Question

China Pride Medical Devices (CPMD), an assembler of sophisticated medical products, must maintain a ready supply of high-quality components to manufacture its products.

To achieve this goal, CPMD’s Purchasing Department checks inventory levels each day by reviewing the inventory items stock list. When the quantity on hand of a particular component reach its economic reorder point, CPMD’s Purchasing Department places a purchase order within its supplier (supplier data is accessed from the supplier list) for that component and files a copy in the purchase order file. When a supplier delivers a shipment along with a bill of lading, Shipping and Receiving (S/R) receives the shipment by performing a three-step process.

First, the S/R clerk verifies the shipment by assessing a copy of the purchase order and comparing it to the bill of lading. If a received item appears on the purchase order and the bill of lading, the verified bill of lading and received items are passed to Inspection. Otherwise, the S/R clerk generates a notice of shipment error, which is sent to the supplier.

Next, inspection inspects the valid shipment items by accessing the quality criteria form the inspection criteria folder. If the item meets all the quality criteria, the inspector adds it to an Accepted Items list, which is forwarded to the inventory clerk. If an item doesn’t pass inspection, the inspector creates a notice of defective shipment, which is sent to the supplier along with the defective items.

Finally, the inventory clerk updates the inventory items by adding the current on hand quantity of each item to the accepted-item quantity, reflecting an updated quantity.

1. Create a Context Diagram of the above system.

Answer 1

Decision variable Xz -Number ofunits shipped from location"" to Here,i-1, 2, 3, 4 j-3,4, 5, 6, 7 Objective function: Objective is to minimize the total shipping cost. Subject to s +X,S1000 Manufcaturing capacity 1000 50 s -500 Demand constraints +610 Xy3+125-X34-X35-X36-X37=0 Flow in umts at a node should be equal to Flow out unit 4343 45 47 20

solve the problem in excel,

x13 x14 x23x24x34X43 X35X36 x37X45 x46 x47 2 Decision variable 4 Obiective function: $7 $8 $4$7 $3 $3 $25 $6$17 $29 $8 $5 6 Constraints: 7 x13+ x14 8 x23+ x24 9 x35+x45 10 x36+x46 11 x37+X47 12 x13+x23-x34-x35-x36-x37 13 x14+x24-x43-x45-x46-x47 1000 仁 1000 450 500 610 0 0 1 1-1 0

Formulas used,

B CD E F G H JK L M x13 x14 x23 x24 x34 x43 x35 x36 x37 x45x46 x47 2 Decision variable 4 Objective function: 7 8 4 7 3 3 25 6 17 29 8 5 SUMPRODUCT($B$2:$M$2,B4:M4 6 Constraints: 7 x13 +x14 8 x23+ x24 9 x35+x45 10 x36+x46 11 x37+x47 12 x13+x23-x34-x35-x36-x37 1 13 x14+x24-x43-x45-x46-x47 SUMPRODUCT(SB$2:SM$2, B7:M7 -SUMPRODUCT(SB$2:SM$2,B8:M8) SUMPRODUCT(SB$2:SM$2,B9:M9) :SUMPRODUCT($B$2:$M$2,B10:M10) =SUMPRODUCT($B$2:$M$2,B11:M11) :SUMPRODUCT($B$2:$M$2,B12:M12) -SUMPRODUCT($B$2:$M$2,B13:M13) 仁 1000 仁 1000 = 450 500 610 = = = 1-1-1 -0

solver parameter,

Solver Parameters SNS4 Set Objective To:OMax By Changing aiable Cells: SBS2 SMS2 O Min Value O Subject to the Constraints: SNS12 SPS12 SNS13 SPS13 SNS7:SNS8SPS7:SPS8 SNS9: SNS11 = SPS9: SPS11 Add Change Delete Reset All Load/Save Make Unconstrained Variables Non-Negative Select a Solving Method: Simplex LP Options Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non-smooth. Help Solve Clgse

answer,

x13 x14 x23x24x34X43 X35X36 x37X45 x46 x47 0 610 2 Decision variable 0 560 950 50 0 450 500 0 4 Objective function: $7 $8 $4$7 $3 $3 $25 $6$17 $29 $8 $5$25,930 6 Constraints: 7 x13 +x14 8 x23+ x24 9 x35+x45 10 x36+x46 11 x37+X47 12 x13+x23-x34-x35-x36-x37 13 x14+x24-x43-x45-x46-x47 14 1000 1000 仁 1000 500 610 0 0 610 1 1 1-1

Solution:

Units shipped from Madison to Philadelphia = 0

Units shipped from Madison to Knoxville = 560

Total units shipped = 0+560 = 560

Units shipped from Atlanta to Philadelphia = 950

Units shipped from Atlanta to Knoxville = 50

Total units shipped = 950+50 = 1000

Units shipped from Philadelphia to Knoxville = 0

Units shipped from Knoxville to Philadelphia = 0

Units shipped from Philadelphia to Dayton = 450

Units shipped from Philadelphia to Bloomington = 500

Units shipped from Philadelphia to Albany = 0

Units shipped from Knoxville to Dayton = 0

Units shipped from Knoxville to Bloomington = 0

Units shipped from Knoxville to Albany = 610