A good approximation of the inventory level in a (Q, r) perishable inventory system

This paper derives a good approach to approximating the expected inventory level per unit time for the continuous review (Q, r) perishable inventory system. Three existing approximation approaches are examined and compared with the proposed approach. Three stockout cases, including the full backorder, the partial backorder, and the full lost sales cases, which customers or material users generally use to respond to a stockout condition are considered. This study reveals the fact that the proposed approximation is simple yet good and suitable for incorporation into the (Q, r) perishable inventory model to determine the best ordering policy. The results from numerical examples and a sensitivity analysis indicate that severe underestimation or overestimation of the expected inventory level per unit time due to the use of an inappropriate approximation approach would result in great distortion in the determination of the best ordering policy

An Integer Linear Programming Model and a Modified Branch and Bound Algorithm for the Material Requirements Planning Problem

[[abstract]]This study presents a novel integer linear programming (ILP) model and a modified branch and bound (MBB) algorithm to minimize the total project inventory cost for the project material requirements planning (PMRP) problem. Twelve two-step lot-sizing rules are compared with the ILP model based on an experiment involving the single-material and two-material requirement problems. According to the results of the experiment, the ILP model outperforms the twelve two-step lot-sizing rules with an average reduction in the total project inventory cost of about 28.54%. This study further assesses the performance of the twelve two-step lot-sizing rules with respect to several important parameters of the PMRP problem. The results indicate that the performance of the twelve two-step lot-sizing rules is significantly affected by the rule itself, the network density, and the value of the percentage of activities with material requirements (PERC). On the other hand, the effectiveness of the MBB algorithm is also evaluated by comparing it with the ILP model. The results of the comparison reveal that the solution obtained by the MBB algorithm is very close to the optimal solution, and that the proposed algorithm does not consume much computational time. The approaches presented in this study, in which project scheduling and lot sizing are considered simultaneously, could provide project managers with useful tools for making better PMRP decisions

The Economic Design of Control Chart under a Preventive Maintenance Policy

[[abstract]]Studies the economic design of x‐ control charts in a situation in which the duration time that the process remains in the in‐control state follows a general distribution which has an increasing hazard rate. In this situation, the active and persistent action for quality control is to design a process in which a preventive maintenance procedure is performed periodically. Addresses first the relationship between preventive maintenance and x‐ control charts. A cost function which is opposed to those given by Banerjee and Rahim and by Hu is derived. The computational results indicate that the proposed model under a preventive maintenance policy has a lower expected total cost per hour than have those of Banerjee and Rahim’s and Hu’s Weibull shock models. Numerical examples also demonstrate that the model has great flexibility when applied in the situation previously mentioned. Presents the advantages of the combination of a preventive maintenance policy and x‐ control charts and concludes that a preventive maintenance policy performed under a certain condition can be particularly instrumental in reducing the expected total cost per hour

The Economic Design of and Control Charts with Preventive Maintenance and Increasing Hazard Rate

[[abstract]]Develops the joint economic designs of • and S2 control charts under four operating policies to monitor the process in a situation where the occurrence of the assignable cause follows a general distribution with an increasing hazard rate. The four operating policies can be chosen by quality controllers to cope with the specific process situation. Policy I and policy II assume that the process performs the preventive maintenance programme at equal and decreasing sampling time intervals, respectively. Policy III and policy IV in turn merely take samples using the non‐uniform and uniform sampling interval schemes without preventive maintenance. The derivation of the four models is not very difficult, so it can be used to derive another model. Offers numerical examples to compare the economic designs and the total expected costs per hour of the four models. Finds, from the computational results, policy II is the best for adoption in the design of • and S2 control charts. The results also show that the proposed solution procedure is more accurate and better than Rahim et al.’s and Chung and Chen’s procedures. Concludes with remarks and some advantages of introducing the periodic preventive maintenance policy into a process

A Stochastic (Q, r) Inventory Model with Manufacturing Learning and Forgetting Effects on Replenishment Lead Times

[[abstract]]This study considers a (q, r) inventory control system in which the distribution of demand can be modeled by a statistical form and the replenishment lead time is affected by manufacturing learning and forgetting. The learning effect is assumed to follow a power function, and the forgetting effect is a fraction of the learning lost between consecutive production runs. We calculate the replenishment lead time for each order by incorporating these effects into both the setup time and unit production time. After the expected total cost function during the finite planning horizon is formulated. three propositions that a feasible solution must satisfy are addressed. According to these propositions, an exhaustive search algorithm giving the optimal solution with integer decision variables, including order numbers, order sizes, and the reorder level, is then derived. The proposed algorithm is illustrated by means of a numerical example with gamma-distributed demand. A sensitivity analysis is also conducted with respect to cost, learning, and forgetting parameters. Computational results indicate that the learning and forgetting effects on the expected total cost depend on the variations in the order number and the order size. The computational time required to obtain the optimal solution is extremely sensitive only to the production learning