, ''s'' represents the price a unit is sold for, x represents the number of units in inventory that the vendor ordered, ''R'' is a random variable representing a probability distribution for the demand a given day, and ''w'' is the wholesale cost for the vendor to purchase materials. The goal is to optimize the profit to be a maximum. This is achieved by maximizing the amount of inventory on hand to be able to sell while also minimizing the amount of unsold inventory that is void or considered perishable at the end of the day. The salvage cost for any unsold inventory at the end of the sales period is represented by ''v.''		To formulate a standard newsvendor problem to determine profit, the function is <math display="inline">E[profit] = E[s * min(x, R)] - wx </math> . In the formulation, ''s'' represents the price a unit is sold for, x represents the number of units in inventory that the vendor ordered, ''R'' is a random variable representing a probability distribution for the demand a given day, and ''w'' is the wholesale cost for the vendor to purchase materials. The goal is to optimize the profit to be a maximum. This is achieved by maximizing the amount of inventory on hand to be able to sell while also minimizing the amount of unsold inventory that is void or considered perishable at the end of the day. The salvage cost for any unsold inventory at the end of the sales period is represented by ''v.''

	The balance of being understocked and losing potential sales with the potential loss from being overstocked can be represented by the critical fractal. This is illustrated by the formula <math>n=F^{-1} ({s-w \over s})</math> where ''F<sup>-1</sup>'' is the inverse of the cumulative distribution function of R.<ref>"Newsvendor Model.” Wikipedia, Wikimedia Foundation, 12 Nov. 2020, en.wikipedia.org/wiki/Newsvendor_model.		The balance of being understocked and losing potential sales with the potential loss from being overstocked can be represented by the critical fractal. This is illustrated by the formula <math>n=F^{-1} ({s-w \over s})</math> where ''F<sup>-1</sup>'' is the inverse of the cumulative distribution function of R.<ref name=":0">"Newsvendor Model.” Wikipedia, Wikimedia Foundation, 12 Nov. 2020, en.wikipedia.org/wiki/Newsvendor_model.

	</ref><sup>,</sup><ref>Yan Qin, Ruoxuan Wang, Asoo J. Vakharia, Yuwen Chen, Michelle M.H. Seref, “The newsvendor problem: Review and directions for future research.” European Journal of Operational Research. Volume 213, Issue 2. 2011. Pages 361-374, ISSN 0377-2217. <nowiki>https://doi.org/10.1016/j.ejor.2010.11.024</nowiki>.</ref>		</ref><sup>,</sup><ref>Yan Qin, Ruoxuan Wang, Asoo J. Vakharia, Yuwen Chen, Michelle M.H. Seref, “The newsvendor problem: Review and directions for future research.” European Journal of Operational Research. Volume 213, Issue 2. 2011. Pages 361-374, ISSN 0377-2217. <nowiki>https://doi.org/10.1016/j.ejor.2010.11.024</nowiki>.</ref>

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	A historically relevant example of the newsvendor problem would be the working conditions that led to the newsboy strike of 1899 and subsequent labor movements.		A historically relevant example of the newsvendor problem would be the working conditions that led to the newsboy strike of 1899 and subsequent labor movements.

	In the late nineteenth century and before the Spanish-American War, newsboys in New York City could purchase 100 newspapers for 50 cents and sell the newspapers for 8 cents each. If a paper didn’t sell, assume the publisher would buy the newspaper back at 60% cost.<ref>“Labor History Lesson: The ‘Newsies’ Strike.” Labor History Lesson: The "Newsies" Strike \| AFT Connecticut, 25 May 2016, aftct.org/story/labor-history-lesson-newsies-strike</ref>		In the late nineteenth century and before the Spanish-American War, newsboys in New York City could purchase 100 newspapers for 50 cents and sell the newspapers for 8 cents each. If a paper didn’t sell, assume the publisher would buy the newspaper back at 60% cost.<ref name=":1">“Labor History Lesson: The ‘Newsies’ Strike.” Labor History Lesson: The "Newsies" Strike \| AFT Connecticut, 25 May 2016, aftct.org/story/labor-history-lesson-newsies-strike</ref>

