Minimizing Variation of Flow Time in Single Machine Systems

Abstract

This paper addresses the problem of n jobs to be scheduled on a single machine in such a way that flow time variation is minimized. When the measure of variation is total absolute difference of completion times (TADC) the problem is shown to be quite simple. Sufficient conditions are shown for minimal TADC and a simple method for generating an optimal solution is provided. When the measure of variation is variance of flow time the problem is much more difficult. For this case a heuristic method for scheduling is proposed. The heuristic is simple and provides solutions which compare favorably with others found in the literature.production/scheduling: flow shop, programming: heuristic

An Evaluation of Scheduling Policies in a Dual Resource Constrained Assembly Shop

“…(5),JPAR (5,50),XCOMP (5,50), CXOPER (5,50),PITEM (5,50),NASM(5),NCOMP (5,50,5),XMACH (5,50,4), CPT (5,50,4),COUNT,ARR,TPT,CPATH(5),PATH (5,50),CPMOD(5),RWK(1000), CRASM(1000),ROPT(1000),NOPT(5),ZZ (14),A(15),BD (5,50),QMC(4) C,XPATH (5,50) COMMON QSET(50000) EQUIVALENCE (NSET(1),QSET (1) (5,50),XCOMP (5,50), CXOPER (5,50),PITEM (5,50),NASM(5),NCOMP (5,50,5),XMACH (5,50,4), CPT (5,50,4),COUNT,ARR,TPT,CPATH(5),PATH (5,50),CPMOD(5),RWK(1000), CRASM(1000),ROPT(1000),NOPT(5),ZZ (14),A(15),BD (5,50) (4).EQ.ATRIB (7))GO TO 15 RWK(JOB)=RWK(JOB)-ATRIB (7) ROPT(~OB)=~OPT(JOB)-1…”

“…GO TO (20,30,40,50) (7) IF(MACH.EQ.B (10))RETURN MACH=B (10) C**** C**** ITEM=B (4) JTYPE=B ( 1 ) JOB=B ( JTYPE=A ( 1) ITEM=A (4) JOB=A (9) A ( 13 )=TNOW A (11)=A (2) The vita has been removed from the scanned document…”

Minimizing weighted mean absolute deviation of job completion times from their weighted mean

“…There are two main points to make: first, we do not have to enumerate over all n values of q; second, we can get v and v by solving MAD_mC in O(n log (n)) time via the algorithm due to Kanet [10]. Thus, v=v ¼ 4 as before, and we get an O(n 3 /e 2 ) FPTAS for MAD_MC.…”

“…Kanet [10] has given an O (n log (n)) time solution in this case. An optimal schedule here is also V-shaped w.r.t.…”

Optimizing the half-product and related quadratic Boolean functions: approximation and scheduling applications

“…Since the 1970s, the problem has been known to be applicable in various contexts, see, e.g., Merten and Muller (1972) where this objective function is first introduced. Cheng and Kubiak (2005) refer to Kanet (1981) to stress that the CTV as a measure of the schedule quality "is applicable to any service and manufacturing setting where it is desirable to provide jobs or customers with approximately the same level of service" .…”