Operations Research

A mathematical programming system named SilverScreener uses a 0-1 integer programming model to help theater managers decide which movies to show on a weekly basis in a multiple-screen theater (Interfaces, May/June 2001). Suppose that management of Valley Cinemas would like to investigate the potential of using a similar scheduling system for their chain of multiple-screen theaters. Valley selected a small two-screen movie theater for the pilot testing and would like to develop an integer programming model to help schedule movies for the next four weeks. Six movies are available. The first week each movie is available, the last week each movie can be shown, and the maximum number of weeks tha... click for more

Vector problem

Each square n*n region of an image yields a vector of length n^2 such that the components of the vector are the grey levels of the pixels in the square. Let u, v be the vectors obtained from two image patches, let a be the average of the entries in u, let b be the average of the entries in V and let e be the vector of length n^2 such that each entry of e is equal to 1. Show that (u-a e).(v-b v)=u.v - (n^2 a b) NOTE: The textbook is "Image Based Information Processing"

Operations research

Photo-Max, a large photographic outlet, receives 5,000 collapsible tripods annually from Quality Photographic Suppliers to meet annual demand. The ordering cost is $15 per order, and the carrying cost is $0.50 per unit per year. Quality Photographic, building on its established reputation for on-time delivery, is interested in smoothing its own production processes and has initiated a new option for its customers. When an order is placed, Quality Photographic will ship one-third of the order every week for three weeks instead of shipping the entire order at one time. Weekly demand for Photo-Max over the lead time is 100 tripods. a. Determine the order quantity and total cost for Photo-Max... click for more

Operations research

Georgia Pacific offers the following discount schedule for its 4X8 ft. sheets of quality plywood. (see chart in attached file) Ace Lumber and Building Supply regularly stocks this product from Georgia pacific and has an annual demand of 1000 sheets. The carrying cost at Ace Lumber is 20% of product cost, and a cost of $45 is incurred with each order. a. Determine the optimal order quantity for Ace Lumber.

Operations research

A manager of an inventory system believes that inventory models are important decision-making aids. Even though often using an EOQ policy, the manager never considered a backorder model because of the assumption that backorders were inappropriate and should be avoided. However, with upper management's continued pressure for cost reduction, the company needs to analyze the economics of a back-ordering policy for a specific product with D=800 units per year, Co = $150, Ch = $3, and Cb = $20. Assume 250 working days per year. a. Determine the difference in total annual cost between the EOQ model and the planned shortage or backorder model for this product. b. If the manager adds constra... click for more