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An Introduction To Management Science Quantitative Approaches To Decision Making 2nd Edition David Ray Anderson, Dennis J. Sweeney, Thomas Arthur Williams, Mik Wisniewski - Solutions
Consider a two-channel waiting line with Poisson arrivals and exponential service times. The mean arrival rate is 14 units per hour, and the mean service rate is ten units per hour for each channel.a. What is the probability that no units are in the system?b. What is the average number of units in
Agan Interior Design provides home and office decorating assistance to its customers. In normal operation, an average of 2.5 customers arrive each hour. One design consultant is available to answer customer questions and make product recommendations. The consultant averages ten minutes with each
For the Dome single-channel queuing system in Section 11.2, assume that the arrival rate is increased to one customer per minute and that the mean service rate is increased to 1.25 customers per minute. Calculate the following operating characteristics for the new system: P0, Lq, L, Wq, W and Pw.
Films Tonight is a typical DVD movie rental outlet for home viewing customers. During the weeknight evenings, customers arrive at Films Tonight at the average rate of 1.25 customers per minute. The cashier can serve an average of two customers per minute. Assume Poisson arrivals and exponential
The reference desk of a university library receives requests for assistance. Assume that a Poisson probability distribution with a mean rate of ten requests per hour can be used to describe the arrival pattern and that service times follow an exponential probability distribution with a mean service
Use the single-channel drive-up bank teller operation referred to in Problems 1–3 to determine the probabilities of zero, one, two and three customers in the system. What is the probability that more than three customers will be in the drive-up teller system at the same time?
Use the single-channel drive-up bank teller operation referred to in Problems 1 and 2 to determine the following operating characteristics for the system.a. The probability that no customers are in the system.b. The average number of customers waiting.c. The average number of customers in the
In the Stad National Bank waiting line system (see Problem 1), assume that the service times for the drive-up teller follow an exponential probability distribution with a mean service rate of 36 customers per hour or 0.6 customer per minute. Use the exponential probability distribution to answer
Stad National Bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. On weekday mornings, arrivals to the drive-up teller window occur at random, with a mean arrival rate of 24 customers per hour or 0.4 customer per minute.a.
Apply the more common queuing models
Explain the principles of queuing
Based on the three-unit organization, how many firefighters should be assigned to each unit? What is the total number of full-time firefighters required for the River City Fire Department?
On a given day, what is the probability that Kelleyday firefighters will be called in to work overtime?
Using a minimum cost criterion, how many additional firefighters should be added to each unit in order to cover the daily absences? These extra daily needs will be filled by the additional firefighters and, when necessary, the more expensive use of overtime by off-duty firefighters.
Assuming no daily absences and taking into account the need to staff Kelley days, determine the base number of firefighters needed by each unit.
Make a recommendation as to whether the company should purchase or manufacture the part. What savings are associated with your recommendation compared with the other alternative?
Include the following in the policies of parts 4(a) and 4(b):a. optimal quantity Q.*b. number of order or production runs per year.c. cycle time.d. reorder point.e. amount of safety stock.f. expected maximum inventory. g. average inventory. h. annual holding cost. i. annual ordering cost. j. annual
A development of the inventory policy for the following two alternatives:a. ordering a fixed quantity Q from the supplier.b. ordering a fixed quantity Q from in-plant production.
An analysis of setup costs for the production operation.
An analysis of ordering costs, including the appropriate cost per order from the supplier.
An analysis of the holding costs, including the appropriate annual holding cost rate.
The pharmacy department in the local hospital is responsible for ensuring the supply of drugs and medicines but is also under pressure to control costs. One particular drug costs 2.95 per unit. The annual holding cost rate is 20 per cent. An order-quantity, reorder point inventory model currently
A firm uses a one-week periodic review inventory system. A two-day lead time is needed for any order, and the firm is willing to tolerate an average of one stock-out per year.a. Using the firm's service guideline, what is the probability of a stock-out associated with each replenishment decision?b.
For Isa Distributors in Problem 17, we were given Q =25, D=200, C = 5 and a normal lead-time demand distribution with 12 and = 2.5.a. What is Isa's reorder point if the firm is willing to tolerate two stock-outs during the year?b. What is Isa's reorder point if the firm wants to restrict the
Isa Distributors, Inc., provides a variety of auto parts to small local garages. Isa purchases parts from manufacturers according to the EOQ model and then ships the parts from a regional warehouse direct to its customers. For a particular type of exhaust, Isa's EOQ analysis recommends orders with
a. What is the recommended order quantity?b. What is the probability that at least some customers will ask to purchase the product after the outlet is sold out? That is, what is the probability of a stock-out, using your order quantity in part (a)?c. To keep customers happy and returning to the
A retail outlet sells a seasonal product for 10 per unit. The cost of the product is 8 per unit. All units not sold during the regular season are sold for half the retail price in an end- of-season clearance sale. Assume that demand for the product is uniformly distributed between 200 and
a. What is the recommended order quantity?b. What is the probability that Gunnarsson will sell all the units it orders?
