Question 3) (40 points) Consider a transportation problem. There are a set of suppliers and a set of customers in a region. The customers have their known demand of a specific product. Suppliers have supply capacities for the product. An operations manager wants to make shipment decisions, i.e., how many items to ship from each supplier to each customer, subject to the demand requirements and supply capacities. The demand and supply information are presented below.

Table 1

	Customer
Supplier	1	2	3	Supply Capacity
A	7	10	10	50
B	9	5	9	50
C	10	10	7	50
D	10	8	5	50

We want to determine a shipment plan to satisfy customers demand in the month of April. We do not have demand information for April. But we have historical demand data for the previous 11 months for each of the customers.

Table 2

		Demand
Period	Month	Customer 1	Customer 2	Customer 3
1	May	48	55	30
2	June	46	47	45
3	July	53	43	33
4	August	58	60	60
5	September	52	54	62
6	October	54	46	67
7	November	65	45	69
8	December	69	44	99
9	January	71	55	102
10	February	74	44	107
11	March	75	33	103

1. Apply the following three forecasting models to predict Aprils demand for each customer.

1. 4-month moving average
2. Exponential Smoothing with =0.4
3. Trend Line (regression)

Answer:

Table 3

	April Demand Forecast
	Customer 1	Customer 2	Customer 3
4 Month Moving Average
Exponential Smoothing
Trend Line (Regression)

2. Use Mean Squared Error (MSE) evaluation method to select the best forecasting model for each customer. Report MSE of each forecasting model for each customer.

Answer:

Table 4

	Mean Squared Error (MSE)
	Customer 1	Customer 2	Customer 3
4 Month Moving Average
Exponential Smoothing
Trend Line (Regression)

3. For each customer, put Aprils prediction of the best model in the table below:

Table 5

	Customer
	1	2	3
April Demand	79	41	120

4. Use Excel solver to solve a transportation problem for the month of April based on cost and supply information of Table 1 and demand information of Table 5. (If you could not solve parts a, b, c, use demands of 60, 70, and 75 for customers 1, 2, and 3 respectively). You should make sure that demand of the customers is satisfied, and supply capacity of the suppliers is not violated. Can you solve this problem? What is the minimum transportation cost for this problem? What is the capacity utilization of supplier 3?