Evaluación de la efectividad del sistema de acciones.

The typicalintegrated newsvendorsetting is illustrated in Figure 4.1. In this case, the only decision that needs to be made is the order quantity q. The reader is at this point reminded that customer demand is assumed to follow the truncated at

zero normal distribution (withμ=140 andσ= 80), because it more closely reflects real cases, where limited information about the distribution of customer demand is available (Gallego and Moon, 1993; Son and Sheu, 2008; Ho et al, 2009). Because of this truncation at zero, demand mean and variance need to be modified according to Barr and Sherrill (1999)’s recommendations toμ’≈147 and

σ’ ≈ 65. It is also assumed that: p=250m.u.(i.e. monetary units); c=50m.u.;g=1 m.u.

If this integrated newsvendor is exclusively interested in maximising the

overall profit ∏_c, then he/she would order as much as ݍ_݅݊ݐ∗ , as given by equation

(2.2), and would consequently generate thefirst-best case maximumprofit of the entire channel ∏_int∗ that is given by relation (2.1). Relations (2.1) and (2.2) are provided inSub-section 2.1.1.InSub-section 2.1.1can also be found the notation that is used here.

Nevertheless, in the case that there are two distinct decision makers in the Newsvendor Problem setting that interact via the wholesale price contract, the setting differs in the way that Figure 4.2 demonstrates. In greater detail, each decision maker needs to make exactly one decision: the manufacturer needs to determine the price w that is charged to the retailer in each time periodt, while

In te gr at ed N ew sv en do r Market (stochastic demandx) min{q,x} q

q

c

q x Material Funds Information Supply  qx pmin ,

Figure 4.2:Thede-centralised operation newsvendorproblem M an uf ac tu re r Re ta ile r _Market (stochastic demand D) min{q,x} q

q

w

pmin

 

q,x w q x Material Funds Information

the retailer needs to specify the chosen order quantity q. If the manufacturer is exclusively interested in maximising his/her individual profit, he/she chargesw*, as given by equation (2.8) (s. Sub-section 2.1.1), whereݍ_௠∗ represents the order quantity that the rationally optimizing retailer would place in response to this price w*, or else ݍ_௠∗ = argൣmax∏_୫(ݓ∗, q)൧=ܨିଵ(௣ା௚ି௪∗

௣ା௚ ). The result is that

the manufacturer would expect to produce a profit of ∏_௠∗ , that is given by equation (2.7). If the retailer is in turn exclusively interested in maximising his/her individual profit, he/she orders exactly ݍ_௥∗ units as calculated by relation (2.4) and subsequently expects to attain a profit of ߎ_௥, according to equation (2.3). When these decisions are combined, they generate an aggregate channel

profit of ∏_{ୡ= ∏௠}∗ _{+ ∏} ௥

∗_{, that is significantly lower than the aggregatefirst-best}

case maximum profit of ∏_௜௡௧∗ (Lariviere and Porteus, 2001; Cachon, 2003). Relations (2.3), (2.4), (2.7) and (2.8) are provided inSub-section 2.1.1.

The results is that theefficiency scorethat is attained by this interaction of w* with ݍ_௥∗ (which in this case happens to coincide with ݍ_ݏ∗) is ܧ݂݂= ∏ౙ

which signifies the wholesale price contract’s inefficiency. The reason is that neither the manufacturer, who is the first to make any decisions and, therefore the Stackelberg leader (Stackelberg, 1934 in: Cachon and Netessine, 2004), nor the retailer, take into account the effect of their decisions on the overall channel’s profit. This phenomenon is known as the double marginalization problem (Spengler, 1950).

Nevertheless, it has already been established that very rarely would human manufacturers and retailers make price and quantity decisions, respectively, that follow the above decision rules. Thus, whether the double marginalization problem perseveres, or else whether the efficiency score attained would remain strictly lower than one, is still open to further exploration. In a number of laboratory experiments that have been conducted with human subjects, it is confirmed that there persists a systematic divergence of both human manufacturers’ prices and human retailers’ order quantities from the corresponding prices and quantities that are predicted by the standard normative models. First, human manufacturers are found to charge prices (w) that are significantly different from the prices that would maximise their individual profits w* (Keser and Paleologo, 2004; Katok and Wu, 2009). Second, human retailers are found to systematically order quantities (q) that are significantly different from the quantities that their rationally profit maximising counterparts would order (ݍ_ݎ∗

)

, that is, in response to the prices w that are charged to them (Schweitzer and Cachon, 2000; Schultz and McClain, 2007; Benzion et al,2008; Bolton and Katok, 2008; Bostianet al, 2008; Kremeret al, 2008; Su, 2008; Lurie and Swaminathan, 2009).

In greater detail, human retailers are found to:i. under-order, namely order less than ݍ_௜௡௧∗ , if the product being exchanged is of the high profit type and ii. over-order, namely order more thanݍ_௜௡௧∗ , if the product being exchanged is of the low profit type (Schweitzer and Cachon, 2000; Benzion et al, 2008; Bolton and Katok, 2008; Bostian et al, 2008). Schweitzer and Cachon (2000) make the distinction that a product is characterized as being of the high profit type if its “critical fractile” is greater than 0.5, while a product is characterized as being of the low profit type, if its critical fractile is less than 0.5. A critical fractile is defined according to relation (4.1) that follows:

Critical Fractile under Centralised Operation

ܥݎ.ܨݎ. =݌+_݌+݃−_݃ܿ (4.1)

Given the aforementioned product specification (i.e.p=250m.u,c=50m.u., g=1 m.u.), the critical fractile becomes according to relation (4.1): ܥݎ.ܨݎ. =

௣ା௚ି௖

௣ା௚ =0.8>0.5, which signifies that the product under study here is of the high

profit type.

This too low/too high systematic pattern of human retailers’ order quantities is known as thepull-to-centre effect(Bostianet al, 2008). A number of different individual behavioural biases are used by different researchers to justify these systematically erroneous decisions of human retailers, such as for example risk-seeking,risk-aversion,reference-dependence,loss-aversion,waste-aversion, stock-out aversion, opportunity costs under-estimation, ex-post inventory error minimisation,mean anchor,demand chasing, or collectivelybounded rationality (Schweitzer and Cachon, 2000; Benzion et al, 2008; Bolton and Katok, 2008;

Bostian et al, 2008; Kremer et al, 2008; Su, 2008; Lurie and Swaminathan, 2009).

The result of the combination of the previous human decisions (i.e. wand q) is that thewholesale price contractis unable to give rise to thefirst-best case maximum profit ∏_୧୬୲∗ ; its inefficiency, thus, predominates and the double marginalization problemremains. Nevertheless, theefficiency scorethat it attains is significantly higher than theoretically predicted. For this reason, it is established that thewholesale price contract‘s overall performance is much better than theoretically expected (Keser and Paleologo, 2004; Katok and Wu, 2009). But it still remains open to further exploration whether it would be possible for the wholesale price contract to coordinate the Newsvendor Problem, namely attain anefficiency scorethat may not statistically differ from 1.

Building on the aforementioned existing results, the section that follows formulates the research hypotheses that this PhD thesis seeks to address for the Newsvendor Problemsetting.

In document Talleres de apreciación creación teatral en la escuela primaria (página 75-105)