Ms = Percentage of defective parts supplied by suppliers, accommodating inspection errors at the seller's end {= (1− 𝛾𝑠)𝑒1+ 𝛾𝑠(1− 𝑒2)}. Mmax = Highest percentage of defects in suppliers' items, accommodating inspection errors at the vendor's end.
BACKGROUND OF THE RESEARCH
- Introduction
- Supply Chains
- Quality
- Learning
- Forgetting
- Why Learning and Quality Together?
- Salameh and Jaber’s (2000) Model
- Summary
A number of supplier-supplier and a supplier-buyer supply chain in models will be considered in the thesis. The number "2" in the denominator was missing from the above equation in Salameh and Jaber (2000), which was pointed out by Cárdenas-Barrón (2000).
LITERATURE REVIEW
Introduction
EOQ/EPQ Models for Imperfect Items
They assumed that (i) production rate is a decision variable, (ii) unit production cost is a function of production scale, (iii) production process quality. The opposite is true when the average time until the process shifts 'out of control' is largely independent of the production rate.
Rework and Scrap
They showed that lot size and rework costs are directly related to the fraction of defects. They assumed there is a limit to the number of defective items and that the rework process is defect free.
Supply Chains
They have shown that incorporating volume discounts at both ends of the supply chain can significantly reduce costs compared to focusing only on the downstream end. The buyer discovers only part of the defective items and passes the rest on to the customers.
Learning, Quality and Investment
That is, the rapid speed of quality improvement can be detrimental to the cost side of the business. Analysis of variance showed that 84% of the variability in average rework time per unit is explained by cumulative production as an independent variable.
Imperfect Inspection
He concluded that type I and type II errors have a significant impact on the performance measures of repetitive inspection plans. Duffuaa and Khan (2005) quantified the effect of inspection errors, mainly on the performance measures of a complete repeat inspection plan (Duffuaa and Khan, 2002).
Fuzzy Set Theory
Duffuaa and Khan (2008) presented an inspection plan for the case where the features' defective rates are statistically dependent. In this thesis, Type I and Type II errors are incorporated into the screening process, both at the end of a seller and a buyer in a two-level supply chain context.
Shortage and Backordering
They showed that the management of a company can select suppliers based on the percentage of defects and the deterioration rate of the products supplied by each supplier. 2006) extended Salameh and Jaber's (2000) work to a single-supplier, single-buyer supply chain with product deterioration. They assumed that a portion of the reworked goods fail in the repair process and thus become scrap. 2007) is considered a single-item, two-echelon, continuous review inventory model.
Consignment Stocks
Li and Hong (2006) extended Braglia and Zavanella's (2003) model in the case of supplier shortages. They derived a common economic lot size model for the supplier's production lot and replenishment lot sizes. They modeled two cases for the supplier-managed system based on the ownership of the warehouse.
Contemporary Trends in EOQ/EPQ Modelling
Hsu and Yu (2009) studied the situation where a supplier is confronted with an excess stock or a change in the production run of a product. Chen and Kang (2009) considered trade credit and imperfect quality in the integrated seller-buyer model for a single product. The cost savings for the buyer would be negative in the integrated model if the warranty costs are the same as in the non-integrated model.
Research Questions
They assumed depreciation cost to be a continuous non-decreasing function of holding time, and process quality cost to be a continuous convex function of production run length. They solved the problem by simulated annealing (SA) and Iterated Local Search (ILS) and found that ILS is better. Is consignment inventory (CS) a better policy than a centralized coordination policy to manage inventory when defective items and errors in inspection exist in a seller-buyer supply chain.
Research Methodology
Extend Salameh and Jaber (2000) to the case of inspection learning when there is complete forgetting, partial transfer, and total learning from cycle to cycle. Extend Salameh and Jaber (2000) for a two-level supplier-vendor supply chain to explore the three different coordination schemes given by Khouja (2003). Present a different model of the two-level (seller-buyer) supply chain, extending Salameh and Jaber's (2000) model in the context of Hill's (1997) approach.
ECONOMIC ORDER QUANTITY (EOQ) FOR ITEMS WITH IMPERFECT
- Introduction
- Model Description
- Mathematical Model
- Numerical Analysis
- Managerial Implications
- Summary and Conclusions
These defective items are later returned to inventory and are shown as B2 in Figure 3.1. In the following analysis, most of the data are taken from the Salameh and Jaber (2000) model. Our results also showed that the costs of type I and type II errors reduce part of the annual profit.
ECONOMIC ORDER QUANTITY MODEL FOR ITEMS WITH IMPERFECT
Introduction
Second, this chapter also addresses the transfer of knowledge in learning when production moves from one cycle to another in three possible scenarios: (i) no transfer of learning, (ii) full transfer of learning, and (iii) partial transfer of learning. to learn .
Mathematical Model
In case of no learning transfer, that is, a worker does not retain knowledge from previous cycles (𝑢𝑖 = 0), it will be taken as Two cases (lost sales and backorders) will now be considered to address shortages in each of the three scenarios for transferring learning from one cycle to another.
Lost Sales
Three learning scenarios will now be considered to develop a mathematical model for a buyer's expected annual profit. Salameh and Jaber (2000) determined the expected annual profit from the expected value of the buyer's annual profit. That is, the expected annual profit should be a ratio of the expected profit per cycle to the expected cycle time.
Backorders
The three learning scenarios discussed in the lost sale case will be considered here to develop a buyer's expected annual profit. The custody costs, the expected profit per cycle and the expected annual profit in Eq. In this case the experience ui in cycle i becomes zero and the inspection time is determined by Eq.
