How to Manage an Overconfident Newsvendor

How to Manage an Overconfident Newsvendor

David C. Croson

Cox School of Business, Southern Methodist University, Dallas, Texas 75275, dcroson@https://www.wendangku.net/doc/a810827854.html,

Rachel Croson

School of Management, University of Texas at Dallas, Richardson, Texas 75080, crosonr@https://www.wendangku.net/doc/a810827854.html,

Yufei Ren1

Department of Economics, University of Texas at Dallas, Richardson, Texas 75080, yufei.ren@https://www.wendangku.net/doc/a810827854.html,

December 2008

Abstract

Previous experimental work has shown that individuals make suboptimal decisions in newsvendor problems (e.g. Schweitzer and Cachon 2000). We present a theoretical (behavioral) model of

overconfident newsvendors that is consistent with these observed results. We show that

overconfident newsvendors place suboptimal orders (which can be either higher or lower than optimal quantities) and earn lower profits than well-calibrated newsvendors. We also derive incentive

contracts using salvage costs and price adjustments which a well-calibrated manager might offer to an overconfident newsvendor in order to induce optimal orders.

Key words: overconfidence, overprecision, newsvendor, inventory, behavioral operations

management

1We thank Xuanming Su, Elena Katok and participants in the 3rd Annual Behavioral Operations Conference, Edmonton, Alberta, July 23-25, 2008, for their invaluable comments. All mistakes are ours.

How to Manage an Overconfident Newsvendor

1. Introduction / Motivation

The newsvendor problem is a staple of Operations Management models, and serves as the basis of many models of inventory management (e.g., Sliver, Pyke and Peterson 1998; Porteus 2002). Although optimal solutions to the newsvendor problem have been known since Arrow, Harris and Marschak (1951), numerous case studie s document firms’ difficulties in implementing these solutions (e.g. Fisher and Raman 1996,Katok et al. 2001). Recently, experimental work has identified systematic deviations in ordering behavior from optimal solutions; in particular, individuals under-order in high-profit regimes and over-order in low-profit regimes (e.g., Schweitzer and Cachon 2000, Bolton and Katok 2008, Bostian et al. 2008, Benzion et al. 2007).

We propose a behavioral explanation for these observations, based on overconfidence. When individuals are overconfident, they believe their information or their estimate to be more precise (accurate) than it actually is (see Moore and Healy 2008 for a review). In the newsvendor setting, we model this overconfidence in precision as a biased belief that the distribution of demand has variance lower than its true variance. Previous research has appealed to overconfidence to explain and describe behavior in other settings (e.g. Camerer and Lovallo 1999, Odean 1998, Malmendier and Tate 2005, Hilary and Menzly 2006). We are the first to investigate the impact of overconfidence in a theoretical inventory management setting.

Given our analysis of overconfident newsvendors’ behavior, we then ask the question “H ow might a well-calibrated manager correct this bias?” We examine two types of corrective incentives. Our mo deling follows the style (although not exactly the letter) of Cachon’s (2003) coordinating contracts. In Cachon’s setting, a principal and agent have identical information and beliefs (and perfect rationality), but their differing incentives induce individual behavior inconsistent with joint profit maximization. Coordinating contracts have the potential to (at least partially) resolve these conflicting incentives, typically yielding second-best outcomes. Our setting is different, emphasizing beliefs rather than

incentives. In contrast, we assume that the manager and newsvendor have no conflicting incentives; both wish to maximize the total profits of the newsstand. They differ in their beliefs about demand, however; the manager is well-calibrated and knows the true distribution of demand, whereas the newsvendor is overconfident about the precision of his estimate of the demand distribution. We then derive incentives which the manager can offer the newsvendor in order to induce him to order the optimal inventory quantities, given the newsvendor’s biased beliefs.

We thus make two main contributions. First, we present a model of an overconfident newsvendor, and show how his orders deviate from optimal orders; the predictions of this model correspond to established experimental observation. We derive the costs of this overconfidence on profitability. Second, we derive incentives which unbiased managers can offer to overconfident newsvendors to induce optimal ordering behavior. We thus identify a technique for solving the problem of managing an overconfident agent.

The paper is organized as follows. Section 2 reviews the relevant literature. Section 3 describes our environment and defines the overconfident newsvendor. Section 4 derives the decisions made by the overconfident newsvendor and demonstrates how they differ from the classical normative solution to the newsvendor problem. Section 5 derives optimal contractual structures for an unbiased manager to offer to an overconfident newsvendor in order to induce optimal ordering. Section 6 concludes.

2. Previous literature

2.1 Overconfidence

While the theoretical operations-management literature generally addresses the actions of a fully rational agent, actual ordering decisions in practice are made by individuals. A substantial body of research from psychology (the field of Judgment and Decision Making) shows that most individuals use heuristics and suffer from a variety of biases in their decision-making. In this paper we examine the impact of one particular bias, overconfidence.

Moore and Healy (2008) present an excellent literature review of over 350 papers demonstrating overconfidence in a variety of settings over a wide range of the population. They distinguish three types of overconfidence demonstrated in the literature, each with its own implications: overestimation, overplacement, and overprecision. In the bias of overestimation, people overestimate their own abilities; they believe these abilities are greater than they indeed are. For example, students robustly overestimate their exam performance (Clayson 2005), and people overestimate the speed with which they can complete a task (Buehler, Griffin and Ross 1994). In the bias of overplacement, people believe they are better than others. For example, in Zenger (1992), 37% of professional engineers in a firm rated themselves among the top 5% of performers at the firm. Although overplacement and overestimation can (and often do) appear together, they are not necessarily causally related. As an example, individuals can simultaneously overestimate their own abilities, while believing that others are even more capable than their true abilities, and thus suffer from overestimation and underplacement simultaneously.

