Separation results for multi-product inventory hedging problems

Sun, Yuemeng; Wissel, Johannes; Jackson, Peter L.

doi:10.1007/s10479-013-1473-6

Cited by 6 publications

(5 citation statements)

References 15 publications

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“…In contrast, our model starts with an elaborate but general demand model in the sense that the rate functions are not assumed to take any functional forms, and the derived solutions are explicit. In addition, in Sun et al (2016), the problem formulation assumes a known Lagrangian penalty parameter (i.e., the objective is "mean -κÁvariance" with given κ>0). This assumption (together with the independent forecast errors) leads to the separation result, but requires the identification of κ beforehand.…”

Section: Literature Reviewmentioning

confidence: 99%

“…Note that (i) independent random variables are associated; (ii) if X is associated, then so is h (X) for any increasing function h:ℜ n ↦fℜ. Refer to Chapter 9 of Ross (1996). LEMMA 3.…”

Section: The Optimal Q Decisionmentioning

confidence: 99%

“…In addition, in Sun et al. (2016), the problem formulation assumes a known Lagrangian penalty parameter (i.e., the objective is “mean ‐ κ ·variance” with given κ >0). This assumption (together with the independent forecast errors) leads to the separation result, but requires the identification of κ beforehand.…”

Section: Introductionmentioning

confidence: 99%

“…In a recent work, Sun et al. (2016) extend the general information setting of Caldentey and Haugh (2006) to a multi‐product one, but with a single financial asset. In particular, the demands are assumed to have independent forecast errors, which leads to a “separation result” that decomposes the production quantity decision, given the hedging strategy, into a set of individual problems, one for each product.…”

Section: Introductionmentioning

confidence: 99%

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Mean–Variance Hedging for Production Planning with Multiple Products

Wang

2021

Production and Operations Management

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We study production planning in a multi‐product setting, in which demand for each product depends on multiple financial assets (such as commodities, market indices, etc). In addition to the production quantity decision at the beginning of the planning horizon, there is also a real‐time hedging decision throughout the horizon; and we optimize both decisions jointly. With a mean–variance problem formulation, we first derive the optimal hedging strategy, given the production quantities. This leads to an explicit objective function with which bounds on optimal production quantities are identified. Thus, optimization of the production policies can be readily solved numerically as a static minimization problem. This way, we are able to give a complete characterization of the mean–variance efficient frontier, and quantify the contribution of the hedging strategy by the variance reduction it achieves. Furthermore, the model and results are extended to allow dynamic production control that tracks the demand rates.

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Section: Literature Reviewmentioning

confidence: 99%

Section: The Optimal Q Decisionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Mean–Variance Hedging for Production Planning with Multiple Products

Wang

2021

Production and Operations Management

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“…For overviews on different features of ERM, we mention, for instance, Olson (2009, 2010a, b), and Wu et al (2011). Applications of ERM are found in fields such as insurance (Gaffney and Ben-Israel 2013), hedging tools (Sun et al 2013), and supply chain risk (Blome and Schoenherr 2011).…”

Section: Introductionmentioning

confidence: 99%

Optimal allocation of a fixed production under price uncertainty

Rodríguez-Puerta

Álvarez-López

2014

Ann Oper Res

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In this paper, we consider a model of production allocation in the context of the theory of the firm under uncertainty. This is the case of a firm that has just produced a known amount of an output and can allocate it to two possible ends: one with a certain price, the other with an uncertain price. We first establish conditions to determine whether the firm will make use of both ends or of only one of them. In particular, we find a limit value for the certain price (which we call the frontier price) below which the firm decides to allocate the total amount of production to the uncertain end. We then study comparative-static effects on the optimal output allocated to each end, and also on the frontier price. Finally, we analyze an application concerning the middleman who buys the firm's output in the certain end. This is a pricing problem: namely obtaining the price in the certain end that the middleman must offer to the producer in order to attain a desired amount of output. In two specific cases, we also provide closed-form expressions for the optimal allocation to both ends and for the frontier price.

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