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The Successful Systems Engineer’s Toolbox
Published in Joseph Eli Kasser, Systems Engineering, 2019
People tend to use solution language to describe functions. For example, we often use the phrase ‘need a car’ when we should be saying ‘need transportation’. Using implementation language in the early stages of problem-solving tends to produce results that may not be the best solution to the problem even if it is a complete solution, as well as generally not being an innovative solution. This is because solution language tends to turn examples into solutions with little exploration of alternative solutions. For example, if the need is stated as ‘we need a car’, the problem-solving process tends to focus on selecting the car to meet the need. A need should be stated from the Operational and Quantitative HTPs as ‘provide a transportation function to move N people with B (kilograms/cubic meters feet) of baggage M kilometers in H hours over terrain of type T with an operational availability of O’. Creating the solution concept in the form of capability or functionality is in accordance with, ‘if a problem can be stated as a function, then the total solution is the needed functionality as well as the process to produce that functionality’ (Hall 1989). In holistic thinking terms, state the need using functional or problem language not structural or solution language. Using the language of functions in the early stages of problem-solving will nudge the stakeholders into abstract thinking rather than fixating on an implementation. For example, they might stop saying ‘I need a car’ and start saying ‘I need transportation’.
Multi-objective optimization and cost-based output pricing of a standalone hybrid energy system integrated with desalination
Published in The Engineering Economist, 2020
Xi Luo, Yanfeng Liu, Xiaojun Liu
The Shapley value, developed by Shapley in (1953), is a solution concept in cooperative game theory. It ensures that the benefit to each player is equal to the average marginal contribution of the player in the coalition. For each cooperative game, this value assigns a unique distribution of the total surplus generated by the coalition of all players (Luo & Liu, 2016). The Shapley value is computed as follows: where is a set of all players in the game. Any subset is called a coalition and refers to the coalitions formed by players in the set based on their interests. For each coalition, is the corresponding characteristic function, which is the profit of each coalition in this study.
Ex post demand information sharing between differentiated suppliers and a common retailer
Published in International Journal of Production Research, 2020
Hui Lei, Jingru Wang, Lusheng Shao, Honglin Yang
We now examine how the suppliers simultaneously decide their wholesale prices in anticipation of the retailer’s response. Without loss of generality, we use Bayesian Nash equilibrium as the solution concept and derive supplier ’s best-response wholesale price to supplier ’s wholesale price . Here, is a function of if supplier is informed and is independent of if supplier is uninformed. For convenience, we use to denote supplier ’s wholesale price throughout this paper whether or not supplier is informed.
Pricing decisions in a decentralized biofuel supply chain with RIN mechanism
Published in Energy Sources, Part B: Economics, Planning, and Policy, 2019
Ghazaleh Allameh, Mohammad Saidi Mehrabad, Seyed Jafar Sadjadi
The objective function (1a) is the maximization of each farmer’s profit which is the income of selling biomass type to biorefineries subtracted from its transportation and production costs. Constraint (1b) assures that the total production of each type of biomass by each farmer should not exceed the capacity limitations. Constraints (1c) assure that the amount of biomass flow to each biorefinery should be equal to the amount of flow transported from each biorefinery to blenders, regardless of harvest loss. Constraints (1d) state that the biomass flow from farmer to biorefineries is reversely and directly sensitive to biomass selling price of farmer and the rival farmers, respectively. The non-negativity of decision variables is stated in constraints (1e). Due to the fact that there is no cooperation among farmers, there are number of optimization models for all farmer that should be solved, simultaneously. The game that interconnects all these optimization problems is a form of generalized Nash equilibrium for which there is an extensive literature (Facchinei and Kanzow 2007; Osborne and Rubinstein 1994). The generalized Nash equilibrium is a solution concept of noncooperative games that provides optimal strategy for several players who are making decisions simultaneously while their decisions depend on the decisions of the others (Yue and You 2014)