The third bias, which we will invoke in our model, is overprecision. In this bias, individuals believe that their estimates are more accurate than they actually are; they are overconfident about their precision. In a classic test of overprecision, participants are asked to provide estimates of varying types of information and confidence intervals around the estimates. Confidence intervals are on average unbiased (centered around an accurate mean) but too narrow; previous studies have shown that fewer than half of responses include the true answers in the offered 90% confidence intervals (e.g., Alpert and Raiffa 1982, Soll and Klayman 2004). In our model we will capture overprecision as a biased belief that a distribution (of demand) has the same mean but a lower variance than it truly has.

Previous research has appealed to overconfidence in its various forms to explain and describe a variety of behavior. Hilary and Menzly (2006) argue that analysts can become overconfident after a short series of accurate predictions, and that this causes lower accuracy in the future. Camerer and Lovallo (1999) argue that overoptimism about one’s level of ability (overestimation) can explain supraoptimal rates of market entry and entrepreneurship. Odean (1998) shows that investors who overestimate the precision of their information signals (overprecision) will trade more than is optimal and have lower

expected utilities as a result. Malmendier and Tate (2005) show that CEOs who suffer from overplacement are more likely to engage in (unprofitable) acquisitions. As far as we know, we are the first to investigate the impact of overconfidence (or overprecision) in an inventory management setting.

2.2 Newsvendor Problems

The newsvendor problem has a rich history which can be traced back to Edgeworth (1888), who first developed it as a model to study the cash holdings of banks. In the newsvendor model, an agent decides how much of a given item (for example, newspapers) to stock each day. There is a single purchasing opportunity before the start of the selling period; for example, the newsvendor has to decide how many papers he wants to purchase the night before he will sell them. The constant marginal cost of acquiring each newspaper (c) and price at which he can sell them (p) are fixed, with price higher than cost. Actual realized demand for the item is assumed to be random, drawn from a known and stationary distribution.

If the newsvendor under-stocks, he runs out of inventory and loses the expected profits from selling newspapers (p-c). If the newsvendor over-stocks, he has newspapers left over at the end of the day and can recover only their salvage value (s), assumed to be less than the marginal cost of acquiring them. He thus loses the difference (c-s) on each unit unsold.

Arrow, Harris, and Marschak (1951) calculated the famous critical fractile solution for the newsvendor problem. This optimal solution is characterized by balancing the expected cost of understocking and overstocking, and will be described in more detail below. This simple problem with its intuitively appealing optimal solution has formed the foundation for an enormous literature on stochastic inventory theory more generally. Reviews of recent theoretical work on the newsvendor model can be found in Sliver, Pyke, and Peterson (1998) and Porteus (2002).

A few previous papers have examined the impact of demand variance on the optimal newsvendor solution. For example, Naddor (1978) demonstrates that optimal orders depend only on the mean and variance of the demand distribution, and not on its specific shape. Gerchak and Mossman (1992) demonstrate that expected profits decrease when the variance of the demand distribution increases,

holding the mean constant (see also Song, 1994). Virtually all of the previous work on the newsvendor problem, however, assumes that the newsvendor fully understands the distribution from which market demand is drawn. In contrast, in our model below, the newsvendor will be mistaken about the demand distribution in a way consistent with the overprecision bias.

2.3 Empirical and Experimental Evidence

Although the optimal newsvendor solution is well-known (and, indeed, taught in virtually every MBA core operations-management course), evidence suggests that inventory managers often deviate from its recommendations. For example, Fisher and Raman (1996) model the inventory management decisions of a Skiwear firm, Sport Obermeyer. They conclude, from a sample of 339 inventory decisions, that Sport Obermeyer’s managers consistently ordered too little; had its managers ordered inventory in a way consistent with the newsvendor solution, the firm’s profits would have increased by 60%. In contrast, in another study by Katok et al. (2001), managers at Jeppesen Sanderson (a company that sells maps) systematically ordered too much. The authors derived a periodic-review inventory system which, when implemented, recommended significantly smaller orders and resulted in $800,000 of cost reduction for the firm.2

Laboratory studies run under controlled conditions help to reconcile these competing findings from the field. In the classic paper by Schweitzer and Cachon (2000), MBA students who have just learned the optimal solution for the newsvendor problem made suboptimal choices. In experimental conditions where the optimal order was higher than the mean demand (the high-profit condition), participants ordered too little (as at Sport Obermeyer). In experimental conditions where the optimal order was lower than the mean demand (the low-profit condition), participants ordered too much (as at Jeppensen Sanderson). Figure 1 from their paper shows the optimal and average orders in the two conditions.

2In a slightly different context, Olivares et al. (2008) use a newsvendor framework to explain operating-room reservations at hospitals. They similarly find suboptimal overordering behavior by doctors.

Figure 1. Results from Schweitzer and Cachon (2000) (Figure 1 from their paper)

Schweitzer and Cachon (2000) examined and rejected a number of competing explanations for

this pattern of results, including risk preferences (risk aversion or risk-seeking), Prospect Theory-based preferences (loss aversion, reflection effects, and probability weighting), waste aversion, stockout aversion, and underestimation of opportunity costs. In the end, they describe two independent and

possible biases which could explain their results: anchoring (and insufficient adjustment) and the desire to minimize ex-post inventory error (rather than ex-ante inventory error). In this paper we show analytically that a different bias -- overconfidence (in particular, overprecision) -- is consistent with their results, and thus emerges as a parsimonious unified explanation for their findings.

Four recent papers replicate the Schweitzer and Cachon (2000) result. Bolton and Katok (2008), Benzion et al. (2007) , Bostian et al. (2008) and Moritz et al. (2008) examine behavior and learning

dynamics in the newsvendor setting. All these papers find that while behavior improves over time, biased orders are still observed. Table 1 contains more detail on results from these previous experimental studies.

