Concept explainers
A
Interpretation: To maximize the profits for the given constraints and objective function.
Concept Introduction: To obtain the objective function is to maximize or minimize the
B
Interpretation: In linear programming, find the better optimal solution using graphic method.
Concept Introduction: In linear programming, graphic method are used to solve the problems by the point of intersection (higher and lower points) between the objective function and regional value of the graph.
C
Interpretation: To Determine the constraints with slack or surplus.
Concept Introduction: In Linear Programming, some mathematics oriented problem will be solved by slack variable and surplus variable. Slack variables is defined as less than (<) or equal (=) type of constraints to getting the equality constraint. Surplus variables is termed as greater than (>) or equal (=) type of constraints to getting the equality constraint.
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OPERATIONS MANAGEMENT CUSTOM ACCESS
- NTS is a Swiss intermodal operator located in Lausanne. When customers need to transport goods between origin and destination, NTS supplies them with one or more empty containers in which the goods can be loaded.Upon arrival at the destination, the goods are unloaded, and the empty containers must be transported to the pickup point for new customers. Therefore, NTS management needs to reallocate empty containers periodically (every week). The company's focus is on the transportation activity of empty containers, which is very expensive (almost 35% of the total operational costs). In May 2023, several empty containers, totaling 20 containers, need to be reallocated among terminals in Amsterdam, Berlin, Munich, Paris, Milan, Barcelona, and Madrid. The available or requested number of empty containers at various terminals is reported, along with the transportation costs (in euros per container) as seen in Figure 1. Determine how to solve the problem with the goal of minimizing…arrow_forwardNTS is a Swiss intermodal operator located in Lausanne. When customers need to transport goods between origin and destination, NTS supplies them with one or more empty containers in which the goods can be loaded. Upon arrival at the destination, the goods are unloaded, and the empty containers must be transported to the pickup point for new customers. Therefore, NTS management needs to reallocate empty containers periodically (every week). The company's focus is on the transportation activity of empty containers, which is very expensive (almost 35% of the total operational costs). In May 2023, several empty containers, totaling 20 containers, need to be reallocated among terminals in Amsterdam, Berlin, Munich, Paris, Milan, Barcelona, and Madrid. The available or requested number of empty containers at various terminals is reported, along with the transportation costs (in euros per container) as seen in Figure 1.Determine how to solve the problem with the goal of minimizing…arrow_forward4.Silicon Valley Transport Commission (SVTC) has a fleet of maintenance vehicles that includes cars, vans, and trucks. SVTC is currently evaluating four different approaches to help them maintain their fleet of cars and vans efficiently at the lowest possible cost. Their options are: (1) No preventive maintenance at all and repair vehicle components when they fail; (2) Take oil samples at regular intervals and perform whatever preventive maintenance is indicated by the oil analysis; (3) Perform an oil change on a regular basis on each vehicle and perform repairs when needed; (4) perform oil changes at regular intervals, take oil samples regularly, and perform maintenance repairs as indicated by the sample analysis. Option #1 costs nothing to implement and results in two possible outcomes: There is a .10 probability that a defective component will occur, requiring emergency maintenance at a cost of $1,200, or there is a chance that no defects will occur and no maintenance will be…arrow_forward
