HW7_Solutions

# HW7_Solutions - IS A warehouse facility in a ttansportation...

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Unformatted text preview: IS. A warehouse facility in a ttansportation system has a number of incoming and outgoing links. At least 111) units but no more than 11301:) units must pass through the facility per unit time. A cost of \$ | 5 is charged for each of the ﬁrst SUD units and EU for each additional unit. Develop a network model for the facility. One answer is below. There are other correct answers. (lower. upper. cost} it], Still]. IS | DU. | limit} [i]. SEE]. 2G} IS. A small university has four buildings. r—‘t through D. and six faculty parking lots. [ through ‘v']. a. With the data in the table below determine the lots to which the building occupants should be assigned to minimise the total walking distance for the faculty. b. Say that five faculty members in each building are full professors. two are associate professors. and the remainder ane assistant professors. Use a goal programming approach to assure that the full professors have priority over all others and that the associate professors have priority over the assistant professors in the assignment of parking spots. Distance to parking lots (blocks) Number of Buildin facult l 11 ll] l‘vr v ‘v'[ A 15 III 1 3 2 l 4 B 2] l 4 3 2 5 3 C l3 2 | I III 2 3 o r s s 5 4 5 7 Capacity of lots 5 IE IS ll] 3 IS Hint: To give priority to the higher ranks. multiply the associate professors1 travel cost by it] and the full professorsr travel cost by IDG. Network Model ['15] [21] ['13] [7’] [fixed flow] Part 3. Numbers on arcs are asoig nmento. The solution has total distance at 105. [ﬁxed flow] [‘5] [21] [13] P] {flow} F'art b. lvlust define a node for each professor type. and an are from each professor type to each parking lot. We multiply the distances for full professors by too, associate professors by to and assistant professors by 1. This gives the required priority structure. The figure below shows the assignment of professors to lots. The total distance traveled by all professors is still 106 as in part a. but here the full and associate professors are given special consideration. Name I II III l'v' 'v' "v'l Min. Max. Prof a o 2 o o s o 1 Prof H s o o e o o Prof c o o o s o 0 Prof o o o o s o o m assoc a o s o o o o Assoc e o o o o o 2 Assoc c o o 2 e o o rises: o o o 2 o o o Assis a o e o o o o mm Assis e o o s e o s see c o o s o o 0 mm Assis o o o o o o o mm Min.: Max: 2 l. A company has two plants. P1 and P2. that manufacture three products. r—‘t. B and C. The number of labor hours needed to produce a unit of each product is shown on the left in the table below. The cost of raw materials is shown on the right. The weekly demand for the three products is 1ooo. 50D and res, respectively. There are ISUU labor hours available at both plants. Set up a network flow model with the objective of minimizing raw material costs, and find thc solution that will mcct the demand for the products without exceeding the labor constraints. Labor hours per Raw material cost {3} unit of product per unit of product Plant Pl P2 Hint: The network should he bipartite with ﬂow going from plants to products. Each arc should have two parameters: costihr and a gain factor in terms of productsr'hr. The units of flow in the network should he ‘hours.‘ [ii-“m mime-“1 [-Dﬁmandl The easiest wattr to few the are CI. 2 gramme-m. [\$1ﬂrpmduc1. 1 . . . a construction Is a series of two Fl ' hi: ' mm - "W'" “3 Hm” area, one changing hours to * graduate and one Charging fer mm“ “we” [Demand] th raw material eeet [SEQIheuL 2 pmduelall'iuur} e ' 0 Flaw in heure 0 Any eeriee arrangement of area can be changed inte a single equivalent are. The structure for the given preblern ie ehewn belew [Fixed Flew] [LI pper. Geet} (Cast, Gain} {1 see, | |_ In the dileeted netwerk below ﬁnd the slmrt path from the met nude ] It! all ether nodes. [theta nee) [?l [22] [30] [41] Order of entry of the nodes into the tree: 1. 3, 2, 4,5,1 5. B, 9. ...
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