Manufacturers often use returns policies to encourage retailers to stock and price items more aggressively. We focus on the effect that such policies have on both a retailer's and a manufacturer's profits when the retailer must commit prior to the selling season to both a stocking quantity and a price at which to sell an item. Such a commitment is often necessary for retailers who sell primarily through catalogues.Pricing, Returns Policies, Newsboy, Manufacturing/Marketing Interface, Supply Chain

This paper first considers the problem of sequencing n jobs on one machine to minimize total tardiness. It proves theorems that establish the relative order in which pairs of jobs are processed in an optimal schedule; frequently they permit the jobs to be completely ordered, thus solving the problem without any searching. In particular, corollaries establish more general conditions than are currently recognized under which sequencing in order of nondecreasing processing times and sequencing in order of nondecreasing due dates are optimal. In general, even large problems may be at least partially ordered to the point that very few schedules remain to be searched. These results are then partly extended to the more general criterion of minimizing a sum of identical, convex, nondecreasing functions of job tardiness, and an efficient algorithm is proposed.

We consider scheduling a set of jobs on parallel processors, when all jobs have a common due date and earliness and lateness are penalized at different cost rates. For identical processors, the secondary criteria of minimizing makespan and machine occupancy are addressed. The extension to different, uniform processors is also solved.

Interval Scheduling problems (IS) address the situation where jobs with fixed start and fixed end times are to be processed on parallel identical machines. The optimization criteria of interest are the maximization of the number of jobs completed and, in case weights are associated with jobs, the subset of jobs with maximal total weight. We present polynomial solutions to several IS problems and study computational complexity issues in the situation where bounds are imposed on the total operating time of the machines. With this constraint, we show that tractability is achieved again when job preemption is allowed.

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