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# The production change cost Thesis

## Tom Salmons – Part I _Answer

 Ebony Bath Soap Solution Question 1) Question 2) Risk is used to simulate 500 iterations of each of 6 values of U (those in the range J13:J18), using a RiskSimtable function in ce The Summary Report shows the results, some of which are copied to the Simulation sheet. Question 3) The mean, standard deviation and confidence intervals for each value of U is tabulated in the Simulation sheet. The smallest yearly value occurs with U= 60, although this could change if the simulation were done with different random numbers. A plot of the mean annual cost is shown below the tabulated results Question 4) Other values of U and L could be tested. Note that the policy as stated never returns to a production level of 120 onve the production level changes. Other policies could be investigated which return to a 120 production level. For example, another policy would be to produce 120 units if inventory crosses the midpoint of the range [L, U].

See the Simulation sheet, columns A-H, for the solution to the 52-week simulation. The major components to calculating the cost for a given week are demand generation, inventory calculation, and production level setting. Column D tracks the inventory which is calculated as last week’s inventory plus this week’s production (which was set last week) minus this week’s demand or zero, whichever is larger.

This ensures that inventory cannot be negative, and thus, no backorders. Column E indicates the production level to be set for the following week. A nested IF statement is used. The first check is to see whether this week’s inventory is less than l (here, 30). If so, next week’s production level is set to 130. If not, the inventory level is checked to whether is greater than u (here, 80).

If so, next week’s production level is set to 110. Otherwise, the production level is unchanged. All that remains is to calculate the inventory and production change cost. The inventory cost calculated in column F is simply the per unit inventory cost (here, 30) multiplied by this week’s inventory. Calculating the production change cost in column G is more challenging.

The production change cost (here, 3000) is multiplied by the results of an IF statement is used to check if the production level has been changed. If there was a change, 3000 is multiplied by one, otherwise, if no change occurred, then 3000 is multiplied by 0. Column H is simply the sum of the two costs for the week. Cell H9 totals the costs over the year.

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