	Assume the newspaper sales in New York City followed the following demand schedule:		Assume the newspaper sales in New York City followed the following demand schedule:
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	The next method that can be used to estimate the demand of a paper can be done using a normal distribution. A normal distribution’s standard deviation positions the curve of demand into being one that can be used to calculate the different demands that a salesman may face amongst the sales of a paper. The normal distribution allocates variations that enable the salesman to take calculated risks based on historical norms. These norms provide contextual evidence to accurately account for the demand that the seller may see.		The next method that can be used to estimate the demand of a paper can be done using a normal distribution. A normal distribution’s standard deviation positions the curve of demand into being one that can be used to calculate the different demands that a salesman may face amongst the sales of a paper. The normal distribution allocates variations that enable the salesman to take calculated risks based on historical norms. These norms provide contextual evidence to accurately account for the demand that the seller may see.

	While a normal distribution can provide estimates into how many papers may need to be printed for the public, it does not take into account the potential profit or loss that the vendor may undertake. The logarithmic method will show at what point the salesman optimal peak profit will be. The logarithmic curve is exponential and will ultimately determine the peak profit and printing point at which the business will succeed. This solution is meant to determine the optimal solution from a profit standpoint.<sup>4,6</sup>		While a normal distribution can provide estimates into how many papers may need to be printed for the public, it does not take into account the potential profit or loss that the vendor may undertake. The logarithmic method will show at what point the salesman optimal peak profit will be. The logarithmic curve is exponential and will ultimately determine the peak profit and printing point at which the business will succeed. This solution is meant to determine the optimal solution from a profit standpoint.<ref name=":0" /><sup>,</sup><ref name=":1" />

	== Applications ==		== Applications ==
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	=== Personal Investments ===		=== Personal Investments ===
	The tradeoff between tying funds up in a stock against holding cash reserves follows the model of the newsvendor problem because putting too much much of your money in stocks could lead to having to sell stocks undervalue to free up cash whole holding too much money in cash reserves could lead to money that is under performing. The newsvendor problem can help investors find an optimal way to allow to minimize risk while allowing enough opportunity to create a large gain. With recent trends of market volatility, evaluating cash positions and market exposure has become ever more important.<~~sup~~>6</~~sup~~>		The tradeoff between tying funds up in a stock against holding cash reserves follows the model of the newsvendor problem because putting too much much of your money in stocks could lead to having to sell stocks undervalue to free up cash whole holding too much money in cash reserves could lead to money that is under performing. The newsvendor problem can help investors find an optimal way to allow to minimize risk while allowing enough opportunity to create a large gain. With recent trends of market volatility, evaluating cash positions and market exposure has become ever more important.<ref name=":2">Birge, J. and Louveaux, F. Introduction to Stochastic Programming, Springer, 2011.</ref>

	=== Emergency Resources ===		=== Emergency Resources ===
	The amount of emergency resources to hold on hand follows the model of the newsvendor problem because holding too many emergency resources could mean throwing out expensive inventory if there is no emergency while not having enough emergency resources could be disastrous in times of peril. Emergencies have the same tendencies of an unknown market. The first responders need to have an optimal amount of supplies to maximize their effectiveness. If items that are perishable are sent in mass quantities, it can bog down the supply lines and lead to important resources becoming expired.<~~sup>6<~~/~~sup~~>		The amount of emergency resources to hold on hand follows the model of the newsvendor problem because holding too many emergency resources could mean throwing out expensive inventory if there is no emergency while not having enough emergency resources could be disastrous in times of peril. Emergencies have the same tendencies of an unknown market. The first responders need to have an optimal amount of supplies to maximize their effectiveness. If items that are perishable are sent in mass quantities, it can bog down the supply lines and lead to important resources becoming expired.<ref name=":2" />

	=== Manufacturing ===		=== Manufacturing ===
	The amount of units of a good to manufacture follows the model of the newsvendor problem because while overproduction would always meet demand, production costs increase and storage costs are introduced for the excess inventory. Manufacturers and wholesalers often rely on razor thin margins. By understanding how to limit excess storage and money that it put out into the materials themselves the business can find an accurate way of maximizing the cash flow. Inventory is often one of the crippling factors of a business. Businesses often can save money on individual units by producing larger quantities, but this ultimately eats away at having a strong cash position to address the concerns of a changing market.<~~sup>6<~~/~~sup~~>		The amount of units of a good to manufacture follows the model of the newsvendor problem because while overproduction would always meet demand, production costs increase and storage costs are introduced for the excess inventory. Manufacturers and wholesalers often rely on razor thin margins. By understanding how to limit excess storage and money that it put out into the materials themselves the business can find an accurate way of maximizing the cash flow. Inventory is often one of the crippling factors of a business. Businesses often can save money on individual units by producing larger quantities, but this ultimately eats away at having a strong cash position to address the concerns of a changing market.<ref name=":2" />

