Scheduling of inventory releasing jobs to minimize a regular objective function of delivery times

Abstract

In this note we provide new complexity and algorithmic results for scheduling inventory releasing jobs, a new class of single machine scheduling problems proposed recently by Boysen et al. We focus on tardiness related criteria, while known results are concerned with inventory levels between fixed delivery points. Our interest is motivated by the fact that deciding whether a feasible schedule exists is NP-hard in the strong sense, provided that all delivery deadlines are fixed, and there are no restrictions on the amount of products released by the jobs, nor on the job processing times. We will establish NP-hardness results, or provide polynomial or pseudo-polynomial time algorithms for various special cases, and describe a fully polynomial approximation scheme for one of the variants with the maximum tardiness criterion.

Approximability of total weighted completion time with resource consuming jobs

“…The algorithm borrows ideas from the FPTAS described in [7,12] and from results for the makespan minimization problem on parallel machines [14]. Since the scheduling problem is NP-hard in the strong sense if q is part of the input, there is no FPTAS in this general case, unless P=NP.…”

Reductions between scheduling problems with non-renewable resources and knapsack problems

“…In this section we recapitulate two resource scheduling problems, the Delivery tardiness problem (see [10]) and the Material consumption problem (see e.g. [5], [15]).…”

“…They proved the NP-hardness of the problem and proposed polynomial algorithms for several variants. Drótos and Kis [10] has introduced the delivery tardiness problem and, among other results, devised an FPTAS for the problem DT P 1 2 . Scheduling of jobs consuming some non-renewable resources (like raw materials, money, energy, etc.)…”

Approximation schemes for single machine scheduling with non-renewable resource constraints

“…S be an ε-approximate solution of (6)- (10), which may violate the constraints (8) S is a feasible solution of (6)- (10).…”

“…This paper is a follow up to Drótos and Kis [8] in which the scheduling of inventory releasing jobs has been studied.…”