Abstract
The realization of supply chain management concepts goes along with the introduction of comprehensive software systems for supporting decisions at the strategic, tactical, and operational planning level. Moreover, in industry the focus has shifted from a pure logistics-oriented view towards the integration of pricing and revenue issues into cross-functional value chain planning models. This paper presents a practical decision support tool for global value chain planning in the production of chemical commodities. The proposed linear optimization model consists of various modules that reflect sales, distribution, production, and procurement activities within a company-internal value chain. The objective of the model is to maximize profit by coordinating all activities within the supply chain. The model formulation is related to a real industry case. It is shown how the model can be used to support decision making from sales to procurement by volume and value.
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Appendix
Appendix
Linear approximation of spot sales quantities and spot sales turnover
Since spot sales price and spot sales quantity depend on each other according to a linear price-quantity function, the profit function is quadratic. In the following, we show how a piecewise linear approximation of the sales turnover function can be achieved. In order to facilitate the presentation, we skip the indices for periods and product–location combinations.
The sales turnover approximation approach illustrated in Figure A1 is based on partial quantity points subdividing the sales turnover curve into multiple sections, for which sales turnover is linearly approximated. Let xmin and xmax denote management-defined control parameters that indicate the minimum and maximum spot demand that needs to be fulfilled, respectively. Partial spot sales quantities q̃ i are determined at each partial quantity point i∈N. Corresponding partial spot sales turnover ỹ i values are calculated for each partial spot sales quantity q̃ i using the exact sales turnover function. Partial spot sales turnover ỹ j between two partial quantity points is approximated based on the spot sales turnover gradient τ j of the linear connection for the partial quantity section j=1…N−1 between two partial quantity points. Corresponding partial spot sales quantities are denoted by x̃ j .
Linear sales turnover approximation.
The total spot sales quantity x equals the sum of the partial spot sales quantities x̃ j .
Partial spot sales quantities x̃ j must fit into the respective section between consecutive partial spot sales quantities q̃ i and q̃i−1.
Partial spot sales turnover ỹ j is determined as the product of the partial quantity x̃ j and the partial sales turnover gradient τ j .
Spot sales turnover y equals the sum of the partial spot sales turnovers ỹ j .
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Kannegiesser, M., Günther, HO. An integrated optimization model for managing the global value chain of a chemical commodities manufacturer. J Oper Res Soc 62, 711–721 (2011). https://doi.org/10.1057/jors.2010.18
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DOI: https://doi.org/10.1057/jors.2010.18