Demand Uncertainty Increases Research Articles

Comparative Statics Analysis of Multiproduct Newsvendor Networks Under Responsive Pricing

We propose a novel analytic approach for the comparative statics analysis of multiproduct multiresource newsvendor networks under responsive pricing. Our approach involves exploiting the properties of the primal mathematical programming formulation and of the dual variables and linking those properties to the concept of convex orders and to properties of the underlying demand function. The use of convex orders allows us to establish our main results without restriction to a specific demand distribution. A major strength of our approach is that it is “scalable,” i.e., it applies to newsvendor networks with any number of “nonindependent” (i.e., demand or resource sharing) products and resources, without an exponential increase in effort as problem size increases. This is unlike the current approaches commonly used in the operations management literature, which typically involve a parametric analysis of the recourse problem, followed by the use of Jacobians and the implicit function theorem. Providing a rigorous framework for comparative statics analysis, which can be applied to other problems that are not amenable to traditional parametric analysis, is our main contribution. We demonstrate this approach on the optimal capacity decision problem in multiproduct newsvendor networks under responsive pricing, formulated as a two-stage stochastic programming problem with recourse: The firm determines the resource capacities ex ante, in the first stage, when demand intercepts are uncertain, and makes the pricing and production decisions ex post, in the second stage, when demand intercepts (e.g., market conditions) are fully observed. This particular problem and its variants are well studied in the operations management literature. A comparative statics analysis is integral to the study of the capacity investment decision, as it allows answers to important questions such as the following: “Does the firm acquire more or less of the different resources available as demand uncertainty increases? Does the firm benefit from an increase in demand uncertainty?” Using our proposed approach, we establish comparative statics results on how the newsvendor's expected profit and optimal capacity decision change with demand risk in multiproduct multiresource newsvendor networks. We also extend our analysis to the study of demand dependence in two-product networks.

In This Issue

In This Issue

Long-term efficiency of water networks with demand uncertainty

Water distribution network (WDN) design problems generally consider minimising network costs while meeting minimum allowable pressure under specified demand patterns. However, extension and renovation of networks based on assessment of demand uncertainty causes an increase in efficiency of the system and monetary savings. Attention to uncertain changes in pattern and the value of nodal demands in an operational period can thus show the effect of uncertainties in the network's efficiency. Using Monte Carlo simulation and shuffled frog leaping algorithm optimisation, this paper analyses the efficiency of a designed network based on nodal demand uncertainty during the operational period. Assessment of a network efficiency index according to a probabilistic normal distribution for nodal demand in an operational period shows that a network design that does not consider nodal demand uncertainty decreases network efficiency, especially at the end of the operational period. Moreover, an increase in demand uncertainty decreases network efficiency. The results of the proposed model for a benchmark WDN show that a network designed deterministically for a 30-year operational period is unable to secure nodal demands with suitable pressure after 10 years. In addition, the minimum required pressure considered in network design is met in approximately the first 18 years of the operational period.

Outsourcing and capacity planning in an uncertain global environment

Firms employing offshore outsourcing strategies may face both exchange rate and demand uncertainties. In this paper, we show that the firms may benefit from operational option to switch production by keeping capacities with both domestic and foreign suppliers. The value of the operational option increases as the exchange rate uncertainty or demand uncertainty increases. In addition, when the firms become risk-averse, they may use domestic capacity to hedge against offshore capacity. As a result, the firms may choose to hold local capacity even if it exhibits negative marginal contribution to the profit. Furthermore, risk-averse firms may keep more total capacity than risk-neutral firms.

Multi-objective Analysis of Periodic Review Inventory Problem with Coordinated Replenishment in Two-echelon Supply Chain System through Differential Evolution

This paper studies a multi-objective analysis of periodic review inventory problem in two-echelon supply chain system. Thereat, three strategies of replenishment are proposed to manage inventory in efficient way while trying to improve the system performance by simultaneously minimizing total cost and loss rate of the supply chain. Associated with the problem, it is apparent that preventing loss rate will increase total cost and vice versa. Then between these conflicting goals, we can examine the profitable situation in which all members in the chain can achieve proportional satisfaction. To concern with the finally formulated problem, we applied multi-objective differential evolution (MODE) after giving the original method a suitable procedure for the resulting problem. Through numerical experiments for a case study, we show that the intimate coordination strategy between manufacturer and retailer become more effective as increase in demand uncertainty.

