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Consider a supplier order allocation problem under multiple sourcing, where it is required to buy 2000 units of a certain product from three different suppliers. The fixed setup cost (independent of the order quantity), variable cost (unit price), and the maximum capacity of each supplier are given in Table 3.5 (two suppliers offer quantity discounts).

The objective is to minimize the total cost of purchasing (fixed plus variable cost). Formulate this as a linear integer programming problem. You must define all your variables clearly, write out the constraints to be satisfied with a brief explanation of each and develop the objective function.

 
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(From Ravindran et al. 1987) A company manufactures three products A, B, and C. Each unit of product A requires 1 hour of engineering service, 10 hours of direct labor, and 3 pounds of material. Producing one unit of product B requires 2 hours of engineering, 4 hours of direct labor, and 2 pounds of material. Each unit of product C requires 1 hour of engineering, 5 hours of direct labor, and 1 pound of material. There are 100 hours of engineering, 700 hours of direct labor, and 400 pounds of materials available. The cost of production is a nonlinear function of the quantity produced as shown in Table 3.6. Given the unit selling prices of products A, B, and C as $12, $9 and $7, respectively, formulate a linear mixed integer program to determine the optimal production schedule that will maximize the total profit.

(From Ravindran et al. 1987) A company manufactures three products A, B, and C. Each unit of product...-1

(From Ravindran et al. 1987) A company manufactures three products A, B, and C. Each unit of product...-2

 
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An M/M/1 queuing system has an arrival rate of 10 customers per hour. The average service time is 9 minutes.

a. What is the system utilization?

b. What is the average queue length?

c. What is the probability that there are more than 3 customers in the queue?

d. What is the probability that a customer will wait for more than 3 minutes for service?

Repeat Exercise 3.10 if there are only 10 customers allowed in the system.

Suppose the service time is not exponentially distributed for Exercise 3.8, but is instead log-normally distributed with μ = 8 and σ = 0.015. Use the P–K formulas to estimate the average waiting time in the queue.

 
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Consider a G/G/3 queuing system. Interarrival times are on average 5 minutes with a standard deviation of 6 minutes. Service times are on average 12 minutes with a standard deviation of 15 minutes. Use Equation 3.70 and Little’s law to determine average waiting time in the queue and average number of customers in the system.

Repeat Exercise 3.14 using the Whitt refinement given in Equations 3.73 through 3.80.

The call volume data for Figure 3.13 is given in Table 3.7. Develop and solve an integer programing formulation to find the minimum number of service agents to staff the offered load. An agent handles on average 10 calls per hour.

Consider a G/G/3 queuing system. Interarrival times are on average 5 minutes with a standard...

 
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