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- Objective function
- Subject to constraints
- 5 LAGRANGIAN DECOMPOSITION AND COORDINATION ALGORITHM
=1 =1 Constraints (15) are production capacity restrictions. The constraints ensure that the number of each item produced multiplied by the variable capacity of each item did not exceed any key resource during the planning horizon.
=1 Constraints (16) are set up constraints; the constraints put a limit on production during each period. The value of M is fixed in terms of both production capacity and item demands.
The model described by (1) to (17) is a mixed integer programming model. Similar to most capacitated lot-sizing problems, the problem for the real-world data is very difficult to solve. A simpler model can be established by substituting = + −1 − into (9) leads ≥ 0 ∀ , ∀ , ∀ which is clearly satisfied. Then, constraints (9) are eliminated. Constraints (6) can be rewritten as ∑ =1 + −1 − = ∀ , ∀ . Similarly, constraints (3) and (12) are satisfied by (2), (9) and (10). Constraints (17) are also satisfied since and are binary variables. Since ∈ {0,1} ∀ , ∀ , constraints (13) and (14) are always satisfied by (10) since ≥ 0 ∀ , ∀ , ∀ . All together implies the following simplified model.
= ∑∑ + ∑ ∑ ∑(( + ) + ( + −1 − ) + ℎ ) + ∑ ∑( ) (18) =1 =1 =1 =1 =1 =1 =1 , , , , ∈ {0,1} ∀ , ∀ , ∀ (19) The approaches for solving the problem are discussed in the next section. 5 LAGRANGIAN DECOMPOSITION AND COORDINATION ALGORITHM The Lagrangian decomposition and coordination method is one of the widely used approaches for capacitated lot-sizing problem (Buschkühl et al., 2010), integrated optimization of production scheduling and distribution planning (Nishi et al., 2007), supply chain coordination (Nishi et al., 2008), multi-product newsvendor problem with supply discount (Zhang, 2010), and so on. The key idea of this method is to relax the coupling constraints through 12  Directory: wp-content -> uploads -> 2017 2017 -> Leadership ohio 2017 -> Ascension Lutheran Church Counter’s Schedule January to December 2017 2017 -> Board of directors juanita Gibbons-Delaney, mha, rn president 390 Stone Castle Pass Atlanta, ga 30331 2017 -> Military History Anniversaries 16 thru 31 January Events in History over the next 15 day period that had U. S. military involvement or impacted in some way on U. S military operations or American interests 2017 -> The Or Shalom Cemetery Community Teaching on related issues of Integral 2017 -> Ford onthult samenwerking met Amazon Alexa en introduceert nieuwe navigatiemogelijkheden van Ford sync® 3 met Applink 2017 -> Start Learn and Increase gk. Question (1) Name the term used for talking on internet with the help of text messege? 2017 -> Press release from 24. 03. 2017 From a Charleston Car to a Mafia Sedan 2017 -> Tage Participants 2017 -> Citi Chicago Debate Championship Varsity and jv previews Download 11.62 Mb. Share with your friends:
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