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At the month end, if the company does not have enough cash to pay the wage or after paying the wage the company does not have enough cash for...

The_PigSkin_Ballet_Shoes Case.jpgThe_PigSkin_Ballet_Shoes (2).jpgThe_PigSkin_Ballet_Shoes (3).jpg Please solve this problem and build the simulation model

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At the month end, if the company does not have enough cash to pay the wage or after paying
the wage the company does not have enough cash for production in the next month, a short-
term loan can be obtained with a monthly interest rate of 10%. The principal and interest must
be paid back at the end of the next month. Note that you cannot borrow money for production in the current month. At the beginning, there are 50 pairs of shoes for each size. The beginning inventory of a month
plus the production quantity for that month amounts to the quantity available for sales in that month. The actual sales quantity will be the smaller of this total inventory and the demand. Shoes produced but not sold in a month can be carried over for sale in the next month. But it is
required that at the end of the year the company must salvage all leftover inventory at a price of $5 per pair. Hence, holding too much inventory towards the end of the year is not profitable. Here is a graphical illustration of what would happen in a month. Production Demand Possible ann & decisions realized, sales interest from previous
made & cash take place, & month paid, new loan
outflow cash inflow received, & wage paid ‘ Everything repeats
V The Current Period The Next Period Your job is to decide the production quantity for each size at the beginning of each month
before the demand is realized. The production quantities will be constrained by the production capacity and the monthly budget. The oal is to maximize the total cash at the end of the ear. Note that a production quantity that is too small will not only affect sales in the current month,
but also will affect sales in the future months. This is because if the demand of the current
month turns out to be high and the inventory is not enough, the company may not be able to
bring the inventory level back immediately due to the capacity limit. 0n the other hand, a production quantity that is too high is also problematic. If too much cash is used and the

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demand turns out to be low in the current month, then the company will not have enough cash to pay the wage and thus has to get the loan. Please collaborate with your teammates to find out a scientific way of deciding on the quantity in each month. You may use techniques such as linear programming and simulation. Your strategy will be tested in class on April 9. On that day, you and your teammates will make
decisions on the fly, and your performance (ending cash) will be compared against other teams.
The team that achieves the highest amount of ending cash will receive a reward. The mark of
each team will be determined according to a comparison against the highest possible amount
of ending cash. The team that does not show up or participate in the competition will receive a zero mark for the project. Table: The marking scheme Your ending cash [the highest possible amount Your mark 0.7 or above 0.6 or above 0.5 or above 0.45 or above 0.4 or above 8/10
0.35 or above 7.5/10
0.3 or above 7/10
0.25 or above 6.5/10
0.2 or above 6/10
0.15 or above 5.5/10
0.1 or above 5/10
0.05 or above 4.5/10 Below 0.05 4/10

The_PigSkin_Ballet_Shoes Case.jpg

THE PIGSKIN BALLET SHOES The PigSkin Company produces ballet shoes for children aged 3 to 7. The shoes have three sizes: S, M, and L. Each size has its independent monthly demand, which identically follows a binary
distribution with D _ {300 with probability 0.25
5‘ _ 100 with probability 0.75 D _ {300 with probability 0.35
M _ 100 with probability 0.65 300 with probability 0.45 D“ = {100 with probability 0.55 where t = 1, 2, ..., 12. The unit production cost for the three sizes are $6, $7, and $8 per pair,
respectively. The selling prices are all 520 per pair. The company has a limited production capacity, and a maximum of 600 pairs of shoes in total
can be produced each month. Besides the capacity constraint, the budget for shoe production
is also constrained each month by the amount of cash available. At the beginning, the company has 55,000 on hand. At the end of each month, the company has to pay a total wage of $6,000. All other expenses excluding productions and wages are ignored.

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