While Schweitzer and Cachon (2000) eliminated theories inconsistent with the observed data, only one previous paper offers a formal model of a behavioral explanation consistent these observations. Su (2008) provides a logit overlay on optimal decision-making in inventory settings. In particular, he assumes that individuals make decisions with noise; they choose the optimal order with a higher probability than suboptimal orders, but not with certainty. He demonstrates that, assuming a uniform or triangular demand distribution, this trembling-hand model of decision making generates predictions consistent with those observed in these experiments.3

Our study makes several contributions to the current literature. We are the first to propose and demonstrate that overconfidence (in fact, overprecision) is a consistent explanation for suboptimal ordering in the newsvendor problem, both in the high- and low-profit settings. Furthermore, we demonstrate the ability of overconfidence to explain these results under a general demand function. We calculate the extent of bias in the orders, and show how the order s’ deviation from optimal levels change as the level of overconfidence increases. We also calculate the cost of these deviations to the biased newsvendor. In section 5 we go one step further, asking how an unbiased manager might construct incentives to manage such an overconfident newsvendor, seeking to align their ordering decisions with those recommended by the critical fractile solution. Thus, in addition to identifying, analyzing, and assessing the impact of the problem, we also propose a possible solution.

3. Our Environment and Overconfidence

3A few contemporaneous papers take a different approach, experimentally examining the relationship between individual personality characteristics and their performance in the newsvendor problem. Moritz et al. (2008) showed that individuals who performed better on a test of cognition performed better in the newsvendor problem. Bolton et al. (2008) compared the performance of first-year undergraduates, graduate students and experienced managers, and found that all three groups behaved similarly (and suboptimally).

We follow the classical treatment of the newsvendor problem and use the following variables and assumptions about their levels, consistent with Cachon (2003):

p = unit sales price (p>0)

c = unit cost (0

s = unit salvage value (0

Q = inventory to be ordered (Q≥0)

D = quantity demanded (D≥0), a realization of a continuous random variable D

μ = mean of D

2σ = variance of D

D F = cumulative distribution function of D

()D m F μ=, the probability that actual demand is less than expected demand.

I n the newsvendor model, each morning the agent decides how many newspapers to purchase

(Q) for marginal (and constant) cost (c) per unit. He sells the newspapers over the course of the day for a constant price (p) each, where p>c. The number of papers demanded is drawn from the demand

distribution D , which is assumed to be stationary. The demand distribution D has mean μ and variance 2σ, and is described by its cumulative distribution function (D F ). When Q>D, excess newspapers are salvaged by the newsvendor with recovery s per unit, where s

β≡Pr D ≤Q =p?c p?s (1)

Since F D is continuous and strictly increasing, we can find a unique optimal solution:

*1()D Q F β-=, where F D -1 denotes the inverse CDF. We will use this benchmark of optimal orders to compare against the orders placed by an overconfident newsvendor.

For our overconfident newsvendor, his estimate of the mean consumer demand is accurate, but

his estimate of the variance of consumer demand is biased. In particular, the true market demand distribution is more variable than the market demand distribution which the newsvendor believes he faces. We adopt the general notion of “more variable ” from Ross (1983): i f 1X and 2X are nonnegative random variables and 12()()E X E X =, then 1X is said to be more variable than 2X (written X 1≥v X 2) if and only if 12[()[()]E h X E h X ≥for all convex functions h .

For practical purposes , we assume that the demand in the overconfident newsvendor’s mind o D is a mean-preserving but variance-reducing transformation of the true consumer demand D , mixing the true distribution with a zero-variance distribution around μ.4

(1),01o D D γγμγ=+-≤≤ (2)

Here γ represents the extent to which the newsvendor is well-calibrated: γ =1 corresponds to a

perfectly-calibrated newsvendor who predicts demand based on its actual distribution D , whereas γ =0 corresponds to an infinitely overconfident newsvendor who believes that Pr D =μ =1. As γ increases, overconfidence thus decreases. We will refer below to the level of overconfidence as (1- γ). Since D o is

an affine transformation of D , E [D o ]=μ and Var D o =γ2σ2, denoted 2o σfor convenience.

P ROPOSITION 3.1 (Basic Properties of D o ): D ≥v D o .

Proof : For any convex function h ,

[()][((1))][()(1)()]

[()(1)()][()](1)()[()](1)[()[()]]o E h D E h D E h D h E h D h E h D h E h D h E h D γγμγγμγγμγγμγμ=+-≤+-+-=+-=+--

The right-hand side is less than or equal to [()]E h D since Jensen’s inequality guarantees that

[()[()]]h E h D μ- is never positive. 4We use this particular formulation for two reasons. First, it accurately captures the well-documented psychological phenomenon of overprecision, dating back to Raiffa and Alpert (1982): on average individual estimates are unbiased, but confidence intervals are too small. Second, we want to isolate the impact of this particular mistake

(underestimating the variance) on ordering behavior from other possible biases. A more general formulation of newsvendor mistakes, a topic for future research, might include a misestimation of both the mean and variance of the demand distribution.

4. Overconfident Newsvendor Decisions

In this section, we study the effects of newsvendor overconfidence on the ordering decision. The results are intuitive: Because the overconfident newsvendor underestimates the variance of demand, he places orders closer to the mean of demand than the optimal order would suggest -- exactly the

empirically-observed result of Schweitzer and Cachon (2000) and subsequent papers. We show that this order bias has a linear relationship with the level of overconfidence (1-γ).

4.1 Biased Orders of Overconfident Newsvendors

We begin by deriving *o Q , the order placed by the overconfident newsvendor, and comparing it

with the optimal order *Q .

P ROPOSITION 4.1.

