Upon reviewing your transportation issues, currently, the optimal transportations cost are $13,600 (as seen below). I recommend using the transportation modeling to find the distribution pattern that will meet the availability and the demand with the least amount of shipping costs. Using transportation model we find that the best and optimal warehouse solution based on the information (current conditions), Shanghai would ship 1300 units to warehouse 2. Shuzworld H would ship 300 units to Warehouse 1, 200 to Warehouse 2 and 1800 units to Warehouse 3. Finally, Shuzworld F would ship 2200 units to Warehouse 1. Using the transportation model to implement this shipping plan would reduce the cost associated with shipping from Shuzworld F to Warehouse 3 which is the most expensive route. Using the transportation model and increasing the production from 1300 units to 2800 units, the optimal transportation costs changes to $13,400.

The increase in supply shows that the best and optimal distribution pattern is Shanghai would ship 1500 units to warehouse 2. Shuzworld H would ship 300 units to Warehouse 1, and 1800 units to Warehouse 3. Finally, Shuzworld F would ship 2200 units to Warehouse 1. The additional units 1500 are shipped to a dummy warehouse, 1300 units are allocated to Shanghai and 200 units are allocated to Shuzworld H. Again, using the transportation model to implement this shipping plan would reduce the cost associated with shipping from Shuzworld F to Warehouse 3 which is the most expensive route. Additionally, increasing the supply units and storing them in a dummy warehouse decreases the transportation costs. By shipping the excess units to a dummy location does not increase the cost for the company. The transportation model finds the lowest cost by analyzing the different shipping methods.

In order to improve reliability, in the event of failure, it is my recommendation that we back up machine one. First we look at the current system reliability which is (.84*.91*.99) .7567. Next, we make the assumption the backup machine automatically starts if machine one fails. The resulting reliability is as follows: Machine One has reliability of .84. The back-up machine should have the same reliability. By adding a backup machine for machine 1, the reliability increases to .9744 as show below. 1-(1-.84)*(1-.84) = .9744

The overall system back up increases from .7566 to .8778.

Next, we make the assumption the backup machine automatically starts if machine two fails. The resulting reliability is Machine two has reliability of .91. The back-up machine should have the same reliability. By adding a backup machine for machine 2, the reliability increases to .9919 as show below. 1-(1-.91)*(1-.91) = .9919. Backing up Machine 2 increases the system reliability to from .7567 to .8248. Next, we make the assumption the backup machine automatically starts if machine three fails. The resulting reliability is as follows: Machine three has reliability of .99. The back-up machine should have the same reliability. By adding a backup machine for machine 3, the reliability increases to .7643 as shown below.

1-(1-.99) * (1-.99) = .7643

After analyzing the information from all three machines, it is my recommendation to back up Machine 1. Backing up machine 1 produces the highest system reliability. By providing system redundancy and backing up machine 1 produces the greatest reduction in system risk. Therefore, reducing cost to the company due to machine/system failure.

The optimum number of shoelaces to order for the Shuzworld Factory is 27386.12788. In order to determine the optimum number of shoelaces to order, the economic order quantity method was used. Based on the following conditions being known such as the demand for the shoelaces which is 300,000 per year, the cost per order is known-$125 and the holding cost is known .10 per pair of shoelaces. Knowing the aforementioned information an equation related to inventory is used to determine what the optimum order quantity should be for the Shuzworld Factory.

The EOQ method was the best decision analysis tool to use because the known facts presented earlier, such as the demand for the shoelaces which is 300,000 per year, the cost per order is known-$125 and the holding cost is known .10 per pair of shoelaces. Using EOQ decision analysis tool helped answer the question of “What is the optimum quantity to order? Thus, EOQ provides the answer to the question how many shoelaces should be ordered. D.

In order to compare the one-cashier and the two-cashier waiting line systems we look at the information we know. First we know that a sales takes place every 10 minutes which means that 6 sales takes place every hour. Additionally we know on average a sales transaction takes 5 minutes which means on average the service is 12 minutes per hour. First, using the one-cashier waiting line method, the average server utilization is .5. The number of customers in the queue is .5 and the average number of customers in the system is 1. The average waiting time in the queue is .083333 and the average time in the system is .166667.

Finally the probability (% of time) the system is empty is .5. Whereas, using the two-cashier waiting method, the average server utilization is .25 verses .5 for the on-cashier waiting line method. The average number of customers in the queue changes for .5 to .03333. The average number of customers in the system changes for 1 to .5333. The average waiting time in the queue decreases from .083333 to .0056. Additionally, using the two-cashier waiting line system changes the average time in the system from .166667 to .0889. Lastly, the probability (% of time) system is empty changes from .5 to .6. Based, on the information above, I recommend using the two-cashier waiting line system.

The two-cashier waiting line system is the best decision analysis tool because it provides the greatest amount of the customer service. Using this method, provides the customers with the service needed to have them return.