Competitive Environment and the Relationship Between IT and Vertical Integration

The information systems (IS) literature suggests that by lowering coordination costs, information technology (IT) will lead to an overall shift towards more use of markets. Empirical work in this area provides evidence that IT is associated with a decrease in vertical integration (VI). Economy-wide data, however, suggests that over the last 25 years the average level of VI has, in fact, increased. This paper studies this empirical anomaly by explicating the moderating impact of two measures of competitive environment, demand uncertainty, and industry concentration, on the relationship between IT and VI. We examine firms included in 1995 to 1997 InformationWeek 500 and the COMPUSTAT database. Consistent with the IS literature, the analysis suggests that IT is associated with a decrease in VI when demand uncertainty is high or industry concentration is low. However, contrary to the IS literature, IT is found to be associated with an increase in VI when industry concentration is high or demand uncertainty is low. Furthermore, as demand uncertainty increases, less vertically integrated firms invest more in IT, while as industry concentration increases, more vertically integrated firms invest more in IT. The analysis also suggests that firms' choice of the level of VI and IT investment, under different levels of demand uncertainty and industry concentration, are rational. When demand uncertainty is high or industry concentration is low, increase in VI may increase coordination and production costs. Thus, less VI is rational. However, when industry concentration is high or demand uncertainty is low, increase in VI may decrease coordination and production costs. Thus, firms choose more VI in such industries. The implications for research and practice are discussed.

Demand uncertainty and the capital–labour ratio in Poland

This paper investigates the effect of demand uncertainty on the capital–labour ratio of non-financial firms in Poland. An eclectic model is used to characterise a utility maximising firm in a transition economy with demand uncertainty and imperfect competition. It is assumed that labour is completely variable and capital is quasi-fixed. The demand for capital, and hence the capital–labour ratio, derives from the optimisation of expected costs and the firm's pricing and output decisions, and crucially depends on the sign of the covariance term, i.e. the firm's risk behaviour. The main testable proposition of the model is that if firms are risk-lovers, an increase in demand uncertainty increases the capital–labour ratio, whereas the capital–labour ratio decreases when firms are risk-averse. The model is estimated using data from a cross-section of 148 non-financial firms in Poland. The results unambiguously show that there exists a significant positive relationship between demand uncertainty and the capital–labour ratio. This finding suggests that Polish firms are risk-lovers, i.e. they respond to demand uncertainty by increasing their capital–labour ratio because they are more concerned to have stable labour costs than they are to have stable profits. The evidence has important implications for the needed set of regulations and corporate governance in Poland as part of the necessary economic reform.

Market segmentation and oligopoly under uncertainty

The paper considers an oligopoly under uncertainty in segmented markets (markets in which risk aversion may vary across firms). With strong segmentation, a firm (rival) will increase (decrease) output and value in response to an increase in demand uncertainty. With weak segmentation, firms' outputs and values decrease with an increase in demand uncertainty. Thus, the plausible suspicion that decreasing demand uncertainty is beneficial to the participants may not be true in strongly segmented markets. A logical inference is that not concealing information about a random element in demand (i.e., reducing demand uncertainty) is the dominant strategy with weak segmentation.

RISKY PRODUCTION WITH EX‐ANTE PRICES UNDER MONOPOLY ANALYTICAL AND SIMULATION RESULTS

ABSTRACTThis paper concerns the case of a monopolist facing multiplicative uncertainty in demand. Karlin and Carr (1962), henceforth KC, show that, when price and production are both chosen ex ante, the uncertainty price exceeds the certainty price. They also give a sufficient condition under which the firm locates above the certainty demand curve, but they do not consider the effect on the output level. In this note we replicate the KC results and then go further. In the special case that the price elasticity of certainty demand is constant, and the probability distribution for the uncertainty parameter in the demand function is uniform, output is unambiguously lower under uncertainty, and KC's condition for the firm to locate above the certainty demand curve can be strengthened to one that is both necessary and sufficient. The robustness of these results is tested under less stringent assumptions on demand, abandoning symmetry for a lognormal distribution of the uncertainty parameter. Simulation confirms that the results hold up, and also determines the effects upon the firm's decisions of an increase in demand uncertainty.

