constant expenditures including depreciation, β —alternative return on assets for one period t , and c i — i -type product cost. To achieve the maximum of function ( 7.28 ) it is necessary to vary the values of variables x i ( t ), y l ( t ), V i ( t ), and q i ( t ), including the constraints (Eqs. 7.22 – 7.27 ). In fact, the set objective is the same as the problem of sales and operations scheduling, which is discussed below in Chap. 10 . References Ierapetritou, M. G., & Floudas, C. A. (1998). Effective continuous-time formulation for short-term scheduling. 1. Multipurpose batch processes. titan.princeton.edu/papers/marianthi/iera_ ﬂoudas_98a.pdf Kestner, W., Blecker, T., & Herstatt, C. (2008). Innovative logistics management . Berlin: Schmidt Erich. Kondili, E., Pantelides, C. C., & Sargent, R. A. (1993). General algorithm for short-term schedul- ing of batch operations. Computers and Chemical Engineering, 17 , 211–227. Li, Z., & Ierapetritou, M. G . (2009). Integrated production planning and scheduling using a decomposition framework . sol.rutgers.edu/staff/marianth/integratePS.pdf Macedo, J. (2000). Implementing fast innovation reinforcement supply chains. conference/index.php/ocs/9/paper/view/1957/926 Mauergauz, Y. (2007). Computer aided operative planning in mechanical engineering . Moscow: Economics (in Russian). Pleshchinsky, A. S. (2004). Optimization of intercompany interactions and intracompany man- agement solutions . Moscow: Nauka (in Russian). Pleshchinsky, A. S., Pachkovsky, E. M., & Mikhailina, I. M. (2008). Coordinated optimization of logistics, production and financial performance of multi-stage enterprises . Moscow: Central Economic and Mathematical Institute of the RAS (in Russian). Prilutsky, M. K., & Vlasov, S. E. (2007). Multi-stage problems of scheduling theory with alterna- tive variants of job performance . iani.unn.ru/assets/files/priluckiy_mh/mnogostad_teoriya_ raspisanii.doc (in Russian). Rodnikov, A. N. (1995). Logistics. Dictionary of terms . Moscow: Ekonomika (in Russian). Stadtler, H., & Kilger, C. (2008). Supply chain management and advanced planning. Concepts, models, software, and case studies (4th ed.). Berlin: Springer. 244 7 Examples of Advanced Planning Models
Part II Planning Processes
Single-Echelon Inventory Planning 8 8.1 Inventory Types and Parameters This chapter discusses the stocks, their characteristics, and methods of stock planning. Stocks are generally classified (Grigoriev et al. 2007 ) by their intended purpose and economic and logistical functions. From the planner’s point of view, the main interest is in the division of all stocks into parts by functions in the logistics process as follows: • Current; • Safety; • Preparatory; • Seasonal. Preparatory stocks are for special preparation or incoming inspection prior to the production process—for example, wood drying, quality assurance laboratory tests, etc. The basis for the stocks calculation is demand values defined by the methods discussed above in Chap. 6 .
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