Numerical Analysis
Similarly, to understand the effect of shortage costs, annual profit was obtained for various lost sales and backorder costs in the case of partial learning transfer. Again, the average annual gain from ten consecutive learning cycles at different was obtained. The annual profit response for the case of lost sales with full learning transfer is shown in Figure 4.8 at different levels of learning.
Summary and Conclusions
Introduction
For each of these extensions, the optimal lot size and annual supply chain cost are determined. The remainder of the chapter is organized as follows: Section 5.2 provides a description and formulation of the models. A number of extensions of the model in Section 5.2 for various human factors are presented in Section 5.3.
Model Description and Development
Therefore, the raw material in each cycle will consist of (i) non-defective parts, (ii) defective parts and (iii) the leftovers. So the total annual cost of the entire supply chain will be for an equal cycle time mechanism. The suppliers' cycle time is an integer multiplier of the basic cycle time T used by the vendor.
Model Extensions
5.5), the total annual cost of the supply chain for the equal cycle time can be written as. 5.8) and (5.22), would be the annual cost of the supply chain in a cycle, for the integer multiplier mechanism. For an approximate value of the multipliers in Eq. Again, an estimated value of the production amount and learning rate would be calculated by iterating Eq.
Numerical Analysis
An interesting outcome of this example suggests that including the defective items results in a reduction in annual supply chain costs. Figure 5-4 shows that the defective items from supplier 2 have more variation in their impact on annual supply chain costs, while those from supplier 1 have little variation in these costs. That is, the misclassified defective items have a major impact on the total cost of the supply chain.
Summary and Conclusions
The rationale is that after certain level of multiples of the cycle time, the total cost of the supply chain starts to rise. This factor is shown to increase the carrying cost of the seller and therefore the overall annual cost of the supply chain. Next, the production process of the seller is assumed to follow, as workers tend to perform the same work at a faster pace.
A VENDOR-BUYER SUPPLY CHAIN WITH INSPECTION ERRORS AND
- Introduction
- Model Description
- Numerical Example
- Conclusions
An optimal production quantity and the number of shipments per cycle will be determined through the total cost of the supply chain. So the total cost of the two-tier, learning-in-production supply chain would be 𝑇𝐶𝑖(𝑄) =𝐴𝑣+ ℎ𝑣𝑄2−𝑏. Find an average of the number of shipments, batch size, and annual cost from the values.
CONSIGNMENT STOCK POLICY FOR A VENDOR-BUYER SUPPLY
- Introduction
- Model Description
- Numerical Example 1
- Inspection Error and Learning
- Numerical Example 2
- Conclusions
The results show that following the approach of Salameh and Jaber (2000) with the consignment stock (CS) policy addressed by Braglia and Zavanella (2003), results in an increase in the annual cost of the supply chain. 168 Figure 7.9 shows the decrease in annual supply chain cost due to learning in the vendor's production process. The results show that the inclusion of inspection errors increases the annual cost of the supply chain due to the increase in the number of shipments per cycle.
CONCLUSIONS AND FUTURE DIRECTIONS
Introduction
Contributions
In the second mechanism, each supplier's cycle time is treated as an integer multiplier of the vendor's cycle time. The results showed that inspection errors increase the cost of inspections and thus the total annual cost of the supply chain. In the next part of the chapter, the buyer verification process is discussed as error-prone.
Future Directions
The model in chapter three could be extended in case the demand is uncertain. The model in chapter six can be extended to investigate the effect of learning in buyer inspection errors. The model in chapter seven could be extended for partial and transfer of learning in production from cycle to cycle.
UNCERTAINTY OF RESULTS IN SALAMEH AND JABER (2000)
An economic order quantity model with demand-dependent unit production costs and imperfect production processes. An Optimal Algorithm for Solving the Dynamic Lot Sizing Model with Learning and Forgetting in Configurations and Manufacturing. Optimal retailer cycle times in the EOQ model with imperfect quality and an allowed credit period.
EXPECTED VALUE OF V IN EQUATION (3.5)
CONCAVITY OF THE ANNUAL PROFIT IN EQ. (4.15)
An optimal solution of a general batch size inventory model with deteriorated and imperfect products, taking into account inflation and time value of money. Determine accelerated time and cost of the final product with defective parts using the critical path method (CPM) and the time cost method. Planning and replenishment plan for an integrated deteriorating inventory model with inventory-dependent sales percentage.
CONVEXITY OF THE ANNUAL COST IN EQ. (5.22)
By definition, each unit of a finished product consists of mµ units, where the unit cost of the finished product is 𝑚𝑐𝑢𝜇+𝑐𝑝 where 𝑐𝑢 and 𝑐𝑝 are the purchase cost per unit of the raw material and the production cost per unit of the product respectively completed.
CONVEXITY OF THE ANNUAL COST IN EQ. (6.14)
It approaches zero faster when n is large and b is close to 1. dQ2E[𝑇𝐶𝑈𝑖] is insignificant as it is very close to zero. 6.14) is convex with a unique reducer.
HILL (1997) GENERALIZED MODEL
OPTIMALITY OF THE ANNUAL COST IN EQ. (7.16)
The effects of learning and forgetting on the optimal production lot size for deteriorating items with time-varying demand and deterioration rates. The effects of learning on the optimal production lot size for deteriorating and partially backordered items with time-varying demand and deterioration rates. Exact closed-form solutions for ''optimal inventory model for items with imperfect quality and backorder shortages'', Omega.
