Heuristic and meta-heuristic approaches for multi-period shelf-space optimization: the case of motion picture retailing

Abstract

The retail industry is in a highly competitive situation currently. The success of the industry depends upon the efficient allocation of products in the shelf space. Several previous authors have developed mathematical models for optimal shelf-space allocation. We extend the prior research in the direction of the multi-period problem and introduce more realistic characteristics, such as product demand perishability, pricing contract and cross-elasticity. The new characteristics help us address the case of the real-life movie allocation problem in multiplexes. We formulate a linear integer programming model to represent the problem. The proposed model shows a potential benefit of at least 11% increase in revenue for a multiplex theatre situation as compared to the existing methods. We also propose two greedy heuristics and a genetic algorithm to solve the same problem. A computational study shows that the genetic algorithm performs better than the existing method.

Keywords:

• shelf-space model
• demand perishability
• contract terms
• genetic algorithm
• multiplex

Acknowledgements

This research was partially supported by a financial grant to Sanjeev Swami under the AICTE career award grant.

Notes

1 For example, in movie retailing problem, a typical contract provides a greater revenue share to the retailer as the allocation period increases.

2 In the past, Swami et al (1999) and Saxena (2000) have proposed modelling approaches for multiplex movie allocation. However, their models either simplify the situation by assuming equal capacity of screens, or result in complex non-linear formulation when addressing the problem completely.

3 Here, the demand is considered in terms of number of people/seats.

4 This sharing percentage can be movie and week-specific depending on the nature of the contract.

5 Type I movie opens with high demand and decay rapidly. Type II movie opens with high demand and decay slowly. Type III movie opens with low demand and decay rapidly. Type IV movie opens with low demand and decay slowly.

6 We estimated the demand pattern for each type of movie by using Equation (34). A constant multiplier was used arbitrarily to get a representative demand curve for each type of movie.

7 Although it also prefers Type II movies, they are much lower in proportion.

8 To randomize the assignment of a movie to a movie type, we use the relative proportions of Type I (19%), II (7%), III (38%) and IV (36%) movies in Jedidi et al (1998) sample. Specifically, a random number is drawn among integers between 1 and 100 for each movie. Then the movie is assumed to be Type I if the random number is between 1 and 19, Type II if it is between 20 and 26, Type III if it is between 27 and 64, and Type IV if it is between 65 and 100.

9 The fitness function for genetic algorithm is calculated as follows: ∑_j=1^N ∑_k=1^S ∑_t=1^Tx_jkt*P_jkt, where x_jkt is equal to 1, if movie j is allocate in screen k at time t, otherwise 0.

10 The heuristic H1 does not consider any parameters to solve the problem.