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We solve a variation of a classic make‐to‐stock inventory problem introduced by Gavish and Graves. A machine is dedicated to a single product whose demand follows a stationary Poisson distribution. When the machine is on, items are produced one at a time at a fixed rate and placed into finished‐goods inventory until they are sold. In addition, there is an expense for setting up the machine to begin a production run. Our departure from Gavish and Graves involves the handling of unsatisfied demand. Gavish and Graves assumed it is backordered, while we assume it is lost, with a unit penalty for each lost sale. We obtain an optimal solution, which involves a produce‐up‐to policy, and prove that the expected time‐average cost function, which we derive explicitly, is quasi‐convex separately in both the produce‐up‐to inventory level Q and the trigger level R that signals a setup for production. Our search over the (Q, R) array begins by finding Q0, the minimizing value of Q for R = 0. Total computation to solve the overall problem, measured in arithmetic operations, is quadratic in Q0. At most 3 Q0 cost function evaluations are required. In addition, we derive closed‐form expressions for the objective function of two related problems: one involving make‐to‐order production and another for control of an N‐policy M/D/1 finite queue. Finally, we explore the possibility of solving the lost sales problem by applying the Gavish and Graves algorithm for the backorder problem.

While conventional rule based, real time flow control of sewer systems is in common use, control systems based on fuzzy logic have been used only rarely, but successfully. The intention of this study is to compare a conventional rule based control of a combined sewer system with a fuzzy logic control by using hydrodynamic simulation. The objective of both control strategies is to reduce the combined sewer overflow volume by an optimization of the utilized storage capacities of four combined sewer overflow tanks. The control systems affect the outflow of four combined sewer overflow tanks depending on the water levels inside the structures. Both systems use an identical rule base. The developed control systems are tested and optimized for a single storm event which affects heterogeneously hydraulic load conditions and local discharge. Finally the efficiencies of the two different control systems are compared for two more storm events. The results indicate that the conventional rule based control and the fuzzy control similarly reach the objective of the control strategy. In spite of the higher expense to design the fuzzy control system its use provides no advantages in this case.

EXECUTIVE SUMMARYThis paper examines the effectiveness of three commonly practiced methods used to resolve uncertainty in multi-stage manufacturing systems: safety stock under regenerative material requirements planning (MRP) updates, safety capacity under regenerative MRP updates, and net change MRP updates, i.e., continuous rather than regenerative (periodic) updates. The use of safety stock reflects a decision to permanently store materials and labor capacity in the form of inventory. When unexpected shortages arise between regenerative MRP updates, safety stock may be depleted but it will be. replenished in subsequent periods. The second method, safety capacity, overstates the MRP capacity requirements at the individual work centers by a prescribed amount of direct labor. Safety capacity either will be allocated to unanticipated requirements which arise between MRP regenerations or will be spent as idle time. The third method, net change, offers a means of dealing with uncertainty by rescheduling instead of buffering, provided there is sufficient lead time to execute the changes in the material and capacity plans.Much of the inventory management research has addressed the use of safety stock as a buffer against uncertainty for a single product and manufacturing stage. However, there has been no work which evaluates the performance of safety stock relative to other resolution methods such as safety capacity or more frequent planning revisions. In this paper, a simulation model of a multistage (fabrication and assembly) process is used to characterize the behavior of the three resolution methods when errors are present in the demand and time standard estimates. Four end products are completed at an assembly center and altogether, the end products require the fabrication of twelve component parts in a job shop which contains eight work centers. In addition to the examination of the three methods under different sources and levels of uncertainty, different levels of bill of material commonality, MRP planned lead times, MRP lot sizes, equipment set-up times and priority dispatching rules are considered in the experimental design.The simulation results indicate that the choice among methods depends upon the source of uncertainty, and costs related to regular time employment, employment changes, equipment set ups and materials investment.For example, the choice between safety stock and safety capacity represents a compromise between materials investment and regular time employment costs. The net change method is not designed to deal effectively with time standard errors, although its use may be preferred over the two buffering alternatives when errors are present in the demand forecasts and when the costs of employment changes and equipment set ups are low. The simulation results also indicate that regardless of the method used, efforts to improve forecasts of demands or processing times may be justified by corresponding improvements in manufacturing performance. INTRODUaIONThis paper examines the effectiveness of t...

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