Consistent notation for presenting complex optimization models in technical writing

Teter, Michael D.; Newman, Alexandra M.; Weiss, Martin

doi:10.1016/j.sorms.2016.05.001

Cited by 12 publications

(6 citation statements)

References 16 publications

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“…The model formulation was done according to the notation presented by Teter et al. (2016): Sets –

\mathcal {T}

: the set of days of the time horizon, –

\mathcal {J}

: the set of blocks of the vineyard. Parameters –

B_{j}

: price of the grape in lot j ($/kilograms),

j \in \mathcal {J}

. –

C_{E}

: cost of hiring ($/worker). –

C_{F}

: cost to lay off ($/worker). –

C_{P}

: cost of keeping labor idle between periods ($/worker per period). –

C_{H}

: cost of harvesting ($/kilograms). – K : maximum daily reception capacity of the winery (kilograms/day). –

S_{j}

: initial amount of grapes in lot j (kilograms),

j \in \mathcal {J}

. –

Q_{jt}

: quality of the grape in lot

j \in \mathcal {J}

at time

t \in \mathcal {T}

. –

\beta _{t}

: effective worker productivity at time

t \in \mathcal {T}

…”

Section: Problem Formulationmentioning

confidence: 99%

See 1 more Smart Citation

Comparing an expected value with a multistage stochastic optimization approach for the case of wine grape harvesting operations with quality degradation

Avanzini

Vergara

Vera

et al. 2021

Int Trans Operational Res

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Operations planning is an important step in any activity as it aligns resources to achieve economic production value. In agriculture operations where uncertainty is present, planners must deal with biological and environmental factors, among others, which add variability and complexity to the production planning process. In this work, we consider operations planning to harvest grapes for wine production where uncertainty in weather conditions will affect the quality of grapes and, consequently, the economic value of the product. In this setting, planners make decisions on labor allocation and harvesting schedules, considering uncertainty of future rain. Weather uncertainty is modeled following a Markov Chain approach, in which rain affects the quality of grapes and labor productivity. We compare an expected value with a multi-stage stochastic optimization approach using standard metrics such as Value of Stochastic Solution and Expected Value of Perfect Information. We analyze the impact of grape quality over time, if they are not harvested on the optimal ripeness day, and also consider differences in ability between workers, which accounts for the impact of rain in their productivity. Results are presented for a small grape harvest instance and we compare the performance of both models under different scenarios of uncertainty, manpower ability, and product qualities. Results indicate that the multi-stage approach produces better results than the expected value approach, especially under high uncertainty and high grape quality scenarios. Worker ability is also a mechanism for dealing with uncertainty, and both models take advantage of this variable.

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“…The model formulation was done according to the notation presented by Teter et al. (2016): Sets –

\mathcal {T}

: the set of days of the time horizon, –

\mathcal {J}

: the set of blocks of the vineyard. Parameters –

B_{j}

: price of the grape in lot j ($/kilograms),

j \in \mathcal {J}

. –

C_{E}

: cost of hiring ($/worker). –

C_{F}

: cost to lay off ($/worker). –

C_{P}

: cost of keeping labor idle between periods ($/worker per period). –

C_{H}

: cost of harvesting ($/kilograms). – K : maximum daily reception capacity of the winery (kilograms/day). –

S_{j}

: initial amount of grapes in lot j (kilograms),

j \in \mathcal {J}

. –

Q_{jt}

: quality of the grape in lot

j \in \mathcal {J}

at time

t \in \mathcal {T}

. –

\beta _{t}

: effective worker productivity at time

t \in \mathcal {T}

…”

Section: Problem Formulationmentioning

confidence: 99%

“…In order to evidence the effects of quality in the decisions, we split the vineyard considering that in a specific block there is only one grape variety. The model formulation was done according to the notation presented by Teter et al (2016):…”

Section: Deterministic Modelmentioning

confidence: 99%

Comparing an expected value with a multistage stochastic optimization approach for the case of wine grape harvesting operations with quality degradation

Avanzini

Vergara

Vera

et al. 2021

Int Trans Operational Res

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“…We assume that we can choose any flux calculation method to pre-compute the flux delivered to each measurement point given a heliostat's selected aimpoint, which serves as a parameter in our model. Our notational convention is adapted from the best practices established in [24] and uses lowercase letters to denote decision variables, capital letters to represent parameters, subscripts to denote indices, and caligraphic letters to denote sets.…”

Section: Aimpoint Optimization Modelmentioning

confidence: 99%

Solar Field Layout and Aimpoint Strategy Optimization

Zolan

Hamilton

Wagner

et al. 2021

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“…In the following Sections A.1-A.6, we present the TCM formulation for indices, index sets, parameters, variables, objective function, and constraints, and then conclude with a brief description. Beale et al (1974) originally documented this ordering, which was adhered to for decades under the label NPS format in hundreds of published theses and papers by Naval Postgraduate School (NPS) students and faculty, with acknowledgment of the original Beale et al reference (Brown and Dell 2007), and recently reintroduced with additional guidance by Teter et al (2016).…”

Section: Appendixmentioning

confidence: 99%

Optimal Allocation of Students to Naval Nuclear-Power Training Units

et al. 2017

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The U.S. Navy operates an impressive fleet of nuclear-powered submarines and aircraft carriers and has safely operated its nuclear fleet for more than 60 years, while steaming over 154 million miles. Rigorous training has been key to maintaining such an impressive record. The U.S. Naval Nuclear Propulsion Training Program develops, certifies, and delivers the nuclear-operator qualification training for enlisted and officer personnel operating its nuclear fleet. This training finishes at one of four nuclear-power training units (NPTUs), operates under a complex set of hard and soft constraints, varies depending on the type of student, and requires significant personnel and equipment resources. We developed and implemented a mixed-integer linear program (MILP) that prescribes how many students of each type to allocate to each NPTU at the start of each class (a group of students who train together) and how allocated students complete NPTU training. The use of MILP has improved student allocation by an estimated eight percent and led to significantly improved use of both NPTU personnel and equipment resources. In this paper, we describe this unique optimization application, the MILP formulation, its path to adoption, its user interface, and impacts from its development and use over the past three years.

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Consistent notation for presenting complex optimization models in technical writing

Cited by 12 publications

References 16 publications

Comparing an expected value with a multistage stochastic optimization approach for the case of wine grape harvesting operations with quality degradation

Comparing an expected value with a multistage stochastic optimization approach for the case of wine grape harvesting operations with quality degradation

Solar Field Layout and Aimpoint Strategy Optimization

Optimal Allocation of Students to Naval Nuclear-Power Training Units

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