Budgetary Constraints and Idle Time Allocation in Common-Cycle Production with non-zero Setup Time

Document Type : Research Paper


1 Dept. of Industrial Engineering, Sharif University of Technology, Teharan, Iran

2 College of Business and Public Administration, Old Dominion University, Virginia 23529


Economic lot size scheduling problem (ELSP) for a multi-product single machine system is a classical problem. This paper considers ELSP with budgetary constraint as an important aspect of such systems. In the real world situations the available funds for investment in inventory is limited. By adopting the common cycle time approach to ELSP, we obtain the optimal common cycle which minimizes the total inventory ordering and holding costs for the case of nonzero setup times. One aspect of the scheduling is to decide what should be the sequence of production runs and how the idle times shall be distributed in the common cycle time. For such a sequencing problem, we consider two cases: a) the common cycle time is given, and b) the common cycle time is a decision variable. In the literature, scheduling rules are introduced for both cases, which assume that the total idle time is located at the end of each cycle. This paper relaxes this assumption and provides: i) a rule to optimize the production sequence and the length of idle times before (or after) producing each item, for both cases (a) and (b), and ii) the optimal common cycle for case (b). The presented rule is interestingly general, simple and easy-to-apply.


Main Subjects

[1] Boctor P.P. (1982), The Two-Product, Single Machine, Static Demand, Infinite horizon Lot Scheduling
Problem; Management Science 27; 798-807.
[2] Carreno J.J. (1990), Economic Lot Scheduling for Multiple Products on Parallel Identical Processors;
Management Science 36; 348-358.
[3] Cook W.D., Saipe A.L., Seiford L.M. (1980), Production Runs for Multiple Products: The Full-Capacity
Heuristic; Operations Research 31; 405-412.
[4] Dobson G. (1987), The Economic Lot-Scheduling problem: Achieving Feasibility Using Time-Varying Lot
Sizes; Operations Research 35; 764-771.
[5] Elmaghraby S.F. (1978), The Economic Lot Scheduling Problem (ELSP): Review and Extensions;
Management Science 24; 587-631.
[6] Fujita S. (1978), The Application of Marginal Analysis to the Economic Lot Scheduling Problem; AIIE
Transactions 10; 354-361.
[7] Goyal S.K. (1973), Scheduling a Multi-Product Machine System; Operational Research 31; 405-412.
[8] Goyal S.K. (1984), Determination of economic Production Quantities for a Two-Product Single Machine
System; International Journal of Production Research 22; 121-126.
[9] Graves S.C. (1979), on the Deterministic Demand Multi-Product Single Machine Lot Scheduling Problem;
Management Science 25; 267-280.
[10] Gunter S.I., Swanson L.A. (1986), A Heuristic for Zero Setup Cost Lot Sizing and Scheduling Problems;
Presented at the ORSA-TIMS Conference, October 27-28; Miami, Florida.
[11] Haessler R.W. (1979), An Improved Extended Basic Period Procedure for Solving the Economic Lot
Scheduling Problem; AIIE Transactions 11; 336-340.
[12] Haji R. (1994), Optimal Allocation of idle times between production runs of a multi-item production
system; Reaserch Proceedings of Department of Industrial Engineering, Sharif University of Technology;
Tehran, Iran (in Persian).
[13] Haji R., Mansouri M. (1995), Optimum Common Cycle for Scheduling a Single-Machine Multi-product
System with a Budgetary Constraint; Production Planing and Control 2; 151-156.
[14] Haji A., Haji R. (2002), Optimum aggregate inventory for scheduling multi-product single machine system
with zero setup time; International Journal of Engineering 15(1); 41-48.
[15] Hanssmann F. (1962), Operations Research in Production and Inventory; John Wiley and Sons; New York.
[16] Hsu W. (1983), On the General Feasibility Test of scheduling Lot Size for several Products on One
Machine; Management science 29; 93-105.
[17] Jones P.C., Inmann R.R. (1989), When is the Economic Lot Scheduling Problem Easy?; IIE Transactions
21; 11-20.
[18] Johnson L.A., Montgomery D.C. (1974), Operation Reaserch in Production Planning, Scheduling and
Inventory Control; John Wiley; New York.
[19] Park K.S., Yun D.K. (1984), A Stepwise Partial Enumeration Algorithm for The Economic Lot Scheduling
Problem; IIE Transactions 16; 363-370.
[20] Parsons R.J. (1966), Multiproduct Lot Size Determination When certain Restrictions are Active; Journal of
Industrial Engineering 17; 360-363.
[21] Zipkin P.H. (1988), Computing Optimal Lot Sizes in The Economic Lot Scheduling Problem; Working
Paper, graduate School of Business; Columbia University.
  • Receive Date: 16 April 2009
  • Revise Date: 11 September 2009
  • Accept Date: 15 January 2010
  • First Publish Date: 01 April 2010