The Gunnarsson Air-Conditioning Company is considering the purchase of a special shipment of portable air conditioners manufactured in Japan. Each unit will cost Gunnarsson E80, and it will be sold for E125. Gunnarsson does not want to carry surplus air conditioners over to the following year.
In the EOQ model with quantity discounts, we stated that if the Q* for a price category is larger than necessary to qualify for the category price, the category cannot be optimal. Use the two discount categories in Problem 13 to show that this statement is true. That is, plot total cost curves for
Apply the EOQ model to the following quantity discount situation in which D ¼ 500 units per year, Co ¼ E40 and the annual holding cost rate is 20 per cent. What order quantity do you recommend?Discount Category Order Size Discount (%) Unit Cost E 1 0 to 99 0 10.00 2 100 or more 3 9.70
Assume that the following quantity discount schedule is appropriate. If annual demand is 120 units, ordering costs are E20 per order, and the annual holding cost rate is 25 per cent, what order quantity would you recommend?
A manager of an inventory system believes that inventory models are important decisionmaking aids. Even though often using an EOQ policy, the manager never considered a backorder model because of the assumption that backorders were ‘bad’ and should be avoided. However, with upper
Assuming 250 days of operation per year and a lead time of five days, what is the reorder point for Suyuti Auto in Problem 9? Show the general formula for the reorder point for the EOQ model with backorders. In general, is the reorder point when backorders are allowed greater than or less than the
Suppose that Suyuti Auto of Problem 4, with D ¼ 12 000 units per year, Ch ¼ (2.50)(0.20) ¼ E0.50 and Co ¼ E25, decided to operate with a backorder inventory policy. Backorder costs are estimated to be E5 per unit per year. Identify the following:a. Minimum cost order quantity.b. Maximum number
A well-known manufacturer of several brands of toothpaste uses the production lot size model to determine production quantities for its various products. The product known as Extra White is currently being produced in production lot sizes of 5000 units. The length of the production run for this
Groebler Publishing Company produces books for the retail market. Demand for a current book is expected to occur at a constant annual rate of 7200 copies. The cost of one copy of the book is E14.50. The holding cost is based on an 18 per cent annual rate and production setup costs are E150 per
Assume that a production line operates such that the production lot size model of Section 10.3 is applicable. Given D ¼ 6400 units per year, Co ¼ E100 and Ch ¼ E2 per unit per year, compute the minimum cost production lot size for each of the following production rates:a. 8 000 units per year.b.
Suppose that Suyuti’s management in Problem 4 likes the operational efficiency of ordering once each month and in quantities of 1000 units. How much more expensive would this policy be than your EOQ recommendation? Would you recommend in favour of the 1000-unit order quantity? Explain. What would
Suyuti Auto purchases a component used in the manufacture of automobile generators directly from the supplier. Suyuti’s generator production operation, which is operated at a constant rate, will require 1000 components per month throughout the year (12 000 units annually). Assume that the
The reorder point [see Equation (10.6)] is defined as the lead-time demand for an item. In cases of long lead times, the lead-time demand and thus the reorder point may exceed the economic order quantity Q*. In such cases, the inventory position will not equal the inventory on hand when an order is
A general property of the EOQ inventory model is that total inventory holding and total ordering costs are equal at the optimal solution. Use the data in Problem 1 to show that this result is true. Use Equations (10.1), (10.2) and (10.3) to show that, in general, total holding costs and total
Suppose that the CBC has a soft drink product that shows a constant annual demand rate of 3600 cases. A case of the soft drink costs CBC E3. Ordering costs are E20 per order and holding costs are 25 per cent of the value of the inventory. CBC has 250 working days per year, and the lead time is five
Incorporate probability into inventory decisions.
Calculate and interpret the common inventory models.
Explain the principles of inventory management.
Using the expected activity times as the normal times and the following crashing information, determine the activity crashing decisions and revised activity schedule for the warehouse expansion project.
Office Automation developed a proposal for introducing a new computerized office system that will improve word processing and interoffice communications for a particular company. Contained in the proposal is a list of activities that must be accomplished to complete the new office system project.
