Northern Plane Company builds airplanes. The last step of the production process

Question

Northern Plane Company builds airplanes. The last step of the production process is to install the jet engines. Northern needs to determine its production schedule for the next 4 months, given the following data: Scheduled Maximum Unit Cost Unit Cost Month Installations Production of Production of Storage 30 30 20 15 35 25 0.4 1.2 0.2 4 Assuming all the scheduled installations should be satisfied in each month, and the production amount for each month could not exceed the maximum production capacity. If an engine is built in the month, a decision should be made that the whether the engine is installed in the month or not. If not, then the storage cost is associated with keeping the engine in the inventory for the month. For example, if we build an engine in month 1 and install in month 3, we pay $1.1 million for building, $0.4 million to hold through month 1 and another $0.4 million to hold through month 2. (Modified from Hillier & Lieberman) Consider this problem as a transportation problem and create a balanced transportation tableau for this problem (no need to solve)

Explanation / Answer

Maximum production over the 4 months (Capacity) = 15+35+25+10 = 85

Scheduled installations (Demand) = 30+30+20+5 = 85

The decision variable is number of units to produce in month i and install in month j

Balanced transportation tableau is as follows

The numbers show the unit cost (sum of production cost and storage cost)

Row headers show production month and columns headers show installation month

Illustration of unit cost: Cost of production of a unit in month 1 and installation in month 4 = 1.1+0.4*3 = 2.3

Similarly cost of production of a unit in month 2 and installation in month 4 = 1.3+0.1*2 = 1.5

And cost of production of a unit in month 3 and installation in month 4 = 1.2+0.2 = 1.4

Production Month 1 Month 2 Month 3 Month 4 Maximum Production Month 1 1.1 1.5 1.9 2.3 15 Month 2 1.3 1.4 1.5 35 Month 3 1.2 1.4 25 Month 4 1.4 10 Scheduled Installations 30 30 20 5

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