SPP

The single-period (news-vendor) problem: literature reviewand suggestions for future research

Moutaz Khouja (1999)1. Importance of Newsvendor ProblemK 537: to find the order quantity which maximizes the expected profit in a single period probabilistic demand framework.D 183: provide an excellent vehicle for examining how operational problems interact with marketing issues to influence decision-making at the firm level.W 93: applies in various settings such as capacity planning, yield management, insurance, and supply chain contracts.K 537 used to aid decision making in the fashion and sporting industries, [and] in managing capacity and evaluating advanced booking of orders in service industries such as airlines and hotels.2. Classical AssumptionsK 537: if any inventory remains at the end of the period, a discount is used to sell it or it is disposed of.W 93: standard newsvendor model is based upon risk neutrality so that managers will select an order quantity to maximize expected profit. counterexamples ~ stockout-avoidance behaviorDecision bias the deviation of the newsvendors optimal order quantity from the profit maximization order quantity(Schweitzer&Cachon 2000): preferences other than risk neutralityLoss aversion model (93): people are more averse to losses than they are attracted to same-sized gains94 intuitively appealing and well supported in finance, economics, marketing, and organizational behavior99 For high-shortage-cost products, a loss-averse newsvendor may order more than the risk-neutral newsvendor, whereas for low-shortage-cost products, loss aversion will cause the newsvendor to order less than a risk-neutral newsvendor.

2.1 The Classical SPPTwo solution approaches:- Minimizing the expected costs of overestimating and underestimating demand; orMaximizing the expected profit; both amount to the same results.x quantity demanded, a random variable.f(x ) the probability density function of x.F(x ) the cumulative distribution function of x.P selling price per unit.C cost per unit.V salvage value per unit.S shortage penalty cost per unit.Co C-V, unit overage cost.Cu P-C+S, unit underage cost.Q order quantity, a decision variable.2.1 The Classical SPP

3. Extensions of the classical single-period modelP&D 183: Increasing prevalence of time-based competition (Stalk and Hout 1990) because as time-based competition intensifies, product life-cycles shrink so that more and more products acquire the attributes of fashion or seasonal goods.K 538: As product life cycles continue their downward trend, the importance of the SPP will grow.

3. Extensions of the classical single-period modelExtensions to the SPP can be classified into 11 categories:1. Extensions to different objectives and utility functions.2. Extensions to different supplier pricing policies.3. Extensions to different news-vendor pricing policies and discounting structures.4. Extensions to random yields.5. Extensions to different states of information about demand.6. Extensions to constrained multi-product.7. Extensions to multi-product with substitution.8. Extensions to multi-echelon systems.9. Extensions to multi-location models.10. Extensions to models with more than one period to prepare for the selling season.11. Other extensions.3.1. Extensions to different objectives and utilityfunctionsmaximizing E() may not reflect reality -> maximizing the probability of achieving a target profit Kabak and Schiff provided a closed-form solution for exponentially distributed demand.Cost-volume-profit (C-V-P) analysis: Total Profit=Sales Volume*(Unit Selling Price - Unit Variable Cost) - Fixed Cost (4)Shih considered the effects of over production and derived a general probability distribution of , its expected value, and its variance as a function of Q.- Louderback showed that for normally distributed demand, the distribution of profit can be far from the normal distribution and is not even symmetrical.3.1. Extensions to different objectives and utilityfunctions- Lau addressed two cases: a shortage cost of S= 0 and S>0. For S= 0, Q is independent of the demand distribution and is given by Q=B/(P-C). For S>0, Q depends on the demand distribution; mean-standard deviation of profit tradeoff using u()=E()-k ().Sankarasubramanian and Kumaraswamy solved the case in which the commodity sold is a luxury item and demand is proportional to income.Lau and Lau identified three approaches to estimating PB and Qi, i =1, (1) simulate the problem, (2) develop an expression for PB and find Qi, i= 1, 2 using a `hill-climbing' procedure and (3) analytically solve the first order conditions.- Atkinson, standard-setting mechanism: Managers Return = Wage + k*(Profit due to managers decision - Profit due to standard quantity)

3.1. Extensions to different objectives and utilityfunctions-Thakkar et al. solved the SPP under two objectives: (a) maximizing E(ROI) and (b) maximizing the probability of achieving a target ROI, PROI.-Magee and later Anvari employed the capital-asset pricing model (CAPM) for the SPP. Magee suggested that the true measure of risk for the NV is not the variance of profit but rather the covariance of profit with the return on a market portfolio of securities.-> Thorstenson a case of capital rationing which is not consistent with the perfect capital-market assumption of the CAPM.- Eeckhoudt et al. examined various comparative statics for the risk-averse NV.3.2. Extensions to dierent supplier pricing policiesJucker and Rosenblatt considered three types of quantity discounts:-All-units quantity discounts.-Incremental quantity discounts.-Carload-lot discounts.+ two types of supplier behavior.Pantumsinchai and Knowles proposed algorithms for solving an SPP in which Q is made up of a number of containers with standard sizes.Khouja considered an SPP in which an emergency supply option exists.Lin and Kroll considered all-units and incremental quantity discounts and dual performance measures.Kabak and Weinberg proposed three extensions to the SPP.3.3 Extensions to different news-vendor pricing policies and discounting structuresMills, Whitin: P* under uncertainty is less than the riskless P*Lau and Lau two cases of demand.Polatoglu considered the simultaneous pricing and procurement decisions.Khouja solved an SPP in which multiple discounts are used to sell excess inventory.4. DiscussionLittle comparative work.No research on the relationship between substitution and different states of information about demand.Extensions to multi-echelon systems do not seem to fit well within the classical assumptions of the SPP model.

5. Further Researchjoint determination of the optimal order quantity and the discounting policy;incorporation of the effects of advertising in the SPP.