(a)When m β>, ()*1*.o S Q F Q μγσβ-=+<

(b)When m β<, ()*1*.o S Q F Q μγσβ-=+> (c)When m β=, **.o

Q Q μ== Proof. Appendix A provides a complete proof. The proof’s basic steps are as follows: Define X as a random variable satisfying D X σμ=+. X is thus a standardized distribution with mean 0 and variance 1. Substitute D X σμ=+ into (2) above, yielding o o D X σμ=+ Now define ()S F x as the CDF

of X and define ()S F b β=and thus 1()S F b β-=. Then *1()D

Q F b βμσ-==+and *1().o o o Q F b βμσ-==+ Since we know o σσ<, the relative order sizes depend only on the sign of b . When β>m then b >0,

and thus **o

Q Q <. When β*Q . When β=m , then b=0 and **.o Q Q μ== We note that when m β>, we are in the high-profit condition as defined by Schweitzer and

Cachon (2000) and used in subsequent experiments (op. cit.). In exactly these cases, the optimal order is higher than mean demand and overconfident newsvendors order less than is optimal – moving their order towards the demand mean. In contrast, when m β

their order towards the demand mean. Our model of overconfidence is thus consistent with the observed data in the experimental literature.

How much are these orders biased? Since 222o σγσ=, we know that **(1),o

Q Q b γσ-=- a linear relationship between the deviation from the optimal order **o

Q Q - and the level of overconfidence (1- γ). As 1-γ approaches 0, the newsvendor’s level of overconfidence (bias) goes down, and the deviation from the optimal order decreases linearly in both the high- and low-profit cases.

The effect of overconfidence also has a positive relationship with the (true) variance of demand since **()(1)o Q Q b γσ

?-=-?. When facing a market demand with higher variation, the overconfident newsvendor makes a more biased order, given the same level of overconfidence – in effect making a larger mistake.

The market ’s inherent profitability also affects the amount of deviation from optimal behavior

caused by overconfidence. More profitable markets lead to more overstocking relative to expected

demand; less profitable markets lead to more understocking relative to expected demand. As the distance b between the optimal solution Q * and the mean market demand μ increases, holding the level of overconfidence (1-γ) constant, the overconfident newsvendor’s orders move fart her away from the optimal order levels, as **()(1)0o Q Q b

γσ?-=->?. We thus expect overconfident newsvendors to make particularly large errors in both highly profitable markets (such as Sport Obermeyer) and very low-profit markets (such as Jeppson-Sanderson).

4.2 The Costs of Overconfidence

The previous section demonstrates that overconfident newsvendors order suboptimal amounts.

We have thus far focused on the newsvendor’s “mistake” in terms of quantity over - or under-ordered. How much does this mistake cost the newsvendor in terms of forgone profitability?

We can rewrite the general form for the profit of the newsvendor as:

(,)()()()()()()(,)D Q p c p c E D Q c s E Q D p c G D Q πμμ++=-------=-- (3)

where ()X + denotes max{X, 0}.

Since ()p c μ-(expected revenue from sales) is fixed, to maximize expected profit the

newsvendor simply minimizes the cost term [G(D,Q)] in (3), which (following the classic formulation of Arrow et al., 1951) includes both economic costs of overstocking and opportunity costs of understocking.

For the optimal order quantity, we can rewrite G(D,*Q )as:

*(,)()()G D Q p s E X X b σ=-≥ (4)

The overconfident newsvendor, however, will face different costs by ordering *o Q :

*(,)()()(1())()()o s G D Q c s b p s F b b p s E X X b γσγσγσγ=----+-≥ (5)

Taking the difference of the two cost functions yields

**(,)(,)(){[(1())(1())]()}b

o s s s b

G D Q G D Q p s b F b F b x f x dx γσγγ-=----+? (6) P ROPOSITION 4.2 . If *Q b μσ=+ and *o o Q b μσ=+, then **(,)(,)o

D Q D Q ππ<. Proof: Appendix B contains a complete proof that whenever m β≠:

****(,)(,)(,)(,)o o G D Q G D Q D Q D Q ππ>?<

When β=m, then ****(,)(,)(,)(,)o

o G D Q G D Q D Q D Q ππ=?=. We have thus shown that the profits of an overconfident newsvendor never exceed the profits of a well-calibrated one, and are strictly less when .m β≠ We can now turn our attention to quantifying the magnitude of these forgone profits.

P ROPOSITION 4.3. The relationship between the level of overconfidence and expected lost profit is positive and convex.

Proof. The lost profit due to overconfidence can be written as:

****(,)(,)(,)(,)o

o D Q D Q G D Q G D Q ππ-=- Taking the first and second derivatives with respect to γ yield: **((,)(,))()[()()]0(1)

o s s D Q D Q p s b F b F b ππσγγ?-=--->?- 7

2**22((,)(,))()()0(1)

o s D Q D Q p s b f b ππσγγ?-=-≥?- 8 Appendix B shows that [()()]s s b F b F b γ-is always negative, while (p-s) and σ are positive by

assumption. Thus (7), representing the first derivative of the difference in profits, is negative,

demonstrating that as (1-γ) approaches 1 (i.e., as overconfidence grows), the magnitude of lost profit increases.

The positive second derivative in (8) tells us that the loss function is not only increasing but

convex. Again, (p-s) is assumed to be positive. 2b , σ and ()s f b γare nonnegative by definition. This implies that the downward response of profits to increases in levels of overconfidence is convex: as the bias gets larger, profits fall faster. We illustrate these relationships in Figure 2, using a Gaussian demand distribution with mean 10 and variance 1 as an example. We set p=1 and s=0.4, and plot the relationship

between the level of overconfidence (1-γ) and the lost profits due to overconfidence **(,)(,)o

D Q D Q ππ-. Figure 2 shows curves for two different levels of c={0.5, 0.6} which generate two different values of β={5/6, 4/6}. Note that, since the normal distribution is symmetric about its mean, these specific cost levels will also determine the value of lost profits for the (different) costs c={0.9, 0.8} generating β ={1/6, 2/6} respectively even though the baseline profits of these four values of β are all distinct. The numerical values of these expected profits for β ={1/6, 2/6, 4/6, 5/6} are {0.85, 2.76, 3.78 , 4.85}

respectively. As shown above, these costs of overconfidence clearly increase and are convex in (1-γ) . 0

0.02

0.04

0.060.080.1

00.10.20.30.40.50.60.70.80.91β=5/6 , c=0.5 or β=1/6 , c=0.9 β=4/6, c=0.6 or β=2/6 , c=0.8

Overconfidence level: 1-γL o s t P r o f i t s

Figure 2: Profits Lost from Overconfidence when p=1, s=0.4, c ={0.5 or 0.9, 0.6 or 0.8}

5. How to Manage an Overconfident Newsvendor

We have shown that overconfident newsvendors make suboptimal inventory decisions and that

these decisions are costly. Now imagine that a well-calibrated manager of newsstands is attempting to manage an overconfident newsvendor. How might she do so?