	=== Real Estate ===		=== Real Estate ===
	House pricing in the real estate market follows the model of the newsvendor problem because if a house is priced too high it will take too long to sell and if the house is priced too low it will sell quickly but at lower price. The housing market is another investment that is exposed to a great deal of volatility and increased market risk. Markets can change rapidly from economic situations to also the crime, schools, and locations around a property. By understanding the market norms, one can find the adequate pricing method for a home using the newsvendor problem algorithm. Appraisers and realtors must focus on understanding these metrics to ensure the estimates are accurate.<~~sup>6<~~/~~sup~~>		House pricing in the real estate market follows the model of the newsvendor problem because if a house is priced too high it will take too long to sell and if the house is priced too low it will sell quickly but at lower price. The housing market is another investment that is exposed to a great deal of volatility and increased market risk. Markets can change rapidly from economic situations to also the crime, schools, and locations around a property. By understanding the market norms, one can find the adequate pricing method for a home using the newsvendor problem algorithm. Appraisers and realtors must focus on understanding these metrics to ensure the estimates are accurate.<ref name=":2" />

	== Conclusion ==		== Conclusion ==
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	== References ==		== References ==

	~~# F. Y. Edgeworth (1888). "The Mathematical Theory of Banking". Journal of the Royal Statistical Society.~~
	~~# R. R. Chen; T.C.E. Cheng; T.M. Choi; Y. Wang (2016). "Novel Advances in Applications of the Newsvendor Model". Decision Sciences.~~
	~~# Whitin, T. M. “Inventory Control and Price Theory.” Management Science, vol. 2, no. 1, 1955, pp. 61–68.~~
	~~# “Newsvendor Model.” Wikipedia, Wikimedia Foundation, 12 Nov. 2020, en.wikipedia.org/wiki/Newsvendor_model.~~
	# Yan Qin, Ruoxuan Wang, Asoo J. Vakharia, Yuwen Chen, Michelle M.H. Seref, “The newsvendor problem: Review and directions for future research.” European Journal of Operational Research. Volume 213, Issue 2. 2011. Pages 361-374, ISSN 0377-2217. <nowiki>https://doi.org/10.1016/j.ejor.2010.11.024</nowiki>.
	~~# “Labor History Lesson: The ‘Newsies’ Strike.” Labor History Lesson: The "Newsies" Strike \| AFT Connecticut, 25 May 2016, aftct.org/story/labor-history-lesson-newsies-strike~~
	~~# Birge, J. and Louveaux, F. Introduction to Stochastic Programming, Springer, 2011.~~

Mm3237: /* References */

2020-12-13T16:49:09Z

References

← Older revision		Revision as of 12:49, 13 December 2020
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	# “Newsvendor Model.” Wikipedia, Wikimedia Foundation, 12 Nov. 2020, en.wikipedia.org/wiki/Newsvendor_model.		# “Newsvendor Model.” Wikipedia, Wikimedia Foundation, 12 Nov. 2020, en.wikipedia.org/wiki/Newsvendor_model.
	# Yan Qin, Ruoxuan Wang, Asoo J. Vakharia, Yuwen Chen, Michelle M.H. Seref, “The newsvendor problem: Review and directions for future research.” European Journal of Operational Research. Volume 213, Issue 2. 2011. Pages 361-374, ISSN 0377-2217. <nowiki>https://doi.org/10.1016/j.ejor.2010.11.024</nowiki>.		# Yan Qin, Ruoxuan Wang, Asoo J. Vakharia, Yuwen Chen, Michelle M.H. Seref, “The newsvendor problem: Review and directions for future research.” European Journal of Operational Research. Volume 213, Issue 2. 2011. Pages 361-374, ISSN 0377-2217. <nowiki>https://doi.org/10.1016/j.ejor.2010.11.024</nowiki>.
	~~# Powell, W. B. “Newsvendor Problem.” Castle Lab Princeton, 2013, castlelab.princeton.edu/html/Presentations/ORF411_2013/ORF%20411%2015%20Newsvendor%20problem.pdf.~~
	# “Labor History Lesson: The ‘Newsies’ Strike.” Labor History Lesson: The "Newsies" Strike \| AFT Connecticut, 25 May 2016, aftct.org/story/labor-history-lesson-newsies-strike		# “Labor History Lesson: The ‘Newsies’ Strike.” Labor History Lesson: The "Newsies" Strike \| AFT Connecticut, 25 May 2016, aftct.org/story/labor-history-lesson-newsies-strike
	# Birge, J. and Louveaux, F. Introduction to Stochastic Programming, Springer, 2011.		# Birge, J. and Louveaux, F. Introduction to Stochastic Programming, Springer, 2011.

