The Loss-Averse Retailer’s Ordering Policy under Yield and Demand Uncertainty - Intelligent Computing for Sustainable Energy and Environment - page 204

the stochastic production capacity and characterize the structure of the opti-
mal policy. Keren [6] studies a single-period problem with deterministic demand
and random yield. The cases of multiplicative production risk and additive pro-
duction risk are considered, respectively. Inderfurth [7] considers a single-period
production-inventory problem where random yield and demand are uniformly
distributed. They indicate that the optimal policy may be non-linear. Note that
all these studies are based on the assumption of risk neutrality.
However, there is growing evidence that managers' decisions often challenge
the risk-neutral assumption (see, e.g., [8] and [9]). Recently, incorporating loss-
averse preferences into inventory model has become an important and growing
area of research. Loss aversion is originated from prospect theory ([10]) and
means for equivalent losses and gains, people have different perceived values
and they are more averse to losses. Since it can better describe the individual
decision-making behavior under risk, the inventory model based on loss aversion
has been studied by some researchers over the past few years. Schweitzer and
Cachon [11] show that the optimal order quantity of a loss-averse newsvendor is
always less than a risk-neutral newsvendor. Wang and Webster [12] further ex-
tend Schweitzer and Cachon's model with consideration of shortage cost and find
that under certain conditions, the loss-averse newsvendor may order more than
the risk-neutral one. Wang [13] investigates a loss-averse newsvendor game and
shows that there exists a unique Nash equilibrium with respect to order quan-
tity. Geng et al. [14] study a single-period inventory problem in which demand is
exponentially distributed. They demonstrate that a state-dependent order-up-to
policy is optimal. Other papers considering the loss-averse preferences include
[15],[16]and[17],etc.
In this paper, we jointly consider these two factors and investigate a single-
period inventory problem with random yield and demand, where the retailer is
loss-averse. To the best of our knowledge, this model has not been considered in
the literature. In Section 2, we obtain the loss-averse retailer's ordering policy
and then carry out the analysis. In Section 3, we conduct numerical experiments
to illustrate our results. In Section 4, we conclude our paper.
2 Model Analysis
Consider a single-period inventory problem with random yield and demand. We
adopt the commonly used stochastically proportional yield model (see e.g., [4]
and [7]). That is, the fraction of good units is a random variable and independent
of the batch size. At the beginning of the period, the retailer makes an order
quantity decision and then orders product from a supplier. The lead time is zero
and the order arrives instantaneously. The retailer performs 100% inspection,
then pays for the good units and returns the defective units to the supplier. The
inspection time and cost are not considered.
The following notations will be used throughout this paper:
c : purchasing cost per unit.
s : selling price per unit.