AGGREGATE PLANNING WITH THE TRANSPORTATION METHOD. Farnsworth Tire Company would like to develop an aggregate plan via the transportation method. Data that relate to production, demand, capacity, and cost at its West Virginia plant are shown in Table 13.6. APPROACH Solve the aggregate planning

Question

AGGREGATE PLANNING WITH THE TRANSPORTATION METHOD. Farnsworth Tire Company would like to develop an aggregate plan via the transportation method. Data that relate to production, demand, capacity, and cost at its West Virginia plant are shown in Table 13.6.

TABLE 13.6	Farnsworth’s Production, Demand, Capacity, and Cost Data
	SALES PERIOD
	MAR.	APR.	MAY
Demand	800	1,000	750
Capacity:
Regular	700	700	700
Overtime	50	50	50
Subcontracting	150	150	130
Beginning inventory	100 tires

COSTS
Regular time	$40 per tire
Overtime	$50 per tire
Subcontract	$70 per tire
Carrying cost	$2 per tire per month

APPROACH [latex]\blacktriangleright[/latex] Solve the aggregate planning problem by minimizing the costs of matching production in various periods to future demands.

Accepted Answer

SOLUTION [latex]\blacktriangleright[/latex] Table 13.7 illustrates the structure of the transportation table and an initial feasible solution.

When setting up and analyzing this table, you should note the following:

1. Carrying costs are $2/tire per month. Tires produced in 1 period and held for 1 month will have a $2 higher cost. Because holding cost is linear, 2 months’ holdover costs $4. So when you move across a row from left to right, regular time, overtime, and subcontracting costs are lowest when output is used in the same period it is produced. If goods are made in one period and carried over to the next, holding costs are incurred. Beginning inventory, however, is generally given a unit cost of 0 if it is used to satisfy demand in period 1.

2. Transportation problems require that supply equals demand, so a dummy column called “unused capacity” has been added. Costs of not using capacity are zero.

3. Because back ordering is not a viable alternative for this particular company, no production is possible in those cells that represent production in a period to satisfy demand in a past period (i.e., those periods with an “×”). If back ordering is allowed, costs of expediting, loss of goodwill, and loss of sales revenues are summed to estimate backorder cost.

4. Quantities in red in each column of Table 13.7 designate the levels of inventory needed to meet demand requirements (shown in the bottom row of the table). Demand of 800 tires in March is met by using 100 tires from beginning inventory and 700 tires from regular time.

5. In general, to complete the table, allocate as much production as you can to a cell with the smallest cost without exceeding the unused capacity in that row or demand in that column. If there is still some demand left in that row, allocate as much as you can to the next-lowest-cost cell. You then repeat this process for periods 2 and 3 (and beyond, if necessary). When you are fi nished, the sum of all your entries in a row must equal the total row capacity, and the sum of all entries in a column must equal the demand for that period. (This step can be accomplished by the transportation method or by using POM for Windows or Excel OM software.)

Try to confirm that the cost of this initial solution is $105,900. The initial solution is not optimal, however. See if you can find the production schedule that yields the least cost (which turns out to be $105,700) using software or by hand.

INSIGHT [latex]\blacktriangleright[/latex] The transportation method is flexible when costs are linear but does not work when costs are nonlinear.

LEARNING EXAMPLE [latex]\blacktriangleright[/latex] What is the impact on this problem if there is no beginning inventory? [Answer: Total capacity (units) available is reduced by 100 units and the need to subcontract increases by 100 units.]

RELATED PROBLEMS [latex]\blacktriangleright[/latex] 13.13–13.18 (13.20–13.22 are available in MyOMLab)
EXCEL OM Data File Ch13Ex5.xls can be found in MyOMLab.

Question 13.EX.5: AGGREGATE PLANNING WITH THE TRANSPORTATION METHOD. Farnswort...

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