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Introductory examples Description
Further explanation of this example: 'Applications of optimization with Xpress-MP', Introductory examples (Chapters 1 to 5) of the book 'Applications of optimization with Xpress-MP'
Source Files By clicking on a file name, a preview is opened at the bottom of this page. Data Files pricebrinc.mos (!****************************************************** Mosel Example Problems ====================== file pricebrinc.mos ``````````````````` Incremental pricebreaks formulated with SOS2 This model represents the situation where we buy a certain number of items and we get discounts incrementally. The unit cost for items between 0 and B1 is C1, whereas items between B1 and B2 cost C2 each, and items between B2 and B3 cost C3 each. This implementation uses Special Ordered Sets of type 2 (SOS2). At the points 0, B1, B2 and B3, we introduce continuous decision variables 'w(i)' (i = 0, 1, 2, 3). We also define cost break points 'CBP(i)' that correspond to the total cost of buying quantities 0, B1, B2 and B3. Then, 'w(i)' defines a SOS2 with reference row coefficients given by the coefficients in the definition of x. In this example, we use 'makesos2' to define the SOS2. (c) 2008 Fair Isaac Corporation author: S. Heipcke, Sep. 2006 *******************************************************!) model "Incremental pricebreaks (SOS2)" uses "mmxprs" declarations NB = 3 ! Number of price bands BREAKS = 0..NB COST: array(1..NB) of real ! Cost per unit within price bands w: array(BREAKS) of mpvar ! Weight variables x: mpvar ! Total quantity bought B,CBP: array(BREAKS) of real ! Break points, cost break points end-declarations DEM:= 150 ! Demand B:: [0, 50, 120, 200] COST:: [0.8, 0.5, 0.3] CBP(0):= 0 forall(i in 1..NB) CBP(i):= CBP(i-1) + COST(i) * (B(i)-B(i-1)) ! Objective: total price TotalCost:= sum(i in BREAKS) CBP(i)*w(i) ! Meet the demand x = DEM ! Definition of x Defx:= x = sum(i in BREAKS) B(i)*w(i) ! Weights sum up to 1 sum(i in BREAKS) w(i) = 1 ! Definition of SOS2 ! (we cannot use 'is_sos2' since there is a 0-valued coefficient) makesos2(union(i in BREAKS) {w(i)}, Defx) ! Solve the problem minimize(TotalCost) ! Solution printing writeln("Objective: ", getobjval, " (avg price per unit: ", getobjval/DEM, ")") forall(i in BREAKS) writeln("w(", i, "): ", getsol(w(i)), " (price per unit: ", if(i>0, CBP(i)/B(i), CBP(i)), ")") end-model | |||||||||||||||||||||||||||||||||||||
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