Jwb389: /* Introduction */

2020-12-13T16:47:45Z

Introduction

← Older revision		Revision as of 12:47, 13 December 2020
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	The mathematical application for the Newsvendor Problem dates back to 1888, when Francis Ysidro Edgeworth used the central limit theorem to find the optimal cash reserves needed to satisfy various withdrawals from depositors.<ref>F. Y. Edgeworth (1888). "The Mathematical Theory of Banking". Journal of the Royal Statistical Society.</ref> The namesake for the problem comes from Morse and Kimball's book from 1951, where they used the term “newsboy” to describe this specific problem.<ref>R. R. Chen; T.C.E. Cheng; T.M. Choi; Y. Wang (2016). "Novel Advances in Applications of the Newsvendor Model". Decision Sciences.</ref> Also referred to as “newsboy problem”, it is named by analogy with the situation faced by a newspaper vendor who must decide how many copies of the day's paper to stock in the face of uncertain demand and knowing that unsold copies will be worthless at the end of the day.		The mathematical application for the Newsvendor Problem dates back to 1888, when Francis Ysidro Edgeworth used the central limit theorem to find the optimal cash reserves needed to satisfy various withdrawals from depositors.<ref>F. Y. Edgeworth (1888). "The Mathematical Theory of Banking". Journal of the Royal Statistical Society.</ref> The namesake for the problem comes from Morse and Kimball's book from 1951, where they used the term “newsboy” to describe this specific problem.<ref>R. R. Chen; T.C.E. Cheng; T.M. Choi; Y. Wang (2016). "Novel Advances in Applications of the Newsvendor Model". Decision Sciences.</ref> Also referred to as “newsboy problem”, it is named by analogy with the situation faced by a newspaper vendor who must decide how many copies of the day's paper to stock in the face of uncertain demand and knowing that unsold copies will be worthless at the end of the day.

	T.M Whitin in 1955 was the first to consider not only the cost minimization portion of the problem, but also the profit maximization.<~~sup~~>3</~~sup~~> To do so he formulated a newsvendor model with price effects, where the selling price and stocking quantity are set simultaneously. He then adapted his model to include a probability distribution for demand as a function of the selling price, therefore making the price of the product a decision variable rather than an assigned variable.		T.M Whitin in 1955 was the first to consider not only the cost minimization portion of the problem, but also the profit maximization.<ref>Whitin, T. M. “Inventory Control and Price Theory.” Management Science, vol. 2, no. 1, 1955, pp. 61–68.</ref> To do so he formulated a newsvendor model with price effects, where the selling price and stocking quantity are set simultaneously. He then adapted his model to include a probability distribution for demand as a function of the selling price, therefore making the price of the product a decision variable rather than an assigned variable.

