Programming optimal decisions

In this section we present dynamic programming models with an infinite time horizon. Although an infinite time horizon is a figment of the imagination, these models often are useful for decision problems with many decision points. Many infinite horizon models also have the desirable feature that there exist stationary deterministic optimal policies. Thus, optimal decisions depend only on the current state of the process and not on the sometimes artificial notion of time, as in finite horizon problems. This characteristic makes optimal policies easier to understand, compute, and implement, which is desirable in apphcations. 

McMillan, Jr., C., Mathematical Programming An Introduction to Design and Application of Optimal Decision Machines, Wiley, New Yoric (1970). 

W. J. Lee. Determining order quantity and selling price by geometric programming Optimal solution, bounds and sensitivity. Decision Sciences, 24(76-87), 1993. 

Chapter 5 discusses the use of integer programming models to make optimal decisions regarding the number and locations of facilities. 

Taking into account that decision-makers do not always care about maximizing revenue, but how to achieve the optimal revenue in the sense of probability, we apply stochastic chance-constrained programming theory to translate the model into the stochastic programming model under chance constraints so that the optimal decision objective with a certain confidence level can be expressed. 

Mathematical programming models are used to optimize decisions concerning execution of certain activities subject to resource constraints. Mathematical programming models have a well-defined structure. They consist of mathematical expressions representing objective function and constraints. The expressions involve parameters and decision variables. The parameters are input data, while the decision variables represent the optimization outcome. The objective function represents modeling objectives and makes some decisions more preferable than others. The constraints limit the values that decision variables can assume. 

DHS has improved information sharing. While information sharing still may not be optimally utilized, a security manager can get a better understanding of the risk environments now than prior to 9/11. Both the public and private sectors need credible, timely, actionable information to ensure that appropriate security investments, programs, and decisions are made to protect organizational assets. DHS has attempted to build a system of trust in both public and private sector security partners regarding shared information. 

Presents multiple criteria mathematical programming models for optimizing decisions regarding the number and location of supply chain facilities and determining optimal distribution strategies... 

Facilities (plants and DCs) play a key role in managing supply chains. Their numbers and locations are generally considered as strategic decisions and directly affect the supply chain performance. Chapters 3-8 and 11 present multiple criteria integer programming models to make optimal decisions regarding the number and location of supply chain facilities and to determine the optimal distribution strategies. 

A hierarchical design procedure for process synthesis can be used in conjunction with a flow-sheeting program to analyze, evaluate, and optimize the options (60). The emphasis is on starting with the simplest possible models that will give answers to a particular question quickly so that the questions to be asked at the next decision level can be formulated. At each stage, it is necessary to ensure that the level of detail in the model is sufficient to give rehable information. 

Once the highest steam level is set, then intermediate levels must be established. This involves having certain turbines exhaust at intermediate pressures required of lower pressure steam users. These decisions and balances should be done by in-house or contractor personnel having extensive utility experience. People experienced in this work can perform the balances more expeditiously than people with primarily process experience. Utility specialists are experienced in working with boiler manufacturers on the one hand and turbine manufacturers on the other. They have the contacts as well as knowledge of standard procedures and equipment size plateaus to provide commercially workable and optimum systems. At least one company uses a linear program as an aid in steam system optimization. 

The result is a deterministic program, where the original second-stage decisions are not a function of the realized scenario, i.e., it is assumed the there is a single scenario problem and all decisions xEV and yEV have to be made before the observation. The corresponding optimization problem is called the expected value problem, (TV problem) and can be written as follows ... 

Planning is done by humans who use computer support tools like simulation, optimization and production planning programs. They gather information from these systems, make trial decisions and monitor the consequences. 

Production planning/optimization always requires a compromise to be found by the humans in charge of decision-making. In the process of finding this compromise, one needs scheduling programs that are integrated into the ERP systems. 

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