Consider the following project network and activity times (in days).The crashing data for this project are as follows.a. Find the critical path and the expected project completion time.b. What is the total project cost using the normal times?c. What is the expected project completion time and cost
Return to the computer installation project in Problem 7 and assume that the project has to be completed in 16 weeks. Crashing of the project is necessary. Use the following relevant information.Develop a complete activity schedule based on the crashed activity times.
The product development group at Landon Corporation has been working on a new computer software product that has the potential to capture a large market share. Through outside sources, Landon’s management learned that a competitor is working to introduce a similar product. As a result, Landon’s
The activities, their immediate predecessors, and the activity time estimates (in weeks) are as follows. Activity Description Immediate Predecessor Optimistic Time (weeks) Most Probable Pessimistic A Meet with board — 1 1 2 B Hire coaches A 4 6 8 C Reserve pool A 2 4 6 D Announce programme B, C 1
The manager of the Oak Hills Swimming Club is planning the club’s swimming team programme. The first team practice is scheduled for May
The Daugherty Porta-Vac project discussed in Section 9.2 has an expected project completion time of 17 weeks. The probability that the project could be completed in 20 weeks or less is 0.9656. The noncritical paths in the Porta-Vac project network are: ADGJ ACFJ BHIJa. Use the information
Andreas Bierhoff is in charge of planning and coordinating next spring’s sales management training programme for his company. Andreas listed the following activity information for this project.Activity Description Immediate Predecessor Optimistic Time (weeks) Most Probable Pessimistic A Plan
Suppose that the following estimates of activity times (in weeks) were provided for the network shown in Problem 6.Activity Optimistic Most Probable Pessimistic A 4.0 5.0 6.0 B 2.5 3.0 3.5 C 6.0 7.0 8.0 D 5.0 5.5 9.0 E 5.0 7.0 9.0 F 2.0 3.0 4.0 G 8.0 10.0 12.0 H 6.0 7.0 14.0 What is the probability
The following estimates of activity times (in days) are available for a small project.Activity Optimistic Most Probable Pessimistic A 4 5.0 6 B 8 9.0 10 C 7 7.5 11 D 7 9.0 10 E 6 7.0 9 F 5 6.0 7a. Calculate the expected activity completion times and the variance for each activity.b. An analyst
Hamilton County Parks is planning to develop a new park and recreational area. Project development activities include clearing playground and picnic areas, constructing roads, constructing a shelter house, purchasing picnic equipment and so on. The following network and activity times (in weeks)
Khobar Technical College is considering building a new multipurpose athletic complex on campus. The complex would provide a new gymnasium for intercollegiate basketball games, expanded office space, classrooms and intramural facilities. The following activities would have to be undertaken before
A project involving the installation of a computer system comprises eight activities. The following table lists immediate predecessors and activity times (in weeks).Activity Immediate Predecessor Time A —3 B —6 C A2 D B, C 5 E D4 F E3 G B, C 9 H F, G 3a. Draw a project network.b. What are the
Consider the following project network and activity times (in weeks).a. Identify the critical path.b. How much time will be needed to complete this project?c. Can activity D be delayed without delaying the entire project? If so, by how many weeks?d. Can activity C be delayed without delaying the
Management Decision Systems (MDS) is a consulting company that specializes in the development of decision support systems. MDS obtained a contract to develop a computer system to assist the management of a large company in formulating its capital expenditure plan. The project leader developed the
Assume that the project in Problem 3 has the following activity times (in months). Activity ABCDEFG Time 4626335a. Find the critical path.b. The project must be completed in one-and-a-half years. Do you anticipate difficulty in meeting the deadline? Explain.
Construct a project network for the following project. The project is completed when activities F and G are both complete. Activity A B CD E F G Immediate Predecessor — — A A C, B C, B D, E
Bridge City Developers is coordinating the construction of an office complex. As part of the planning process, the company generated the following activity list. Draw a project network that can be used to assist in the scheduling of the project activities. Activity A B C D E FGH I J Immediate
The Mohawk Discount Store is designing a management training programme for staff at its corporate headquarters. The company wants to design the programme so that trainees can complete it as quickly as possible. Important precedence relationships must be maintained between assignments or activities
Undertake project scheduling with uncertain activity times.
Determine the critical path for a project network.
Construct project networks for typical business problems.
Include recommendations regarding how the system could be modified to take into account varying traffic conditions that occur throughout the day and changes in driving conditions resulting from temporary road construction projects.
The High-Price Oil Company owns a pipeline network that is used to convey oil from its source to several storage locations. A portion of the network is as follows:Due to the varying pipe sizes, the flow capacities vary. By selectively opening and closing sections of the pipeline network, the firm
If the Frankfurt highway system described in Problem 11 has revised flow capacities as shown in the following network, what is the maximal flow in vehicles per hour through the system? How many vehicles per hour must travel over each road (arc) to obtain this maximal flow?