	In general, this model can be used in any application with a perishable good and unknown, randomized demand.		In general, this model can be used in any application with a perishable good and unknown, randomized demand.
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	To formulate a standard newsvendor problem to determine profit, the function is <math display="inline">E[profit] = E[s * min(x, R)] - wx </math> . In the formulation, ''s'' represents the price a unit is sold for, x represents the number of units in inventory that the vendor ordered, ''R'' is a random variable representing a probability distribution for the demand a given day, and ''w'' is the wholesale cost for the vendor to purchase materials. The goal is to optimize the profit to be a maximum. This is achieved by maximizing the amount of inventory on hand to be able to sell while also minimizing the amount of unsold inventory that is void or considered perishable at the end of the day. The salvage cost for any unsold inventory at the end of the sales period is represented by ''v.''		To formulate a standard newsvendor problem to determine profit, the function is <math display="inline">E[profit] = E[s * min(x, R)] - wx </math> . In the formulation, ''s'' represents the price a unit is sold for, x represents the number of units in inventory that the vendor ordered, ''R'' is a random variable representing a probability distribution for the demand a given day, and ''w'' is the wholesale cost for the vendor to purchase materials. The goal is to optimize the profit to be a maximum. This is achieved by maximizing the amount of inventory on hand to be able to sell while also minimizing the amount of unsold inventory that is void or considered perishable at the end of the day. The salvage cost for any unsold inventory at the end of the sales period is represented by ''v.''

	The balance of being understocked and losing potential sales with the potential loss from being overstocked can be represented by the critical ~~fractile~~. This is illustrated by the formula <math>n=F^{-1} ({s-w \over s})</math> where ''F<sup>-1</sup>'' is the inverse of the cumulative distribution function of R.<sup>4,5</sup>		The balance of being understocked and losing potential sales with the potential loss from being overstocked can be represented by the critical fractal. This is illustrated by the formula <math>n=F^{-1} ({s-w \over s})</math> where ''F<sup>-1</sup>'' is the inverse of the cumulative distribution function of R.<ref>"Newsvendor Model.” Wikipedia, Wikimedia Foundation, 12 Nov. 2020, en.wikipedia.org/wiki/Newsvendor_model.

			</ref><sup>,</sup><ref>Yan Qin, Ruoxuan Wang, Asoo J. Vakharia, Yuwen Chen, Michelle M.H. Seref, “The newsvendor problem: Review and directions for future research.” European Journal of Operational Research. Volume 213, Issue 2. 2011. Pages 361-374, ISSN 0377-2217. <nowiki>https://doi.org/10.1016/j.ejor.2010.11.024</nowiki>.</ref>

	=== Detailed Solution Steps ===		=== Detailed Solution Steps ===
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	A historically relevant example of the newsvendor problem would be the working conditions that led to the newsboy strike of 1899 and subsequent labor movements.		A historically relevant example of the newsvendor problem would be the working conditions that led to the newsboy strike of 1899 and subsequent labor movements.

	In the late nineteenth century and before the Spanish-American War, newsboys in New York City could purchase 100 newspapers for 50 cents and sell the newspapers for 8 cents each. If a paper didn’t sell, assume the publisher would buy the newspaper back at 60% cost.<~~sup~~>7</~~sup~~>		In the late nineteenth century and before the Spanish-American War, newsboys in New York City could purchase 100 newspapers for 50 cents and sell the newspapers for 8 cents each. If a paper didn’t sell, assume the publisher would buy the newspaper back at 60% cost.<ref>“Labor History Lesson: The ‘Newsies’ Strike.” Labor History Lesson: The "Newsies" Strike \| AFT Connecticut, 25 May 2016, aftct.org/story/labor-history-lesson-newsies-strike</ref>

	Assume the newspaper sales in New York City followed the following demand schedule:		Assume the newspaper sales in New York City followed the following demand schedule:

Jwb389: /* Introduction */

2020-12-13T16:39:10Z

Introduction

← Older revision		Revision as of 12:39, 13 December 2020
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	== Introduction ==		== Introduction ==
	The mathematical application for the Newsvendor Problem dates back to 1888, when Francis Ysidro Edgeworth used the central limit theorem to find the optimal cash reserves needed to satisfy various withdrawals from depositors.<~~sup~~>1</~~sup~~> The namesake for the problem comes from Morse and Kimball's book from 1951, where they used the term “newsboy” to describe this specific problem.<~~sup~~>2</~~sup~~> Also referred to as “newsboy problem”, it is named by analogy with the situation faced by a newspaper vendor who must decide how many copies of the day's paper to stock in the face of uncertain demand and knowing that unsold copies will be worthless at the end of the day.		The mathematical application for the Newsvendor Problem dates back to 1888, when Francis Ysidro Edgeworth used the central limit theorem to find the optimal cash reserves needed to satisfy various withdrawals from depositors.<ref>F. Y. Edgeworth (1888). "The Mathematical Theory of Banking". Journal of the Royal Statistical Society.</ref> The namesake for the problem comes from Morse and Kimball's book from 1951, where they used the term “newsboy” to describe this specific problem.<ref>R. R. Chen; T.C.E. Cheng; T.M. Choi; Y. Wang (2016). "Novel Advances in Applications of the Newsvendor Model". Decision Sciences.</ref> Also referred to as “newsboy problem”, it is named by analogy with the situation faced by a newspaper vendor who must decide how many copies of the day's paper to stock in the face of uncertain demand and knowing that unsold copies will be worthless at the end of the day.

