Question

Transportation Method (Example) Mar 800 Demand Capacity: 1000 1,100 Regular Overtime Subcontracting 800 100 200 100 Costs 700 100 300 700 50 150 Beginning invento $30 per tire $50 per tire Regular time Overtime Subcontracting$60 per tire Carrying $4 per tire per month

We use the transportation tableau to find the optimal solution

please show working

Answer 1

In order to formulate the problem as a transportation model, we need to create the parameter table. Rows of the parameter table show supply period and columns indicate demand period. Regular cost of production in a supply period to fulfil the demand of same period is as given in the problem. For example regular production cost in period 1 to fulfil the demand of period 1 is $ 30 and overtime cost in the same supply and demand period is $ 50. Subcontract cost is $ 60.

Regular time Cost of fulfilling demand of n months later than the current month increases by n times the carrying cost. For example, cost of fulfilling demand of month 3 (2 periods later) from overtime time supply of month 1 = 50+3*4 = 62

While calculating net demand, opening inventory is subtracted from first month demand and required closing inventory is added to the last month demand.

EXCEL Formulas:

Cell	Formula	Copy to
K11	=SUM(H11:J11)	K11:K19
H20	=SUM(H11:H19)	H20:J20
K8	=SUMPRODUCT(B11:D19,H11:J19)

Total cost = $ 99,500