One possibility, of course, is a hierarchical command-and-control solution; with complete

authority over the newsvendor’s actions, the manager could simply force the newsvendor to order Q*. Given that the newsvendor (and not the manager) must choose the quantity ordered, however, and that the newsvendor has both motive and method to substitute her own judgment for the manager’s, our analysis instead explores incentives or simple contractual arrangements which the manager might use to induce the newsvendor to order the optimal amount.

We are thus invoking the spirit (if not hewing to the letter) of Cachon’s (2003) method of creating coordinating contracts. In contrast, we assume there are no incentive problems between the manager and the newsvendor; both want to maximize the profits of the newsstand to the best of their abilities. We instead assume that the manager and the newsvendor have different levels of understanding of the demand distribution; the manager knows the true demand distribution, whereas the newsvendor is mistaken about it. Our challenge is thus to design an incentive structure to induce the newsvendor to order the optimal amount given his biased beliefs.5

The most straightforward way to correct the biased behavior is by changing the cost structure

facing the newsvendor, thereby inducing him to choose his order to be the same as the optimal order. The

design of this cost structure entails finding o β to solve the problem:**(,)(,)o

o o Q D Q D ββ=. Under this 5One might object that this is simply a communication problem: that the unbiased manager could simply “tell ” the overconfident newsvendor the true variance of demand. However, the overconfident newsvendor has no reason to believe that the manager’s est imate is better than his own; indeed, we can safely assume that this communication has already occurred and has already been factored into the newsvendors’ overconfident beliefs and thus into the γ-weighting from (2).

o β regime, the newsvendor who orders the optimal amount given his own beliefs will, in fact, order the correct amount given the true demand distribution.

P ROPOSITION 5.1. Define o αββ=-and *αas the value of α which induces the agent to choose

**.o Q Q = Then

111()

*()()()b

s s F s s F b

f x dx f x dx γγββα--==?? (9) Proof: if we want the agent to choose **o Q Q =, we need to set 1()s o b F βγ-=, since

**11111()()()()()o s o s s o s s o b Q Q F F F F F μγσβμσβγβββγ-----=?+=+?=?= Since *()b s b f x dx γα=?, we can find 11()

1()()()()b

s o s F s o s s o F b b f x dx f x dx F γβββββγ---=-=?=??.

From the definition of *αas the quantity adjustment required to achieve the optimal order, we can derive the following relationships from Proposition 4.:1:

If m β>, then *0α>. If m β<, then *0α<, and if m β=, *0α=.

When the optimal order is larger than the mean of the demand distribution, the manager wants the overconfident newsvendor to order more than he normally would. She thus needs to add *α to the o β he would otherwise face. The reverse holds when the optimal order is less than the mean of the demand distribution.

The manager has numerous tools available to alter the o βthat goes into the newsvendors’

decision. Here we discuss two common and easily-implemented tools frequently investigated in the operations management literature: (a) altering the salvage cost facing the newsvendor using a buyback contract (as examined in Song et al., 2008) or (b) altering the basic unit cost schedule facing the

newsvendor (as in Lariviere and Porteus, 2001).

5.1 Using Buyback Contracts

By using a buyback contract, the manager could augment the true salvage value s with a bonus

(or penalty) s I for each unit left at the end of the period. Thus the effective salvage value facing the newsvendor, which we call the return value, would be (s+s I ). Intuitively, if the overconfident

newsvendor would order less than optimal, the manager should choose a positive s I (making the return value higher than the true salvage value – a classic buyback contract), whereas if he would order more than optimal, the manager should choose a negative s I (making the return value lower than the true salvage value, e.g. demanding a fee to return, presumably coupled with monitoring to ensure that the

inventory is not surreptitiously sold to avoid the penalty). Recall that the optimal order quantity given the true salvage value is *11()()d d p c Q F F p s

β---==-. P ROPOSITION 5.2 The unique s I which induces **

o Q Q =is 2**

*()(())s

p s I p c p s αα-=-+-. Proof. When facing a return value of (s+I s ), the newsvendor will order

*11()()o o o o s

p c Q F F p s I β---==--. (10) We can rewrite *s o s s I p c p c p c p s I p s p s p s I ββα---=

=+=+------, Therefore,

***2*2***()()()(())()()(())

s s s s s

s I p c p c I p s p s I p c p s I p s p s I p s p s I p c p s αααααα-=?-=---?-+-----=-?=-+-.

We can see that the denominator is strictly positive for any value of α:

()000o p c p c p s p s ααβαβαβ--+->?>-?>-?+>?>-. Since p>c and 2()p s -is always positive, *s I has the same sign as *α.

P ROPOSITION 5.3. In the high-profit condition, *s I >0; in the low-profit condition *s I <0.When

β=m, *s I =0.

In the high-profit regime (β>m), the manager should offer to supplement the existing salvage

value by *s I to encourage the overconfident newsvendor to order more. This implies that the manager will

(probabilistically) buy back unsold goods at the end of the period at a price above the true salvage value. On the other hand, in the low-profit regime (β

buy back unsold goods below their true salvage value.

Note, however, that given an overconfidence level γ, the extra salvage value and the extra

salvage penalty are not simply negatives of each other, which would require a linear relationship between

*

s I and *

.αIn particular *2**2()()(())s I p s p c p c p s αα?--=?-+- which is not constant given that p ≠s . *s I thus does not have a linear relationship with *αand the optimal adjustments to salvage value are asymmetric.

