UAMS - IBS Moscow Executive MBA Program Management Decision Methods Control Homework#1_1 (стр. 4 )

	Site 1	Site 2	Site 3	Site 4	Site 5	Site 6	Site 7
W1	25	55	60	20	25	35	25
W 2	65	20	25	65	45	40	50
W 3	40	15	40	50	30	35	35

a.  Make the transportation plan that minimizes the transportation costs for delivery from plants to sites, from plants to warehouses and from warehouses to sites simultaneously. Please, take into account that 505 blocks for the second order can be distributed between the warehouses in the following way: 150 blocks for W1, 150 blocks for W2 and 205 blocks for W3.

b.  What would the transportation costs be of you split the problem by the two parts: first one transportation problem is for Plants – Sites, and the second one is for Plant – Warehouses and Warehouses - Sites?.

The available capacities of each plant for this order are the following

P1	P2	P3	P4	P5
290	165	235	255	105

A company would like to invest some excess free cash – $ to certificates of deposit with 1, 3 and 6 months repayment periods. (After the repayment period the certificate turns into cash plus interest rate). All invested money should turn into cash in 6 months. Every month the company needs some cash for operations (the required amounts of cash are presented in the table 2. Negative amount means that additional cash can be invested in CD). In addition to these requirements the financial director would like to have “safety stock” of $60000 during this 6-month period.

Table 1

CD repayment period	Interest rate	CD price
1 month	12%	2000
3 months	16%	3000
6 months	18%	5000

Table 2

	July	August	September	October	November	December
Cash for operations	75000	-10000	-20000	80000	50000	-15000

Make up the investment plan that maximizes the income and meets the constraints for the amount of free cash for operations.

A company is going to produce 4 new models of computer processors Celeron, Pentium-3 , Pentium-4 and Xeon-4 at 4 plants, which have additional capacities at the moment. These models will bring the profits $25, $40, $130 and $300 per piece correspondingly.

Each model requires store space for keeping silicon backing wafer delivered once a month in a super clean stores before using in the production. These requirements are 1.1, 1.5, 1.8 and 2.1 м2 for 1000 processors of each model correspondingly. Working time required for producing each model at each plant is presented in the table, as well as the storage space available.

	Working time (hours) required for producing 1000 processors	Storage space available м2
Celeron	Pentium III	Pentium 4	Xeon 4
Plant 11	0.6	0.7	-	-	800
Plant 12	0.65	0.65	0.9	-	950
Plant 30	0.37	-	0.47	0.9	1200
Plant 32	-	-	0.42	0.8	500

Estimated monthly market demand for each model is 1100, 300, 750 and 200 thousands pieces correspondingly.

The plants can work 12 hours a day, 26 days a month.

a.  What amount of each model has to be produced at each plant so to maximize the profit?

b.  Is it enough capacity to meet market demand? If not, what is the bottleneck?

c.  Which constraint is more strict: production capacity or storage space?

Space Bank has problems with staff scheduling, because of big variation in customers arrival rate during a day. In the rush hours arrival rate is 5-6 times greater then in the morning or at the end of the day. Using Queuing theory the amount of clerks necessary for high-quality service was calculated in every 1-hour time period during the working hours form 9 a. m. till 7 p. m. The results are in the table.

Time Period	9-10	10-11	11-12	12-13	13-14	14-15	15-16	16-17	17-18	18-19
The amount of clerks	16	30	31	45	66	72	61	34	16	10

Clerks hired for full time job work either from 9 to 17 with the break for lunch from 12 to 13, or from 11 till 19 with the time for lunch from 14 till 15. Their salary is 8 $ per hour.

It is also possible to use part – time clerks (4 hours a day). Their payment depends on the time period they work in (see the table).

Working time	9-17	11-19	9-13	10-14	11-15	12-16	13-17	14-18	15-19
Payment $ per hour	8	8	6	7	9	10	8	6	6

a.  What is the optimal number of full-time and part time clerks? Give a staff schedule. What is the total payment for all hired clerks per day?

b.  The HR manager is not satisfied by this optimal staff schedule. He requires that any time there were not less then 4 full-time clerks in the bank. Give a new staff schedule. What is the total payment for all hired clerks per day now?

c.  Now financial director does not like the presented staff schedule, because the total amount of clerks exceeds 100 people, which means that the bank will belong to another tax category, and taxes will rise dramatically. So you have to make up such a schedule that total amount of clerks will not exceed 94 persons. Give a new staff schedule. What is the total payment for all hired clerks per day finally?

The manager - coordinator of the educational programs has to distribute 37 instructors from 5 branches of the School (S1,S2... S5) over 11 clients (D1,D2...D11) to deliver lectures. The average profit per instructor of each branch, lecturing for each client along with demands and with the number of instructors available at each branch are given in the table. Find the optimal distribution of instructors over the clients in order to maximize profit, taking into account that instructors from the branch S1 can’t deliver the lectures required by the D4 and D5 clients, instructors from the branch S2 can’t deliver the lectures required by the D10 client, instructors from the branch S3 can’t deliver the lectures required by the D5 and D9 clients,

and instructors from the branch S5 can’t deliver the lectures required by the D1,D2 and D7 clients. How many instructors of each branch stay idle?

	D1	D2	D3	D4	D5	D6	D7	D8	D9	D10	D11	Supply
S1	18	36	19			16	15	36	18	16	28	12
S2	15	27	29	22	17	35	23	14	20		20	16
S3	35	30	23	37		31	28	33		21	35	4
S4	33	31	35	28	13	28	37	17	14	24	31	2
S5			29	17	13	31		14	28	24	29	3
Demand	2	3	3	3	1	1	1	3	3	1	6