Note—Note on “Optimal Ordering Quantity to Realize a Pre-Determined Level of Profit”

Sankarasubramanian, E.; Kumaraswamy, Sumathi

doi:10.1287/mnsc.29.4.512

Cited by 64 publications

(24 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For the strictly riskaverse case, if r − 2k ≤ 0, from (26) we get lim v→∞ ϕ(z|m, v) ≤ [U ((r − k)z) − U (−kz)]k/2 < 0 for all z > 0 (the second inequality due to U being strict decreasing), and hence, z * (∞) = 0. If r − 2k > 0, expression (26) as a function of z has a zero iff equation (13) has a solution.…”

Section: Casementioning

confidence: 99%

“…This has led to alternative heuristic formulations. Sankarasubramanian and Kumaraswamy [26] maximize the probability of exceeding a target profit for specific demand distributions, and Li et al [22] extended that model to study two products with uniformly distributed demands. Additional formulations can be found in Anvari [4], Chung [13], and Anvari and Kusy [5].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Risk‐sensitive sizing of responsive facilities

Chayet

Hopp

2008

Naval Research Logistics

View full text Add to dashboard Cite

Abstract:We develop a risk-sensitive strategic facility sizing model that makes use of readily obtainable data and addresses both capacity and responsiveness considerations. We focus on facilities whose original size cannot be adjusted over time and limits the total production equipment they can hold, which is added sequentially during a finite planning horizon. The model is parsimonious by design for compatibility with the nature of available data during early planning stages. We model demand via a univariate random variable with arbitrary forecast profiles for equipment expansion, and assume the supporting equipment additions are continuous and decided ex-post. Under constant absolute risk aversion, operating profits are the closed-form solution to a nontrivial linear program, thus characterizing the sizing decision via a single first-order condition. This solution has several desired features, including the optimal facility size being eventually decreasing in forecast uncertainty and decreasing in risk aversion, as well as being generally robust to demand forecast uncertainty and cost errors. We provide structural results and show that ignoring risk considerations can lead to poor facility sizing decisions that deteriorate with increased forecast uncertainty. Existing models ignore risk considerations and assume the facility size can be adjusted over time, effectively shortening the planning horizon. Our main contribution is in addressing the problem that arises when that assumption is relaxed and, as a result, risk sensitivity and the challenges introduced by longer planning horizons and higher uncertainty must be considered. Finally, we derive accurate spreadsheet-implementable approximations to the optimal solution, which make this model a practical capacity planning tool.

show abstract

Section: Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Risk‐sensitive sizing of responsive facilities

Chayet

Hopp

2008

Naval Research Logistics

View full text Add to dashboard Cite

show abstract

“…Some works deal with the consideration of dierent objectives, such as maximizing the probability of achieving a target prot or the use of utility functions (Lau, 1980, Sankarasubramanian and Kumaraswamy, 1983, Lau and Lau, 1988. Other works consider supplier pricing policies, like quantity discounts, and dierent retailer pricing policies, random yield and dierent states of information about demand.…”

Section: Inventory Management and The Newsvendor Modelmentioning

confidence: 99%

The Economic and Environmental Sustainability of Dual Sourcing

Rosic¹

2012

View full text Add to dashboard Cite

“…The recourse w ij (z) represents the slack at the arc (i, j). Using Algorithm 1, we reduce the problem (29) to solving a sequence of subproblems in the form of stochastic optimization problems with CVaR objectives. Since the project management problem has complete recourse, accordingly, we use sampling approximation to obtain solutions to the subproblem as follows:…”

Section: Computation Studiesmentioning

confidence: 99%

“…However, maximizing the probability of achieving a target is generally not a computationally tractable model. As such, studies along this objective have been confined to simple problems such as the Newsvendor problem; see Sankarasubramanian and Kumaraswamy [29], Lau and Lau [17], Li et al [19] and Parlar and Weng [25].…”

Section: Introductionmentioning

confidence: 99%

Goal-Driven Optimization

Chen

2009

Operations Research

View full text Add to dashboard Cite

Achieving a targeted objective, goal or aspiration level are relevant aspects of decision making under uncertainties. We develop a goal driven stochastic optimization model that takes into account an aspiration level. Our model maximizes the shortfall aspiration level criterion, which encompasses the probability of success in achieving the goal and an expected level of under-performance or shortfall. The key advantage of the proposed model is its tractability. We show that proposed model is reduced to solving a small collections of stochastic linear optimization problems with objectives evaluated under the popular conditional-value-at-risk (CVaR) measure. Using techniques in robust optimization, we propose a decision rule based deterministic approximation of the goal driven optimization problem by solving a polynomial number of second order cone optimization problems (SOCP) with respect to the desired accuracy. We compare the numerical performance of the deterministic approximation with sampling approximation and report the computational insights.

show abstract

Note—Note on “Optimal Ordering Quantity to Realize a Pre-Determined Level of Profit”

Cited by 64 publications

References 1 publication

Risk‐sensitive sizing of responsive facilities

Risk‐sensitive sizing of responsive facilities

The Economic and Environmental Sustainability of Dual Sourcing

Goal-Driven Optimization

Contact Info

Product

Resources

About