5.2 Using Price Contracts

Instead of altering the effective salvage value facing the overconfident newsvendor, the well-

calibrated manager can subsidize (or increase) his unit cost by adding an additional cost or subsidy c I for each unit ordered. The marginal cost facing the newsvendor, which we call the apparent cost, would thus be (c+ I c ). In the high-profit regime, the overconfident newsvendor would order less than is optimal and thus the manager should choose a negative I c (making the apparent cost lower than the true marginal cost to induce larger orders). Conversely, in the low-profit regime, the overconfident newsvendor would order more than optimal and the manager should thus choose a positive I c (making the apparent cost higher than the true marginal cost). We can solve for the unique c I for a given level of overconfidence and market structure.

P ROPOSITION 5.4. The unique c I which cause **o Q Q = is **().c I p s α=--

Proof. Recall that the overconfident newsvendor’s optimal order is *1()o o o Q F β-= and that

*11()()d d p c Q F F p s

β---==- is the optimal order from the manager’s perspective . Under the additional cost (subsidy) condition, ()c c c o p c I I I p c p c p s p s p s p s p s β----=

=-=+------. Therefore, *

**()()()()b b c s c s c b b I f x dx I p s f x dx I p s p s γγαα=-=?=--?=---??. Unlike the analogous salvage value, we can see that *c I has a simple negative linear relationship

with *α. We can therefore conclude:

P ROPOSITION 5.5. In the high-profit condition,*c I <0; in the low-profit condition, *c I >0.When

β=m, *c I =0.

Thus the optimal cost adjustment for high-profit market is a subsidy (encouraging the

newsvendor to order more), while the optimal cost adjustment for low-profit markets is a surcharge (encouraging the newsvendor to order less).

5.3 Relationship between Overconfidence Level and Size of Incentive

Here we describe the relationship between the newsvendor’s level of overconfidence and the size of the incentive that the unbiased manager must offer.

P ROPOSITION 5.6. The size of the incentive is positively related to the extent of the bias.

Proof. Taking the derivative of a * (the required adjustment) with respect to the level of overconfidence yields

*2()()(1)(1)b

s b s f x dx b b f γαγγγγ??==?-?-? (11) Therefore, *(1)

αγ??-has the same sign as b . I f β>m, then *0(1)αγ?>?-. If β

0(1)αγ?

0(1)

αγ?=?-.

When the manager uses an augmented salvage value to align the newsvendor’s actions, the

derivate of s I with respect to (1-γ) yields:

*2*

*2()()(1)(1)(())(1)

s s dI I p s p c d p c p s ααγαγαγ??--?==-??--+-?- The numerator being unambiguously nonnegative, (1)

s dI d γ-will have the same sign as *.(1)αγ??-If β>m, then s I >0, *

0(1)

αγ?>?- and thus 0(1)s dI d γ>-. Similarly, when β

We can derive a similar result for adjusting marginal cost. Taking the first derivative of c I with respect to (1-γ) yields

**

*()(1)(1)(1)

c c dI I p s

d ααγαγγ???==---??-?- Sinc

e p>s, (p-s) is always positive and thus (1)

c dI

d γ- has th

e opposite sign from *(1)αγ??- and thus o

f b , given that price reductions increase quantity ordered (and vice versa for price increases). Usin

g similar reasoning, we thus find that the absolute size of the incentive (positive or negative) that the manager needs use to adjust the marginal cost is positively related to the level of overconfidence.

Figure 3a and 3b illustrate the relationship between the required subsidies (or bonuses) and the

newsvendor’s level of overconfidence using the same normal distribution and parameters as in Figure 2. In Figure 3a we show the optimal price adjustment *c I as a function of overconfidence level (1- γ). We

again depict *c I for different levels of c (ranging from 0.5 to 0.9), yielding β ranging from 1/6 to 5/6.

When β>12 (the high-profit condition) *c I is negative and decreases even further as overconfidence

勤奋就是成功之母

勤奋就是成功之母 1、人类要在竞争中生存，便要奋斗。——孙中山 2、聪明的资质、内在的干劲、勤奋的工作态度和坚韧不拔的精神。这些都是科学研究成功所需的其它条件。——贝弗里奇 3、时间是个常数，但也是个变数。勤奋的人无穷多，懒惰的人无穷少。——字严 4、聪明出于勤奋，天才在于积累。——华罗庚 5、天才是不足恃的，聪明是不可靠的，要想顺手拣来的伟大科学发明是不可想象的。——华罗庚 6、对搞科学的人来说，勤奋就是成功之母!——茅以升 7、勤奋就是成功之母。——茅以升 8、努力学习，勤奋工作，让青春更加光彩。——王光美 9、不闻不若闻之，闻之不若见之，见之不若知之，知之不若行之，学至于行而止矣。——荀况 10、世上无难事，只要肯攀登。——毛泽东 11、形成天才的决定因素应该是勤奋。…有几分勤学苦练是成正比例的。——郭沫若 12、什么是天才!我想，天才就是勤奋的结果。——郭沫若

13、天才这个字本来含意极其暖昧，它的定义，决不是所谓“生而知之，不学而能” 的。天地间生而知之的人没有。不学而能的人也没有。天才多半由于努力养成。天才多半由于细心养成。——郭沫若 14、哪里有天才，我是把别人喝咖啡的功夫，都用在工作上的。——鲁迅 15、在学习上做一眼勤、手勤、脑勤，就可以成为有学问的人。——吴晗 16、在天才和勤奋两者之间，我毫不迟疑地选择勤奋，她是几乎世界上一切成就的催产婆。——爱因斯坦 17、精神的浩瀚、想象的活跃、心灵的勤奋：就是天才。——狄德罗 18、“天才就是勤奋”，曾经有人这样说过。如果这话不完全正确，那至少在很大程度上是正确的。——李卜克内西 19、所谓天才人物指的就是具有毅力的人、勤奋的人、入迷的人和忘我的人。——萧伯纳 20、业精于勤，荒于嬉;行成于思，毁于随。——韩愈 21、天才就是无止境刻苦勤奋的能力。——卡莱尔 22、发明是百分之一的聪明加百分之九十九的勤奋。——爱迪生

