Advertising is the primary source of revenue for newspaper companies. Over the past 10 to 15 years, the newspaper industry has been adjusting to changes in the mix of services that produce this revenue. The two main categories of services are run on press (ROP) advertising and preprinted insert advertising. ROP advertising is printed in the newspaper during the live press run each night, whereas pre-printed inserts are produced for the nightly production run and are inserted into or delivered with the newspaper. Pre-printed inserts offer several advantages for advertisers. Different sizes and quality of paper stock can be used to make as unique as and more colourful than possible on a newspaper printing press. Also, advertisers can tightly control quality for pre-printed inserts unlike newspaper quality that varies widely.

Although revenue has been increasing in both categories of advertising, revenue from pre-printed inserts has been growing at a higher rate than ROP advertising. For many newspaper companies, this shift in revenue mix has created scheduling challenges in the production area. With inserts, advertisers can select the zones to which specific sets of advertisements are distributed. A zone is a distinct geographical area where all the papers delivered in the area receive the same set of advertising inserts. The challenge for newspaper companies is to schedule the production run to process the correct combination of inserts for all the different zones and complete the run early enough to get the papers to the circulation department on time. For many papers, the problem is exacerbated by advertiser’s desires to micro zone or have more zones of smaller size, increasing the specificity with which different groups of consumers can be targeted.

Mr. Carter is the production manager for a medium-size newspaper company. Each night, he and his employees must design a schedule for combining the appropriate advertising inserts for 36 different delivery zones into the newspaper. Mr. Carter's company owns 4 inserting machines that can be loaded with the inserts for a particular zone. 2 of the inserting machines operate at a rate of 12,000 papers per hour, whereas the other 2 machines operate at a rate of 11,000 per hour. The equipment inserts the loaded set of inserts into newspapers coming off the production press until all the papers for a particular zone are completed.

When the inserts for a particular zone are completed, the inserting machine is stopped and reloaded with the inserts for the next zone. This reloading process takes different amounts of time depending on how much work is required to load the machine with the next Zone's set of inserts. The zones can be processed in any order and on any of the4 inserting machines. However, all the advertising for a particular zone must be processed on the same inserting machine (that is, the inserts for a single zone are not distributed across multiple inserting machines).

Mr. Carter has asked you to develop a model to design an optimal production schedule for the inserting equipment. In particular, he wants to determine which zones should be assigned to each of the four machines in the optimal order for processing the jobs assigned to each machine. His objective is to minimize the amount of time it takes to complete all the newspapers.