	T.M Whitin in 1955 was the first to consider not only the cost minimization portion of the problem, but also the profit maximization.<sup>3</sup> To do so he formulated a newsvendor model with price effects, where the selling price and stocking quantity are set simultaneously. He then adapted his model to include a probability distribution for demand as a function of the selling price, therefore making the price of the product a decision variable rather than an assigned variable.		T.M Whitin in 1955 was the first to consider not only the cost minimization portion of the problem, but also the profit maximization.<sup>3</sup> To do so he formulated a newsvendor model with price effects, where the selling price and stocking quantity are set simultaneously. He then adapted his model to include a probability distribution for demand as a function of the selling price, therefore making the price of the product a decision variable rather than an assigned variable.

Mm3237: /* Demand Distributions */

2020-12-13T15:39:23Z

Demand Distributions

← Older revision		Revision as of 11:39, 13 December 2020
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	=== Personal Investments ===		=== Personal Investments ===
	The tradeoff between ~~typing~~ funds up in a stock ~~and~~ holding cash reserves follows the model of the newsvendor problem because putting too much much of your money in stocks could lead to having to sell stocks undervalue to free up cash whole holding too much money in cash reserves could lead to money that is under performing. The newsvendor problem can help investors find an optimal way to allow to minimize risk while allowing enough opportunity to create a large gain. With recent trends of market volatility evaluating cash positions and market exposure has become ever more important.<sup>6</sup>		The tradeoff between tying funds up in a stock against holding cash reserves follows the model of the newsvendor problem because putting too much much of your money in stocks could lead to having to sell stocks undervalue to free up cash whole holding too much money in cash reserves could lead to money that is under performing. The newsvendor problem can help investors find an optimal way to allow to minimize risk while allowing enough opportunity to create a large gain. With recent trends of market volatility, evaluating cash positions and market exposure has become ever more important.<sup>6</sup>

	=== Emergency Resources ===		=== Emergency Resources ===
	The amount of emergency resources to hold on hand follows the model of the newsvendor problem because holding too many emergency resources could mean throwing out expensive inventory if there is no emergency ~~and~~ not having enough emergency resources could be disastrous in times of peril. Emergencies have the same tendencies of an unknown market. The first responders need to have an ~~optial~~ amount of supplies to maximize their effectiveness. If items that are perishable are sent in mass quantities it can bog down the supply lines and lead to important resources becoming expired.<sup>6</sup>		The amount of emergency resources to hold on hand follows the model of the newsvendor problem because holding too many emergency resources could mean throwing out expensive inventory if there is no emergency while not having enough emergency resources could be disastrous in times of peril. Emergencies have the same tendencies of an unknown market. The first responders need to have an optimal amount of supplies to maximize their effectiveness. If items that are perishable are sent in mass quantities, it can bog down the supply lines and lead to important resources becoming expired.<sup>6</sup>

	=== Manufacturing ===		=== Manufacturing ===
	The amount of units of a good to manufacture follows the model of the newsvendor problem because while overproduction would always meet demand, production costs increase and storage costs are introduced for the excess inventory. Manufacturers and wholesalers often rely on razor thin margins. By understanding how to limit excess storage and money that it put out into the materials themselves the business can find an accurate way of maximizing the cash flow. Inventory is often one of the crippling factors of a business. Businesses often can save money on individual units by producing larger quantities but this ultimately eats away at having a strong cash position to address the concerns of a changing market.<sup>6</sup>		The amount of units of a good to manufacture follows the model of the newsvendor problem because while overproduction would always meet demand, production costs increase and storage costs are introduced for the excess inventory. Manufacturers and wholesalers often rely on razor thin margins. By understanding how to limit excess storage and money that it put out into the materials themselves the business can find an accurate way of maximizing the cash flow. Inventory is often one of the crippling factors of a business. Businesses often can save money on individual units by producing larger quantities, but this ultimately eats away at having a strong cash position to address the concerns of a changing market.<sup>6</sup>