- Silicon Valley Transport Commission (SVTC) has a fleet of maintenance vehicles that includes cars, vans, and trucks. SVTC is currently evaluating four different approaches to help them maintain their fleet of cars and vans efficiently at the lowest possible cost. Their options are: (1) No preventive maintenance at all and repair vehicle components when they fail; (2) Take oil samples at regular intervals and perform whatever preventive maintenance is indicated by the oil analysis; (3) Perform an oil change on a regular basis on each vehicle and perform repairs when needed; (4) perform oil changes at regular intervals, take oil samples regularly, and perform maintenance repairs as indicated by the sample analysis. Option #1 costs nothing to implement and results in two possible outcomes: There is a .10 probability that a defective component will occur, requiring emergency maintenance at a cost of $1,200, or there is a chance that no defects will occur and no maintenance will be…arrow_forwardSilicon Valley Transport Commission (SVTC) has a fleet of maintenance vehicles that includes cars, vans, and trucks. SVTC is currently evaluating four different approaches to help them maintain their fleet of cars and vans efficiently at the lowest possible cost. Their options are: (1) No preventive maintenance at all and repair vehicle components when they fail; (2) Take oil samples at regular intervals and perform whatever preventive maintenance is indicated by the oil analysis; (3) Perform an oil change on a regular basis on each vehicle and perform repairs when needed; (4) perform oil changes at regular intervals, take oil samples regularly, and perform maintenance repairs as indicated by the sample analysis. Option #1 costs nothing to implement and results in two possible outcomes: There is a .10 probability that a defective component will occur, requiring emergency maintenance at a cost of $1,200, or there is a chance that no defects will occur and no maintenance will be…arrow_forwardCleveland Area Rapid Delivery (CARD) operates a delivery service in the Cleveland metropolitan area. Most of CARD's business involves rapid delivery of documents and parcels between offices during the business day. CARD promotes its ability to make fast and on-time deliveries anywhere in the metropolitan area. When a customer calls with a delivery request, CARD quotes a guaranteed delivery time. The following network shows the street routes available. The numbers above each arc indicate the travel time in minutes between the two locations. Min s.t. Node 1 Flows Node 2 Flows Node 3 Flows Node 4 Flows Node 5 Flows Node 6 Flows 35 For all X;; = 0, 1. (a) Develop a linear programming model that can be used to find the minimum time required to make a delivery from location 1 to location 6. (Express your answers in the form where each Xij represents the arc from node i to node j as either 1 or Xijr 0.) 30 12 p.m. 3 Need Help? Read It 18 15 39 12 16 5 (b) How long (in minutes) does it take to…arrow_forward
- Smith Inc. is a retail mail order firm that currently uses a centralized collection system that requires all checks to be sent to its flotation headquarters. An average of 6 days is required for mailed checks to be received, 3 days for Smith Inc. to process them, and 2 days for the checks to clear through its bank. A proposed lockbox system would decrease the mailing and processing time to 2 days and the check clearing time for 1 day. Smith Inc. has an average daily collection of P250,000. If Smith Inc. adopts this proposed lockbox system, its average cash balance will increase by. A. 1.2M B. 450k C. 750k D. 2Marrow_forwardA fertilizer manufacturer has to fulfill supply contracts to its two main customers (650 tons to Customer A and 800 tons to Customer B). It can meet this demand by shipping existing inventory from any of its three warehouses. Warehouse 1 has 400 tons of inventory onhand, Warehouse 2 (W2) has 500 tons, and Warehouse 3 (W3) has 600 tons. The company would like to arrange the shipping for the lowest cost possible, where the per-ton transit costs are as follows: W 1 W 2 W 3 $7.50 $6.75 $6.25 $7.00 $6.50 $8.00 Customer A Customer B Write the objective function and the constraint in equations. Let V;= tons shipped to customer i from warehouse j, and so on. For example, VA1 = tons shipped to customer A from warehouse W1. This exercise contains only parts b, c, d, e, and f. b) The objective function for the LP model = Minimize Z = $7.50 + $6.25 + $6.50 (shipping cost to customer A) V + $6.75 + $7.00 + $8.00 (shipping cost to customer B) c) Subject to: Customer A's demand Customer B's demand…arrow_forwardeBook Problem 10-31 A long-distance telephone company uses a fiber-optic network to transmit phone calls and other information between locations. Calls are carried through cable lines and switching nodes. A portion of the company's transmission network is shown here. The numbers above each arc show the capacity in thousands of messages that can be transmitted over that branch of the network. To keep up with the volume of information transmitted between origin and destination points, use the network to determine the maximum number of messages that may be sent from a city located at node 1 to a oty located at node 7. 3 Maximum number of messages -arrow_forward
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