Page 371, Problem 3

Notice: Parisay’s comments are in red.

Solution by: Mr.Ta-Lun Huang

WINQSB Input

WINQSB Output

WINQSB Output: Range of Optimality

WINQSB Output: Range of Feasibility

Sensitivity Analysis for one of the Capacities (Month 4, Regular Time)

Tablet View

Graphical View

Sensitivity Analysis for one of the Unit Cost (Month 1 Regular Time Producing for Month 1 Demand)

Tablet View

Graphical View

Report to the Manager (Page 371 Problem 3)

Based on my research and WINQSB result, the optimal minimized cost of $10,660 can be achieved by producing at following optimal production schedule:

Optimal Production Schedule for Shoe Production
Labor Type at / Producing for / Amount of / Unit / Total
Different Month / Demand at / Production / Cost / Cost
Month 1, Regular Time / Month 1 / 200 / 7 / $1,400
Month 2, Regular Time / Month 2 / 200 / 7 / $1,400
Month 2, Overtime / Month 2 / 60 / 11 / $660
Month 3, Regular Time / Month 3 / 200 / 7 / $1,400
Month 3, Overtime / Month 3 / 40 / 11 / $440
Month 3, Overtime / Month 4 / 40 / 12 / $480
Month 4, Regular Time / Month 4 / 200 / 7 / $1,400
Month 4, Overtime / Month 4 / 100 / 11 / $1,100
Month 5, Regular Time / Month 5 / 190 / 7 / $1,330
Month 6, Regular Time / Month 6 / 150 / 7 / $1,050
Optimal Minimized Cost: / $10,660

Above optimal production schedule yields extra (unused) resource of the following list.

Overtime resource is not usually of importance to manager. They do not want to use them any way. So it is better to eliminate them from the following table.

Unutilized Resource
Labor Type at / Unused Unit
Different Month / of Production
Month 1, Overtime / 100
Month 2, Overtime / 40
Month 3, Overtime / 20
Month 5, Regular Time / 10
Month 5, Overtime / 100
Month 6, Regular Time / 50
Month 6, Overtime / 100

These extra resources can be allocated for other use if the company is producing at above optimal production schedule.

As shown in the above table, only Month 3 and Month 4 labor are producing for other month’s demand (For example, Month 3 Overtime labor is producing 40 unit for Month 4’s demand) and other months are not producing any unit for later month’s demand. This is due to the fact that it will increase the cost if the company is doing so. For example, Month 2 is using all 200 unit of regular time labor and 60 unit of overtime labor capacity to produce for Month 2’s 260 unit demand. Month 2 is not producing any unit for Month 3, Month 4, etc, even though Month 2 has extra unused 40 unit of overtime labor capacity. If the company wants to use Month 2 overtime labor capacity to supply for Month 3’s demand, the cost must be reduced at least by $1 from $12 to $11 before the company can do so. The other situation that might change the optimal solution is when the cost of using specific month’s labor to supply a specific month’s demand changes. For example, currently Month 2 regular time labor supplies Month 2’s demand at the cost of $7. The schedule remains optimal only when the cost is between $7 and $8. This means that when the cost is below $7 or above $8 the optimal production schedule will have to be reconsidered (recalculated) and it might not be the optimal solution anymore.

Changing the amount (in unit) of supply or demand can also affect the optimal solution. For example, for every extra unit Month 1’s regular time labor supplies, it will reduce the optimal cost by $3. This is effective for Month 1’s regular time labor supply of 200 up to 260 units. If the company wants to reduce Month 1’s regular time labor supply below 200 or increase it above 260, the problem will have to be reconsidered.

For sensitivity of one of the Capacities, I choose the supply from Month 4’s regular time labor. I choose this specific capacity because month 4 has highest demand among all months, it has 140 units more than Month 4’s regular time labor can handle. From the optimal production schedule, Month 4’s regular time labor can supply (produce) 200 units for Month 4’s demand. From analysis, every extra unit Month 4’s regular time labor supplies can reduce the optimal cost by $5 and this will be true if Month 4’s regular time labor is producing from 200 to 240 units. From the table and it’s graphical view, when Month 4’s regular time labor is producing less than 200 units the optimal cost will be higher and higher, the more Month 4’s regular time labor can supply, the less the cost. The statement of “every extra unit it supplies reduces the cost by $5” is only correct when the supply is between 200-240 units. When the supply is below 200 units or above 240 units, a new calculation will need to be done to calculate optimal solution.

For sensitivity for one of the Unit Cost I choose the cost of Month 1 regular time labor supplying Month 1’s demand. I choose this because the cost is without considering overtime or inventory. For this cost analysis, the unit cost is $7. From the graph, the more the cost, the higher the optimal cost will be. At range of up to $8, every $1 increase in cost will increase the optimal solution by $200 and vies-versa. To calculate the optimal solution of cost more than $8, a new calculation will have to be done.

As you can see the current solution does not include many possible combinations of labor type and production month. This result is due to various reasons. For Month 1, Month 1 is only using regular time labor to produce 200 unit of product to meet the demand of exactly 200 units. This means that Month 1 is not producing any unit for other months as well as using overtime labor, which costs more. If the company want to use Month 1 overtime, or even regular time labor, to produce for other month, the cost must be reduced (mainly inventory cost, or the company need to produce the product at lower cost). For example, if the company wants to use month-1’s overtime labor to produce for month-2’s demand, the cost muse be reduced by $1 from $12 to $11 (most likely can be achieved if there is no inventory cost). Month 2 is using both regular time and overtime labor to meet Month-2’s demand. If the company wants to use Month-2’s production capacity to meet future month’s demand the cost must be reduced as well. Month-3 and Month-4 are both using regular time to produce for current month and next month’s demand. Both months are using overtime to meet current month’s demand.

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