	=== Real Estate ===		=== Real Estate ===
	House pricing in the real estate market follows the model of the newsvendor problem because if a house is priced too high it will take too long to sell and if the house is priced too low it will sell quickly but at lower price. The housing market is another investment that is exposed to a great deal of volatility and increased market risk. Markets can change rapidly from economic situations to also the crime, schools and locations around a property. By understanding the market norms one can find the adequate pricing method for a home using the newsvendor problem. Appraisers and realtors must focus on understanding these metrics to ensure the estimates are accurate.<sup>6</sup>		House pricing in the real estate market follows the model of the newsvendor problem because if a house is priced too high it will take too long to sell and if the house is priced too low it will sell quickly but at lower price. The housing market is another investment that is exposed to a great deal of volatility and increased market risk. Markets can change rapidly from economic situations to also the crime, schools, and locations around a property. By understanding the market norms, one can find the adequate pricing method for a home using the newsvendor problem algorithm. Appraisers and realtors must focus on understanding these metrics to ensure the estimates are accurate.<sup>6</sup>

	== Conclusion ==		== Conclusion ==
	The newsboy formulation is used to optimize the amount of profit while minimizing the excess materials that hold no value after a given period of time. This formulation can be adapted for different probabilities and distributions of expected sales. Additionally, nuances such as accounting for a salvage price for unsold perishable goods can also be added to the problem for added complexity to mimic a given situation. From that, the salesperson can determine how many of a perishable product should be purchased for resale at a given time.		The newsboy formulation is used to optimize the amount of profit while minimizing the excess materials that hold no value after a given period of time. This formulation can be adapted for different probabilities and distributions of expected sales. Additionally, nuances such as accounting for a salvage price for unsold perishable goods can also be added to the problem for added complexity to mimic a given situation. From that, the salesperson can determine how many of a perishable product should be purchased for resale at a given time in order to optimize their profits.

	== References ==		== References ==

Mm3237: /* Numerical Example */

2020-12-13T15:28:09Z

Numerical Example

← Older revision		Revision as of 11:28, 13 December 2020
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	The '''wholesale cost price''' of the newspapers is $0.05/100 = $0.005 per newspaper		The '''wholesale cost price''' of the newspapers is $0.05/100 = $0.005 per newspaper.

	The '''selling price''' of the newspapers is $0.08 per newspaper		The '''selling price''' of the newspapers is $0.08 per newspaper.

	The '''salvage value''' of the newspapers is $0.003 per newspaper		The '''salvage value''' of the newspapers is $0.003 per newspaper.

	The '''marginal profit''' is equal to $0.08 - $0.005 = $0.075 per additional newspaper sold		The '''marginal profit''' is equal to $0.08 - $0.005 = $0.075 per additional newspaper sold.

	The '''marginal loss''' is equal to $0.005 - $0.003 = $0.002 per unsold newspaper		The '''marginal loss''' is equal to $0.005 - $0.003 = $0.002 per unsold newspaper.

	[[File:Table for newsvendor wiki.png\|thumb\|Tabulated Values]]		[[File:Table for newsvendor wiki.png\|thumb\|Tabulated Values]]

	<math>c^o = $0.005 - $0.005(0.6) = $0.002</math>per unit		<math>c^o = $0.005 - $0.005(0.6) = $0.002</math> per unit

	<math>c^u = $0.08</math>per unit		<math>c^u = $0.08</math> per unit

	x = purchase quantity, where <math>x \in (700, 800, 900, 1000, 11000)</math>		x = purchase quantity, where <math>x \in (700, 800, 900, 1000, 11000)</math>

Mm3237: /* Numerical Example */

2020-12-13T15:26:54Z

Numerical Example

← Older revision		Revision as of 11:26, 13 December 2020
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	The '''cost price''' of the newspapers is $0.05/100 = $0.005 per newspaper		The '''wholesale cost price''' of the newspapers is $0.05/100 = $0.005 per newspaper

	The '''selling price''' of the newspapers is $0.08 per newspaper		The '''selling price''' of the newspapers is $0.08 per newspaper