While building on the classic strengths of the original text, the author continues to find new ways to make this book current and relevant to students. One way is by incorporating a wealth of state-of-the-art, user-friendly software and more coverage of business applications than ever before. The hallmark features of this edition include clear and comprehensive coverage of the fundamentals of operations research, an extensive set of interesting problems and cases, and state-of-the-practice operations research software used in conjunction with examples from the text.
Sample questions asked in Introduction to Operations Research:
The Mountain Top Hotel is a luxury hotel in a popular ski resort area. The hotel always is essentially full during winter months, so reservations and payments must be made months in advance for week-long stays from Saturday to Saturday. Reservations can be canceled until a month in advance but are nonrefundable after that. The hotel has 100 rooms and the room charge for a week’s stay is $3,000. Despite this high cost, the hotel’s wealthy customers occasionally will forfeit this money and not show up because their plans have changed. On the average, about 10 percent of the customers with reservations are no-shows, so the hotel’s management wants to do some overbooking. However, it also feels that this should be done cautiously because the consequences of turning away a customer with a reservation would be severe. These consequences include the cost of quickly arranging for alternative housing in an inferior hotel, providing a voucher for a future stay, and the intangible cost of a massive loss of goodwill on the part of the furious customer who is turned away (and surely will tell many wealthy friends about this shabby treatment). Management estimates that the cost that should be imputed to these consequences is $20,000. Use the overbooking model presented in Sec. 18.8, including the normal approximation for the binomial distribution, to determine how much overbooking the hotel should do.
The Audiofile Company produces boomboxes. However, management has decided to subcontract out the production of the speakers needed for the boomboxes. Three vendors are available to supply the speakers. Their price for each shipment of 1,000 speakers is shown below. In addition, each vendor would charge a shipping cost. Each shipment would go to one of the company’s two warehouses. Each vendor has its own formula for calculating this shipping cost based on the mileage to the warehouse. These formulas and the mileage data are shown below. Whenever one of the company’s two factories needs a shipment of speakers to assemble into the boomboxes, the company hires a trucker to bring the shipment in from one of the warehouses. The cost per shipment is given next, along with the number of shipments needed per month at each factory. Each vendor is able to supply as many as 10 shipments per month. However, because of shipping limitations, each vendor is able to send a maximum of only 6 shipments per month to each warehouse. Similarly, each warehouse is able to send a maximum of only 6 shipments per month to each factory. Management now wants to develop a plan for each month regarding how many shipments (if any) to order from each vendor, how many of those shipments should go to each warehouse, and then how many shipments each warehouse should send to each factory. The objective is to minimize the sum of the purchase costs (including the shipping charge) and the shipping costs from the warehouses to the factories. (a) Draw a network that depicts the company’s supply network. Identify the supply nodes, transshipment nodes, and demand nodes in this network. (b) Formulate this problem as a minimum cost flow problem by inserting all the necessary data into this network. Also include a dummy demand node that receives (at zero cost) all the unused supply capacity at the vendors. (c) Formulate and solve a spreadsheet model for this problem. (d) Use the computer to solve this problem without using – Excel.
Consider the following problem. ? subject to ? and ? (a) Construct the dual problem for this primal problem. (b) Solve the dual problem graphically. Use this solution to identify the shadow prices for the resources in the primal problem. (c) Confirm your results from part ( b ) by solving the primal problem automatically by the simplex method and then identifying the shadow prices.
Consider the minimum cost flow problem shown below, where the b i values are given by the nodes, the c ij values are given by the arcs, and the finite u ij values are given in parentheses by the arcs. Obtain an initial BF solution by solving the feasible spanning tree with basic arcs A ? C , B ? A , C ? D , and C ? E , where one of the nonbasic arcs ( D ? A ) is a reverse arc. Then use the network simplex method yourself (you may use the interactive procedure in your IOR Tutorial) to solve this problem.