Supplement D - Solution Manual Krajewski Operations Management Processes and Supply 11th Edition - Managing Supply Chains

Linear Programming l SUPPLEMENT D l D-29


b. The minimized cost to satisfy all demand is $1,490,900 and is achieved by executing the
following plan:

Beginning Regular Time Overtime Ending Demand
Inventory Production Production Inventory Satisfied
Quarter 1 40,000 400,000 0 340,000 100,000
Quarter 2 340,000 400,000 40,000 370,000 410,000
Quarter 3 370,000 400,000 40,000 40,000 770,000
Quarter 4 40,000 400,000 40,000 40,000 440,000

The formulation and solution are provided in the POM for Windows output below:




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, D-30 l PART 3 l Managing Supply Chains




c. A new formulation is required to include subcontracting.
New decision variable Si = Subcontracted production in pounds for quarter i
Minimize Z = .81P1 + .81P2 + .81P3 + + .81P4 + 1.1S1 + 1.1S2 + 1.1S3 + 1.1S4
+ .9O1 + .9O2 + .9O3 + .9O4 + .11I1 + .11I2 + .11I3 + .11I4
Subject to:
Production in Q1: P1 + S1 + O1 + I1 - I2 = 100,000
Production in Q2: P2 + S2 + O2 + I2 - I3 = 410,000
Production in Q3: P3 + S3 + O3 + I3 - I4 = 770,000
Production in Q4: P4 + S4 + O4 + I4 - I5 = 440,000
Regular Time Q1: P1 ≤ 400,000
Regular Time Q2: P2 ≤ 400,000
Regular Time Q3: P3 ≤ 400,000
Regular Time Q4: P4 ≤ 400,000
Overtime Q1: O1 ≤ 40,000
Overtime Q2: O2 ≤ 40,000
Overtime Q3: O3 <= 40,000
Overtime Q4: O4 ≤ 40,000
Beginning Inventory: I0 = 40,000
Ending Inventory: I4 = 40,000


The minimized cost to satisfy all demand is now $1,489,300 and is achieved by executing
the following plan:

Beginning Regular Overtime Subcontracted Ending Demand
Inventory Time Production Production Inventory Satisfied
Production
Quarter 1 40,000 360,000 0 0 300,000 100,000
Quarter 2 300,000 400,000 40,000 0 330,000 410,000
Quarter 3 330,000 400,000 40,000 0 0 770,000
Quarter 4 0 400,000 40,000 40,000 40,000 440,000




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