设计概论思考题

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化工原理》实验思考题题目及答案

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个进水阀，检查导压管内是否有气泡存在。若倒置U型管内液柱高度差不为零，则表明导压管内存在气泡，需要进行赶气泡操作。 开大流量，使倒置U型管内液体充分流动，以赶出管路内的气泡；若认为气泡已赶净，将流量阀关闭；慢慢旋开倒置U型管上部的放空阀，打开底部左右两端的放水阀，使液柱降至零点上下时马上关闭，管内形成气-水柱，此时管内液柱高度差应为零。然后关闭上部两个放空阀。 4、测压孔的大小和位置、测压导管的粗细和长短对实验有无影响为什么 有，有影响。跟据公式 hf=Wf/g=λlu平方/2d也就是范宁公式，是沿程损失的计算公式。因此，根据公式，测压孔的长度，还有直径，都是影响测压的因素。再根据伯努利方程 测压孔的位置，大小都会对实验有影响。 5、在测量前为什么要将设备中的空气排净怎样能迅速地排净 因为如果设备含有气泡的话，就会影响U型管的读数，读数不准确，便会影响实验结果的准确性。要迅速排净气体，首先要开大流量，使倒置U型管内液体充分流动，以赶出管路内的气泡；若认为气泡已赶净，将流量阀关闭。 6、在不同设备（包括相对粗糙度相同而管径不同）、不同温度下测定的λ-Re数据能否关联在同一条曲线上 答，不能，因为，跟住四个特征数，分别是长径比l/d,雷诺数Re，相对粗糙度 E/d，还有欧拉数Eu=wf/u的平方。即使相对粗糙度相同的管，管径和温度不同都会影响雷诺数及摩

成功是成功之母的例子

成功是成功之母的例子 人们常说，成功孕育于失败之中。此话当然不假。然而，是否曾想到过成功也是成功之母呢?以下是为大家整理的关于成功是成功之母的例子，欢迎阅读! 成功是成功之母的例子1： “成功是成功之母，失败是失败之母”可信吗? 2007年11月《南方人物周刊》记者采访中国80后作家韩寒：“你怎么看待成功?” 韩寒：“成功这个东西，很难说，我今天心情好，我会觉得我成功了，如果心情不好，我就觉得不算成功。” 记者：“比如说一个男人到了30岁，说我没有车，没房……” 韩寒：“那肯定不够成功。……成功是成功之母，失败是失败之母。就像我们赛车一样，如果你在一个拐弯出了问题，以后你每次到这个拐弯的时候，你都会心虚。如果你一直成功，一直成功，你就会一直特别有信心。很多事情都是这样的。” 韩寒面对记者的提问，从个人感觉和心情好坏出发，仿照“失败是成功之母”成语，提出“成功是成功之母，失败是失败之母。”，认为“很多事情”成功就一直成功，失败就永远失败。这种说法可信吗? 如何看待成功与失败，正确对待两者之间关系，这是青年朋友历

来关注的一个问题，也是一个人的人生态度问题。古人早就说过：“失败者成功之母。”这是一条约定俗成的成语，是人民群众从改造世界和认识世界的长期实践中总结出来的经验。它告诫我们无论做什么事情，都要从失败中找出差距，吸取教训，就能变失败为成功。 历史上许多名人成就大事业，往往都经历过失败的挫折的。春秋末期孔子57岁周游列国，遭到无数次的冷落和打击，没有一个君主采用他的治国学说。他潜心治学，整理《诗》《书》《春秋》等西周文献，办私学培养“三千弟子，七十二贤人”，成为世界最伟大的教育家，儒家学说的创始人。西汉时期司马迁因为李陵事件遭受腐刑，他忍受难以启齿的屈辱，以顽强的毅力发愤著文，完成了史学巨著《史记》，彪炳千秋，光照万代，开创了我国纪传体通史的先河。这不都验证了“失败是成功之母”的道理吗? 我们在人生征途上遇到的不都是鲜花、阳光和彩虹，有时也有毒草、阴云和风雨，正如一首歌唱道：“不经历风雨，哪能见彩虹?”人生的历史不是直线的，而是波浪式的不能只要成功，回避失败，不能只喜欢顺境，拒绝逆境。我们要客观地看待成功与失败，不能以个人感觉和心情来评断，韩寒说“我今天心情好，我会觉得我成功了，如果心情不好，我就觉得不算成功。”这句话至少是本末倒置了，我认为心情好与不好，决定不了能否成功与失败，而恰恰相反，你的成功与失败才能带来心情的好与不好。试想，哪一个成功者不为事业上的成就而喜笑颜开、心花怒放呢? 我们顺着韩寒的感觉走，理解他的“成功是成功之母，失败是失

关于成功的三大定律

成功三大定律 关于成功，有很多定律，比较有名的就是荷花定律、竹子定律和金蝉定律。 无论是荷花定律、竹子定律，还是金蝉定律，他们都有共同的意义： 成功，需要厚积薄发， 要忍受煎熬，要耐得住寂寞， 坚持，坚持，再坚持， 直到最后成功的那一刻。 荷花定律 一个池塘里的荷花，每一天都会以前一天的2倍数量在开放。 如果到第30天，荷花就开满了整个池塘。 请问：在第几天池塘中的荷花开了一半？第15天？错！是第29天。这就是荷花定律。 第一天开放的只是一小部分，第二天，它们会以前一天的两倍速度开放。 到第29天时荷花仅仅开满了一半，直到最后一天才会开满另一半。 也就是说：最后一天的速度最快，等于前29天的总和。 这就是著名的荷花定律。

