【正文】 全國領(lǐng)先的工作效率提升平臺 第五講 Transportation and Network Models 全國領(lǐng)先的工作效率提升平臺 Introduction Several specific models (which can be used as templates for reallife problems) will be introduced. TRANSPORTATION MODEL ASSIGNMENT MODEL NETWORK MODELS 全國領(lǐng)先的工作效率提升平臺 Introduction TRANSPORTATION MODEL ASSIGNMENT MODEL Determine how to send products from various sources to various destinations in order to satisfy requirements at the lowest possible cost. Allocating fixedsized resources to determine the optimal assignment of salespeople to districts, jobs to machines, tasks to puters … NETWORK MODELS Involve the movement or assignment of physical entities (., money). 全國領(lǐng)先的工作效率提升平臺 Transportation Model An example, the AutoPower Company makes a variety of battery and motorized uninterruptible electric power supplies (UPS’s). AutoPower has 4 final assembly plants in Europe and the diesel motors used by the UPS’s are produced in the US, shipped to 3 harbors and then sent to the assembly plants. Production plans for the third quarter (July – Sept.) have been set. The requirements (demand at the destination) and the available number of motors at harbors (supply at origins) are shown on the next slide: 全國領(lǐng)先的工作效率提升平臺 Demand Supply Assembly Plant No. of Motors Required (1) Leipzig 400 (2) Nancy 900 (3) Liege 200 (4) Tilburg 500 2021 Harbor No. of Motors Available (A) Amsterdam 500 (B) Antwerp 700 (C) Le Havre 800 2021 Balanced 全國領(lǐng)先的工作效率提升平臺 Graphical presentation of Le Havre (C) 800 Antwerp (B) 700 Amsterdam (A) 500 Supply Liege (3) 200 Tilburg (4) 500 Leipzig (1) 400 Nancy (2) 900 and Demand: 全國領(lǐng)先的工作效率提升平臺 Transportation Model AutoPower must decide how many motors to send from each harbor (supply) to each plant (demand). The cost ($, on a per motor basis) of shipping is given below. TO DESTINATION Leipzig Nancy Liege Tilburg FROM ORIGIN (1) (2) (3) (4) (A) Amsterdam 120 130 41 (B) Antwerp 61 40 100 110 (C) Le Havre 90 122 42 全國領(lǐng)先的工作效率提升平臺 The goal is to minimize total transportation cost. Since the costs in the previous table are on a per unit basis, we can calculate total cost based on the following matrix (where xij represents the number of units that will be transported from Origin i to Destination j): Transportation Model 全國領(lǐng)先的工作效率提升平臺 TO DESTINATION FROM ORIGIN 1 2 3 4 A 120xA1 130xA2 41xA3 B 61xB1 40xB2 100xB3 110xB4 C 90xC2 122xC3 42xC4 Total Transportation Cost = 120xA1 + 130xA2 + 41xA3 + … + 122x C3 + 42xC4 Transportation Model 全國領(lǐng)先的工作效率提升平臺 Two general types of constraints. 1. The number of items shipped from a harbor cannot exceed the number of items available. For Amsterdam: xA1 + xA2 + xA3 + xA4 500 For Antwerp: xB1 + xB2 + xB3 + xB4 700 For Le Havre: xC1 + xC2 + xC3 + xC4 800 Note: We could have used an “=“ instead of ““ since supply and demand are balanced for this model. Transportation Model 全國領(lǐng)先的工作效率提升平臺 2. Demand at each plant must be satisfied. For Leipzig: xA1 + xB1 + xC1 400 For Nancy: xA2 + xB2 + xC2 900 For Liege: xA3 + xB3 + xC3 200 Note: We could have used an “=“ instead of ““ since supply and demand are balanced for this model. For Tilburg: xA4 + xB4 + xC4 500 Transportation Model Two general types of constraints. 全國領(lǐng)先的工作效率提升平臺 Variations on the Transportation Model Suppose we now want to maximize the value of the objective function instead of minimizing it. In this case, we would use the same model, but now the objective function coefficients define the contribution margins (., unit returns) instead of unit costs. Solving Max Transportation Models 全國領(lǐng)先的工作效率提升平臺 When supply and demand are not equal, then the problem is unbalanced. There are two situations: When supply is greater than demand: When Supply and Demand Differ In this case, when all demand is satisfied, the remaining supply that was not allocated at each origin would appear as slack in the supply constraint for that origin. Using inequalities in the constraints (as in the previous example) would not cause any problems. Variations on the Transportation Model 全國領(lǐng)先的工作效率提升平臺 In this case, the LP model has no feasible solution. However, there are two approaches to solvi