Nonstationary inventory problems with set-up costs, proportional ordering costs, and stochastic demands occur in a large number of industrial, distribution, and service contexts. It is well known that nonstationary (s, S) policies are optimal for such problems. In this paper, we propose a simple, myopic heuristic for computing the policies. The heuristic involves approximating the future problem at each period by a stationary one and obtaining the solution to the corresponding stationary problem. We numerically compare our heuristic with an earlier myopic heuristic and the optimal dynamic programming solution procedure. Over all problems tested, the new heuristic averaged 1.7% error, compared with 2.0% error for the old procedure, and is on average 399 times as fast as the D.P. and 2062 as fast as the old heuristic. Moreover, our heuristic, owing to its myopic nature, requires the demand data only a few periods into the future, while the dynamic programming solution needs the demand data for the entire time horizon—which are typically not available in most practical situations.
This paper, motivated by the experiences of major US−based broadcast television network, presents algorithms and heuristics to schedule commercial videotapes. Major advertisers purchase several slots to air commercials during a given time period on a broadcast network. We study the problem of scheduling advertiser's commercials in the slots it purchased when the same commercial is to be aired multiple times. Under such a situation, the advertisers typically want the airings of a commercial to be as much evenly spaced as possible. Thus, our objective is to schedule a set of commercials on a set of available slots such that multiple airings of the same commercial are as much evenly spaced as possible. A natural formulation of this problem is a mixed integer program that can be solved using third party solvers. We also develop a branch−and−bound algorithm based on a problem specific bounding scheme. Both approaches fail to solve larger problem instances within a reasonable timeframe. We present an alternative mixed integer program that lends itself to efficient solution. For solving even larger problems, we present multiple heuristics. Various extensions of the basic model are discussed. November 2002Abstract This paper, motivated by the experiences of major US-based broadcast television network, presents algorithms and heuristics to schedule commercial videotapes. Major advertisers purchase several slots to air commercials during a given time period on a broadcast network. We study the problem of scheduling advertiser's commercials in the slots it purchased when the same commercial is to be aired multiple times. Under such a situation, the advertisers typically want the airings of a commercial to be as much evenly spaced as possible. Thus, our objective is to schedule a set of commercials on a set of available slots such that multiple airings of the same commercial are as much evenly spaced as possible. A natural formulation of this problem is a mixed integer program that can be solved using third party solvers. We also develop a branch-and-bound algorithm based on a problem specific bounding scheme. Both approaches fail to solve larger problem instances within a reasonable timeframe. We present an alternative mixed integer program that lends itself to efficient solution. For solving even larger problems, we present multiple heuristics. Various extensions of the basic model are discussed.
We consider a single item periodic review inventory problem with random yield and stochastic demand. The yield is proportional to the quantity ordered, with the multiplicative factor being a random variable. The demands are stochastic and are independent across the periods, but they need not be stationary. The holding, penalty, and ordering costs are linear. Any unsatisfied demands are backlogged. Two cases for the ordering cost are considered: The ordering cost can be proportional to either the quantity ordered (e.g., in house production) or the quantity received (e.g., delivery by an external supplier). Random yield problems have been addressed previously in the literature, but no constructive solutions or algorithms are presented except for simple heuristics that are far from optimal. In this paper, we present a novel analysis of the problem in terms of the inventory position at the end of a period. This analysis provides interesting insights into the problem and leads to easily implementable and highly accurate myopic heuristics. A detailed computational study is done to evaluate the heuristics. The study is done for the infinite horizon case, with stationary yields and demands and for the finite horizon case with a 26-period seasonal demand pattern. The best of our heuristics has worst-case errors of 3.0% and 5.0% and average errors of 0.6% and 1.2% for the infinite and finite horizon cases, respectively.
The NBC television network, a subsidiary of the General Electric Company (GE), uses optimization-based sales systems to improve its revenues and productivity. GE's corporate research and development center (CRD) developed these systems using operations research and management science techniques to improve NBC's sales processes. These systems remove bottlenecks caused by manual development of sales plans, helping NBC to respond quickly to client requests with sales plans that meet their requirements. These systems also enable NBC to make the most profitable use of its limited inventory of valuable advertising slots by estimating demands for airtime by show and by week and to schedule commercials. Between 1996 and 2000, the systems increased revenues by over $200 million, improved sales-force productivity, reduced rework by over 80 percent, and improved customer satisfaction. They have become an integral and essential part of NBC's sales process.
Television networks sell advertising slots to clients by the shows on which the commercials air. The networks determine the exact location in the show that a commercial will air at a later stage, usually close to the airdate of the show. There are several criteria the networks must meet in scheduling commercials in a show. The schedule should be such that no two commercials promoting competing products from different clients air in the same break. The audience ratings tend to be higher at the start and end of a commercial break than during the middle of the break. Therefore, advertisers generally prefer the first and last positions in a commercial segment, to those in the middle. TV networks normally promise their clients an equitable rotation of commercials among the positions within a commercial break. The scheduling of commercials on shows is traditionally done manually and is a cumbersome, time-intensive, and error-prone process. We formulate the commercial scheduling problem as an integer program and develop near-optimal heuristics for automatically scheduling the commercials to meet all the requirements. We implemented our algorithm at the National Broadcasting Company (NBC). In addition to reducing sales personnel costs by automating the scheduling of commercials, our work has increased customer satisfaction by minimizing errors in meeting customer requirements.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.