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实验二不可压缩流体恒定流能量方程（伯诺利方程）实验 成果分析及讨论 1.测压管水头线和总水头线的变化趋势有何不同？为什么？ 测压管水头线（P-P）沿程可升可降，线坡J P可正可负。而总水头线（E-E）沿程只降不升，线坡J 恒为正，即J>0。这是因为水在流动过程中，依据一定边界条件，动能和势能可相互转换。测点5至测点7，管收缩，部分势能转换成动能，测压管水头线降低，Jp>0。测点7至测点9，管渐扩，部分动能又转换成势能，测压管水头线升高，J P<0。而据能量方程E1=E2+h w1-2, h w1-2为损失能量，是不可逆的，即恒有h w1-2>0，故E2恒小于E1，（E-E）线不可能回升。(E-E) 线下降的坡度越大，即J越大，表明单位流程上的水头损失越大，如图2.3的渐扩段和阀门等处，表明有较大的局部水头损失存在。 2.流量增加，测压管水头线有何变化？为什么？ 有如下二个变化： （1）流量增加，测压管水头线（P-P）总降落趋势更显著。这是因为测压管水头 ，任一断面起始时的总水头E及管道过流断面面积A为定值时，Q增大， 就增大，则必减小。而且随流量的增加阻力损失亦增大，管道任一过水断面上的总水头E相应减 小，故的减小更加显著。 （2）测压管水头线（P-P）的起落变化更为显著。 因为对于两个不同直径的相应过水断面有 式中为两个断面之间的损失系数。管中水流为紊流时，接近于常数，又管道断面为定值，故Q增大，H亦增大，（P-P）线的起落变化就更为显著。 3.测点2、3和测点10、11的测压管读数分别说明了什么问题？ 测点2、3位于均匀流断面（图2.2），测点高差0.7cm，H P=均为37.1cm（偶有毛细影响相差0.1mm）， 表明均匀流同断面上，其动水压强按静水压强规律分布。测点10、11在弯管的急变流断面上，测压管水头差为7.3cm，表明急变流断面上离心惯性力对测压管水头影响很大。由于能量方程推导时的限制条件之一是“质量力只有重力”，而在急变流断面上其质量力，除重力外，尚有离心惯性力，故急变流断面不能选作能量方程的计算断面。在绘制总水头线时，测点10、11应舍弃。 4.试问避免喉管（测点7）处形成真空有哪几种技术措施？分析改变作用水头（如抬高或降低水箱的水位）对喉管压强的影响情况。 下述几点措施有利于避免喉管（测点7）处真空的形成： （1）减小流量，（2）增大喉管管径，（3）降低相应管线的安装高程，（4）改变水箱中的液位高度。

设计概论练习题

第一章设计概述 第一节设计含义与元素 一、填空题 1.“设计”的英文“design”一词，最早可追溯到拉丁语“desegnare”其意为。 2.古汉语“设计”是之意，并不是一个艺术概念。 3.绘画与科学据现有资料最早提出“工艺美术”这个词的是蔡元培，它在1920年的一文中写道“美术有狭义的、广义的，狭义的是专指建筑造像雕刻图画与美食工艺等。 4.广义的设计是一种人类对秩序和规律的渴望和冲动。 5. 是有意味的形式，是最能表达人类的情绪和感情的形式。 二、选择题 1.艾维斯色相环的三原色不包括（） A. 蓝 B. 绿 C. 黄 D. 红 2.工艺美术运动的创始人是（） A. 沃特·格罗皮乌斯 B. 米斯·凡·德·罗 C. 威廉·莫里斯 D. 维克多·巴巴纳克 3. 是为了展现空间的总体势或者突出空间的主题而创造的空间先后次序组合关系（） A. 动线 B. 序列 C. 主轴线 D. 动态线 4. 又称质感或质地，是物质表面所呈现出来的色彩、光泽、纹理、粗细、厚薄、透明度等多种外面特性的综合表现。 A. 触觉 B. 肌理 C. 感觉 D. 明度 5. 是界定一种颜色时所用的名字，它指的是颜色最单纯的状态，是色彩特质的基础； A. 色相 B. 肌理 C. 纯度 D. 明度 三、名词解释 1. 动线 2.主轴线 3. 序列 4.艾维斯色相环 5.孟塞尔色彩理论 四、简答题 1.简述线条在设计中的作用。 2.简述二维平面幻想空间的营造方法。

3.简述色彩性质和色彩关系。 4.简述材料的特质。 第二节设计思维与方法 一、填空题 1.创造性思维的特征有。 2.设计思维主要有三大类型。 3.设计中有时会迸发出灵感和直觉，在心理学的研究中被称为或，灵感的出现常常给人们渴求已久的智慧之光。 4.设计思维是科学思维的和艺术思维的的有机整合。 二、选择题 1. 是抽象思维和形象思维、发散思维和聚合思维、顺向思维和逆向思维、横向思维和纵向思维等多种思维方式的协调统一。（） A.创造性思维 B.理性思维 C. 感性思维 D. 逻辑思维 2.与创造性思维关系更紧密的是（） A. 抽象思维 B.形象思维 C. 感性思维 D. 逻辑思维 3. 通过中常用的归纳和演绎、分析和综合等方法，设计可以得到理性的指导，从而使创意具有独特的视角，挖掘潜在的市场需求，引起受众的共鸣。（） A. 抽象思维 B. 形象思维 C. 感性思维 D. 逻辑思维 4. 是以整体分析及系统观点来解决各种领域中具体问题的科学方法。 A. 头脑风暴法 B. 艺术论方法 C. 系统论方法 D. 功能论方法 5. 是把产品的功能问题放在设计活动的重要位置，在产品功能分析中排除一切不必要的多余的成分，从而达到降低成本的目的。 A. 头脑风暴法 B. 艺术论方法 C. 系统论方法 D. 功能论方法 三、名词解释 1.联想 2.设计创意 3.头脑风暴法 4.艺术论方法 5.系统论方法 四、简答题 1.简述设计思维中的科学思维和艺术思维，以及它们的作用方式。 2.创造性思维如何催生设计创意？