# problem Bank Assignments

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Problem Bank

Problems 1-2 from Chap. 3 in Problem Bank
Problems 1-3 from Chap. 7 in Problem Bank
Problem in Chap 10 in Problem Bank

Chapters 1 and 2:

1. A manager wishes to produce a product at the rate of 20 units per hour from a machine. The processing time per unit product is 2 minutes on the machine. The batch size to be used must be 50. What is the maximum allowable set-up time, assuming there is no waiting time at the machine?
2. A supply chain manager needs to order raw material for a product.  The demand for this raw material translates into, on the basis of the forecast of the demand for the product, to be about 200 units per month.  The fixed cost per order is \$2000, while the holding cost per unit per month (of the raw material) is about 60 cents.

a. What should be order size?

b. What will be the total cost per month under this order size?

c. If the demand is approximately constant, what should be the level of inventory when the order is placed when the ordering lead time is about 2 weeks?

1. A batch of material must visit 5 workstations in a series to be converted to finished product.
1.  Each batch consists of 100 units.  The setup time at each workstation is 1 hour.  The processing time of each unit is 2 minutes.  Assume the material handling time to be nearly zero.  Compute the lead time of the batch.
2. Now if the batch is split into 10 transfer batches, what will be lead time be?  If the product is demanded at the rate of 200 units per day, what will be the average work-in-process inventory in the system for this product?  Assume a 24-hr shift per day.
1. A system operates under MTS. The fixed costs for manufacturing a product per production cycle are about \$500.  The demand forecast for this product is 10 units per day. The inventory holding costs for the finished product are about 2 cents per day per unit.  How many items should be produced in one production cycle (that is, the production quantity or the lot size)? [Hint: Use the EOQ (also called “square-rooted”) formula to determine the answer (i.e., the production quantity), using the fixed costs to equal A in the EQO formula].
2. A company has annual sales of 35 million dollars and the inventory at the end of the year is about 10 million dollars.  Calculate the inventory turns for this company.

Chapter 3:

1. A firm has discovered that its sales are highly correlated to a certain economic parameter. The value for that parameter has been predicted to be 15 for the next year (7th year). Use regression modeling to develop a forecast for the next year.
 Year 1 2 3 4 5 6 Econ. Parameter 16.2 14.9 18.5 16.1 13.8 15.4 # Sales 120 100 165 140 100 110

1. Exponential smoothing is to be used in forecasting as the only independent variable (parameter) available in the data is the year. Assume the value of the smoothing coefficient to be 0.25. Develop the forecast for the 6th month.
 Month 1 2 3 4 5 6 Sales 17 17.4 18 17.2 21.4 ?

Chapter 4:

1. A product manufactured in-house costs \$1.12 per unit and the fixed costs of manufacturing are \$13,500 per year.  It can be bought from the vendor for \$1.55 per unit.  The expected demand for this product within the company is about 20,000 per year.  Should you produce this in-house or buy it from the vendor?
2. The cost of holding inventory for a product is about \$2.00 per year.  The annual demand for this product is about 150 units.  The set-up cost is \$145. The average order size for this product is about 30 units.  The annual cost of tracking the inventory in MTS is about \$400.  The backordering penalty is about \$100 per order.  Should this item be MTS or MTO?

Chapter 7:

1. Push carts are being used in a system run on kanbans, where there is one kanban per cart load. A cart load is the production quantity, and each cart holds 12 parts. The lead time for production of one cart is 4 hours, while the demand in one shift of 8 hours is about 100 parts. Use a factor of safety (l) of 0.1. How many kanbans are needed in this system?

1. A kanban system has a rate of delivery, which equals the rate of arrival to the system, of 60 batches in a 10-hr day. Each batch contains 8 parts, and the processing time of a batch is exactly 8 minutes. The time between arrivals is known to have the exponential distribution. Compute the proportion of time the system is busy (ρ), the lead time, and the WIP (in terms of batches).

1. In the problem above, now assume that the inter-arrival time of one load is uniformly distributed between 10 and 15 minutes, while the processing time is now a random variable. Sample data collected for the processing time (in minutes) are as follows:

 6.4 8.2 7.7 9.5 6.8 9.6 10.2 4.3 9.2 8.1

Re-compute the proportion of time the server is busy, the lead time, and the WIP (in terms of batches).  Note: Sample Variance is computed as follows: i=1k(xi-x)2k-1  where k denotes the number of samples, x  denotes the mean, and x(i)  denotes the i th sample.

Chap 10:

Control charts need to be set up for a process where the underlying dimension being monitored displays a normal distribution. From the data, X=12.6  and R=1.5.

Compute the upper and lower control limits for the X - and the R-chart if the sample size in each subgroup equals 7. Also compute the process standard deviation. Finally, compute the process capability if the LSL is 12.2 and the USL is 13. 