CHAPTER 8 CONCLUSIONS AND FUTURE DIRECTIONS
8.2 Contributions
A thorough review of the literature is presented in chapter two. This review covers the work concerning different aspects studied in the thesis in the context of EOQ model for imperfect items. The review in chapter two provides a useful resource for researchers currently engaged in the work on inventory systems with imperfect items, and hopefully may provide new ideas for further stimulating this field of research.
The first contribution in the thesis is presented in chapter three. This chapter makes use of Salameh and Jaber (2000) and Duffuaa and Khan (2002) models to suggest that an inspector may make Type I and Type II errors while screening for defective items. The annual profit with inspection errors remained concave with respect to the order size. The significance of inspection errors was indicated by the fact that annual profit becomes much smaller than that in Salameh and Jaber (2000) and that it keeps on reducing with an increase in fraction of defectives. It was emphasized that the misclassifications are critical if the parts under inspection are of an aircraft, a space shuttle or a complex gas ignition system. So, it is vital for a buyer to be aware of not only the accurate parameters of error about his inspectors but also the ways to mitigate these errors.
This work has been published in a journal (Khan et al., 2011a).
The second contribution in the thesis is presented in chapter four. This chapter is an extension of Salameh and Jaber (2000) for the case where the buyer’s inspection process undergoes learning while screening for defective items in a lot. A 100% inspection is carried out with an error free screening and the rate of screening tends to increase by virtue of learning. This counters an assumption in Salameh and Jaber (2000) that the inspection rate is fixed and is always greater than demand. Having a screening rate lesser than demand rate in the beginning of the screening process, incurs shortages which are tackled in the chapter as both lost sales and backorders. Three scenarios of learning, available in the literature, are compared for the above set-up. These scenarios are (i) total forgetting, where an inspector starts in every cycle with no prior experience, (ii) total transfer of learning, where the inspector does not lose any knowledge
172 or skills in the breaks and the learning curve continues as if there were no interruptions, and (iii) partial transfer of learning, where an inspector carries part of his experience to the subsequent cycles. The last situation is the most generalized and the realistic one. The results indicate that total transfer of learning remains better for both the lost sales and the backorders set-up. Besides, the annual profit tends to increase with the learning exponent in screening. That is, the faster the learning in screening the lesser is the screening time. A similar finding of the research is that the annual profit can be increased by retaining more and more knowledge in screening process. This was pointed out by experimenting different levels of time for total forgetting, at fixed values of the learning exponent. It was noticed that an increase in the percentage of defectives decreases the annual profit at a fixed exponent of learning. The unit cost of lost sales was also shown to have a similar effect on the annual profit. It was shown that an increase in the unit screening cost reduces the annual profit to great extent at the slower rates of learning. This work has been published in a journal (Khan et al., 2010a).
The third contribution in the thesis is presented in chapter five. In this chapter, a two-stage, multi-supplier, single-vendor supply chain is formulated. A vendor is supposed to ask for a number of components from different suppliers, which are needed to make a single product.
Suppliers are believed to be providing a certain fixed percentage of defectives in their supplies.
The vendor institutes a 100% inspection process and sells the defectives in the local market at a discounted price. Two mechanisms, as in Khouja (2003) were studied for the coordination between suppliers and the vendor. The first mechanism is governed by an equal cycle time for all the stakeholders of the supply chain. In the second mechanism, each supplier’s cycle time is taken to be an integer multiplier of the vendor’s cycle time. The results indicated that the suppliers are supposed to follow a relaxed and practical approach of the integer multipliers cycle time rather than forcing themselves to follow an equal cycle time. A number of human factors are brought into the picture in this chapter. First of all, a scenario is considered in which the inspectors at the vendor’s end make misclassifications. Next, the production process of the vendor is assumed to follow learning as workers tend to perform the same job at a faster pace.
Lastly, the quality of the suppliers’ items is assumed to follow a logistic learning curve. It was observed that the inspection errors tend to increase the annual cost of the supply chain, learning in production drops this cost to great extent while the learning in supplier’s quality results in a situation as if there are no defectives from the suppliers. The savings in the annual cost of a
173 model that incorporates all of the above human factors were lesser than those experienced in the case of learning in production only. Parts of this work have been accepted for publication in two journal articles: Khan and Jaber (2011) and Khan et al. (2011b).
The fourth contribution in the thesis is presented in chapter six. In this chapter, a two-stage, single-vendor, single-buyer supply chain is formulated. A vendor is supposed to make a single product for its buyer and it is believed that a known fraction of its lots is defective. The buyer institutes a 100% inspection process to separate these defective products. A model depicting this scenario is formulated to find an optimal batch size and the number of shipments for each order.
Two human factors are brought into the picture in this chapter. First of all, a scenario is considered in which the inspectors at the buyer’s end make misclassifications. Next, the production process of the vendor is assumed to follow learning as workers tend to perform the same job at a faster pace. The results showed that inspection errors increase the inspection cost and thus the overall annual cost of the supply chain. Type I error has a pronounced effect on the supply chain as compared to the Type II errors because of an increased order size and the inspection cost. On the other hand, increasing the level of learning at vendor’s production process brought more and more savings to the supply chain. Part of this work has been presented in a conference (Khan et al., 2010b).
The fifth contribution in the thesis is presented in chapter seven. This chapter again takes a two-stage, single-vendor, single-buyer supply chain. The vendor is supposed to make a single product and it is believed that a known fraction of its lots is defective. The buyer institutes a 100% inspection process to separate these defective products. They follow a consignment stock policy according to which the vendor keeps on supplying its inventory to the buyer’s warehouse with regular intervals. The buyer withdraws from this warehouse according to the market demand. A model depicting this scenario is formulated to find an optimal lot size and the number of shipments per batch for the vendor. This work is an extension of the work of Braglia and Zavanella (2003) and Salameh and Jaber (2000). In the next part of the chapter, buyer’s screening process is taken to be error prone. That is, the inspectors make Type I and Type II errors in screening. Besides, the vendor’s production process follows learning from cycle to cycle. A model depicting this scenario is formulated to find an optimal lot size and the number of shipments per batch for the vendor. The results showed that the annual cost increases when one moves from Hill (1997) model to Braglia and Zavanella (2003) and then to our model in this
174 chapter. Besides, it was observed that the annual costs in this model are better than that in chapter 6 when holding costs go higher than a threshold value. The chapter dealt with some interesting issues such as:
1. Finding an appropriate lot size when the cost for intercepting defects is considered.
2. Balancing the time for inspection cycle and defective items percentage. This time may be reduced by sacrificing the efficiency in intercepting defective items, as inBraglia and Zavanella (1994).
3. Correcting the production capacity at the vendor’s side with respect to process defectiveness (when defects are intercepted at the buyer’s side).
Part of this work has been presented in a conference (Khan et al., 2010c).