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

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.