The north–south highway system passing through Frankfurt, Germany, can accommodate the capacities shown.Can the highway system accommodate a north–south flow of 10 000 vehicles per hour?
The Metrovision Cable Company just received approval to begin providing cable television service to a suburb of a large city. The nodes of the following network show the distribution points that must be reached by the company’s primary cable lines. The arcs of the network show the number of km
North Yorkshire University is installing a secure electronic mail system. The following network shows the possible electronic connections among the offices. Distances between offices are shown in km. Develop a design for the office communication system that will enable all offices to have access to
In a large soap products plant, quality control inspectors take samples of various products from the different production areas and deliver them to the lab for analysis. The inspection process is slow, and the inspectors spend substantial time transporting samples from the production areas to the
The City of Copenhagen recently purchased land for a new country park, and park planners identified the ideal locations for the lodge, cabins, picnic groves, boat dock and scenic points of interest. These locations are represented by the nodes of the following network. The arcs of the network
Cairo City Cab Company identified ten primary pickup and drop locations for cab drivers. In an effort to minimize travel time and improve customer service and the utilization of the company’s fleet of cabs, management would like the cab drivers to take the shortest route between locations
Morgan Trucking Company operates a special speedy pickup and delivery service in a large city for ten clients who have a pickup contract with Morgan. When Morgan receives a request for service, it dispatches a truck from its HQ to the requesting service as soon as possible. With both fast service
Find the shortest route between nodes 1 and 10 in the following network:
In the original GDA problem, we found the shortest distance from the office (node 1) to each of the other nodes or construction sites. Because some of the roads are highways and others are country tracks, the shortest-distance routes between the office and the construction sites may not necessarily
For the GDA problem (see Figure 8.1), assume that node 7 is GDA’s warehouse and supply centre. Several daily trips are commonly made from node 7 to the other nodes or construction sites. Using node 7 as the starting node, find the shortest route from this node to each of the other nodes in the
Find the shortest route from node 1 to each of the other nodes in the transportation network shown.
Maximal flow networks.
Minimal spanning tree networks.
Shortest-route networks.
The charity is discussing with its Swedish and German suppliers the possibility of them supplying some of the zones directly. Under review are the possibilities of the German supplier shipping directly to Wales at a cost of E0.30 per set and to the Southeast at a cost of E0.70 per set. Similarly,
The company is willing to consider altering its current strategy so that any of the three distribution centres could supply any of the zones (where this is logistically feasible). Can costs be reduced? If so, by how much?
If the charity maintains its current supply and distribution strategy, what will its supply and distribution costs be for the coming year?
Use the Hungarian method to solve the Salisbury Discount, problem by using the profit data in Table 7.27.
Using the Hungarian method, obtain the optimal solution.
Refer to Problem
Refer again to the Contois Carpets problem for which the network representation is shown in Figure 7.12. This problem can also be formulated and solved as a transportation problem.a. Develop a network representation of it as a transportation problem. (Hint: Eliminate the inventory arcs, and add
Use the per-unit cost changes for each unoccupied cell shown in Table 7.10 to do the following:a. Consider the arc connecting Brazil and Dubai as a candidate for the incoming arc. Allocate 1 unit of flow, and make the necessary adjustments on the stepping-stone path to maintain feasibility. Compute
Consider the following minimum cost transportation problem.a. Use the minimum cost method to find an initial feasible solution.b. Use the transportation Simplex method to find an optimal solution.c. Using your solution to part (b), identify an alternative optimal solution.
Consider the following minimum cost transportation problem.a. Use the minimum cost method to find an initial feasible solution.b. Use the transportation Simplex method to find an optimal solution.c. How would the optimal solution change if you must ship 100 units on the Tucson–San Diego route?d.
Consider the following transportation tableau with four origins and four destinations.a. Use the MODI method to determine whether this solution provides the minimum transportation cost. If it is not the minimum cost solution, find that solution. If it is the minimum cost solution, what is the total
The distribution system for the Herman Company consists of three plants, two warehouses and four customers. Plant capacities and shipping costs (E) from each plant to each warehouse are: Warehouse Plant 1 2 Capacity 1 4 7 450 2 8 5 600 3 5 6 380 Customer demand and shipping costs per unit (in E)
Assume that in Problem 9 an additional employee is available for possible assignment. The following table shows the assignment alternatives and the estimated completion times. Client Project Leader 1 2 3 Jackson 10 16 32 Ellis 14 22 40 Smith 22 24 34 Burton 14 18 36a. What is the optimal
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