Answered>Order 20282

URETEN Company is a manufacturer of a new brand of toothpaste. While managing its inventory costs, URETEN wants to minimize its total costs. The inventory management policy of URETEN can be described as follows: The production can be done at only three levels per week: 50, 70, 100 units. There is a cost of changing production level from one week to another week given as $5000. Holding cost of a unit of toothpaste is given as $20 per week.

Company planners think that the demand for this toothpaste can be modeled with a Triangular distribution that is considered to be a good approximation; with minimum demand assumed to be 70 units, most likely demand 80 units and maximum demand of 100. The company does not operate with backorders. That is, if the demand is higher than the on hand inventory, it is lost for good.

The production process of URETEN is managed with a simple rule based policy: Every week, current inventory level is monitored by the decision makers. If the current inventory is less than 10 units, then URETEN will produce 100 units in the next week. If the current inventory is higher than 30 units, it will produce 50 units in the next week. If these two conditions are not satisfied, then the production level will be kept at the same level of the previous week. You are employed as an operations consultant to the company. And your analysis begins with the current values of on hand inventory which is 100 units and the production level of last week as 100 units.

You are expected to provide answers to the following questions:

1. Develop a simulation model for this company for 36 weeks. Comment on the total annual cost (inventory holding and production cost change) distribution for the 36 weeks. Present the necessary statistical summaries as well as charts for its distribution. Also provide simulation results for the average inventory distribution for 36 weeks. Simulation can be run for 1000 iterations.

2. The company uses fixed lower and upper inventory bounds, 10 and 30 respectively. Given fixed lower bound of inventory level that is 10 units, conduct a sensitivity analysis on the upper bound. In other words, run a simulation for different values of the upper bound and analyze how the total annual cost as well as average inventory level change. You may use a range of [10,30] with increments of 5 units.

3. Once the total annual cost distribution is generated for different simulations of varying upper bounds in question 2, using your statistical knowledge, create 95% confidence interval for the average 36 week total annual cost for each value of the upper inventory bound. Then, chart the changes of the average total cost with respect to the upper bound and find the best value of the upper bound that minimizes the average total cost for 36 weeks. Also show how the average inventory changes with respect to the upper inventory bound with a graph. Finally, provide an intuitive explanation for the connection with the average inventory level changes with the annual total cost changes.