Robust Capacity Planning Under Uncertainty

The existence of uncertainty influences the investment, production and pricing decision of firms. Therefore, capacity expansion models need to take into account uncertainty. This uncertainty, may arise because of errors in the specification, statistical estimation of relationships and in the assumptions of exogenous variables. One such example is demand uncertainty. In this paper, a cautious capacity planning approach is described for solving problems in which robustness to likely errors is needed. The aim is to cast the problem in a deterministic framework and thereby avoid the complexities inherent in nonlinear stochastic formulations. We adopt a robust approach and minimize an augmented objective function that penalises the sensitivity of the objective function to various types of uncertainty. The robust or sensitivity approach is compared with Friedenfelds' equivalent deterministic demand method. Using numerical results from a large nonlinear programming capacity planning model, it is shown that as caution against demand uncertainty increases, the variance of the total objective function (profit) decreases. The cost of such robustness is a deterioration in the deterministic risky performance. This method is also applied to an industry simulation model in order to assess the effect of uncertainty in market demand on optimal capacity expansion and capacity utilisation.

COMPETITIVE INDUSTRY EQUILIBRIUM UNDER UNCERTAINTY AND FREE ENTRY

This paper investigates the properties of industry equilibrium under price uncertainty given free entry and exit. For any form of risk‐averse behavior, it is shown that an increase in demand uncertainty (as measured by a mean‐preserving spread) increases mean output price and reduces output of firms in long‐run equilibrium.

Location and the Theory of the Imperfectly Competitive Firm under Demand Uncertainty

There is a large and growing literature on location and the theory of the firm in a heterogeneous space, i.e., in the space where markets are given at discrete points, such as Weber [22], Isard [7], Moses [15], Sakashita [18, 19], Bradfield [3], Emerson [5], Woodward [23], Khalili, Mathur and Bodenhorn [8], Miller and Jensen [14], Mathur [13], Eswaran, Kanemoto and Ryan [6], and Mai and Shieh [11]. What is, perhaps, surprising is that within this large body of literature nothing has been said about how the firm would and should locate theoretically under conditions of uncertainty. It only with Webber [21] and Mai [10] that any real indication is given that uncertainty due to imperfect market information may exert an influence on locational choice.' In particular, Mai [10] presented a formal mathematical model to show that the results and implications of the optimum location of the firm under demand uncertainty is different from that applicable to the state of certainty. However, Mai's analytical framework is restricted to the case of pure competition, where price is given, all buyers are assumed to be concentrated at given market point, and each firm seeks to minimize expected cost and is thus risk neutral. The purpose of this paper is to extend the location theory of the competitive firm under demand uncertainty to the case where the imperfectly competitive quantity-setting firms are not risk neutral and are interested in maximizing expected utility from profit, including cost and demand factors.2 This expected utility approach will provide a more general formulation of the firm's attitude toward risk for analyzing its location decisions. The basic model evaluating the firm's location and input choices is presented in section II. Section III examines the overall impacts of demand uncertainty on the optimum location and input demands. The effect of a marginal increase in demand uncertainty on the optimum location is investigated in Section IV. Section V analyzes the effect on the optimum location of a change in the expected output price. Section VI then evaluates the

A Putty-Clay Model of Demand Uncertainty and Investment

A simple model is used to explore the effects of demand on business fixed investment. We show that within a putty-clay framework an increase in demand uncertainty can be expected to have two countervailing effects. On the one hand increasing risk tends to induce a firm to increase its capacity, but on the other hand the optimal capital-intensity of that capacity decreases.

Long-run industry equilibrium with uncertainty

In this paper we consider the effects of uncertainty on industry equilibrium when firms must commit themselves to production before prices are revealed. We show that (a) an increase in demand uncertainty will (i) not affect the equilibrium number and size of firms if they are risk neutral, (ii) reduce the equilibrium number of firms if they are risk averse, but will have an ambiguous effect on their size. (b) In equilibrium, firms operate at capacity if they are risk neutral, but at excess capacity if they are risk averse.