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In this paper, we consider an assembly system where a firm faces random demand for a finished product which is assembled using two critical components. The components are procured from the suppliers who. due to production yield losses, deliver a random fraction of the order quantity. We formulate the exact cost function where the decision variables are the target level of finished products to assemble, and the order quantity of the components from the suppliers. Since the exact cost function is analytically complex to solve, we introduce a modified cost function and derive bounds on the difference in the objective function values. Using the modified cost function, we determine the combined component ordering and production (assembly) decisions for the firm. The benefit of coordinating ordering and assembly decisions is numerically demonstrated by comparing the results with two heuristic policies commonly used in practice. In an extension to the model, we consider the case when the firm has the added option of ordering both the components in a set from a joint supplier. First, we consider the case when the joint supplier is reliable in delivery and obtain dominance conditions on the suppliers to be chosen. The maximum price a firm would be willing to pay to ensure reliable supply of components is determined. Later, we consider the uncertainty in the deliveries from the joint supplier and determine conditions under which there is no diversification, that is, either the individual suppliers are used, or the joint supplier is used, but never both.

In this paper, we consider an assembly system where a firm faces random demand for a finished product which is assembled using two critical components. The components are procured from the suppliers who. due to production yield losses, deliver a random fraction of the order quantity. We formulate the exact cost function where the decision variables are the target level of finished products to assemble, and the order quantity of the components from the suppliers. Since the exact cost function is analytically complex to solve, we introduce a modified cost function and derive bounds on the difference in the objective function values. Using the modified cost function, we determine the combined component ordering and production (assembly) decisions for the firm. The benefit of coordinating ordering and assembly decisions is numerically demonstrated by comparing the results with two heuristic policies commonly used in practice. In an extension to the model, we consider the case when the firm has the added option of ordering both the components in a set from a joint supplier. First, we consider the case when the joint supplier is reliable in delivery and obtain dominance conditions on the suppliers to be chosen. The maximum price a firm would be willing to pay to ensure reliable supply of components is determined. Later, we consider the uncertainty in the deliveries from the joint supplier and determine conditions under which there is no diversification, that is, either the individual suppliers are used, or the joint supplier is used, but never both.

In this paper, we consider an assembly system where a firm faces random demand for a finished product which is assembled using two critical components. The components are procured from the suppliers who. due to production yield losses, deliver a random fraction of the order quantity. We formulate the exact cost function where the decision variables are the target level of finished products to assemble, and the order quantity of the components from the suppliers. Since the exact cost function is analytically complex to solve, we introduce a modified cost function and derive bounds on the difference in the objective function values. Using the modified cost function, we determine the combined component ordering and production (assembly) decisions for the firm. The benefit of coordinating ordering and assembly decisions is numerically demonstrated by comparing the results with two heuristic policies commonly used in practice. In an extension to the model, we consider the case when the firm has the added option of ordering both the components in a set from a joint supplier. First, we consider the case when the joint supplier is reliable in delivery and obtain dominance conditions on the suppliers to be chosen. The maximum price a firm would be willing to pay to ensure reliable supply of components is determined. Later, we consider the uncertainty in the deliveries from the joint supplier and determine conditions under which there is no diversification, that is, either the individual suppliers are used, or the joint supplier is used, but never both.

In this paper we consider an assembly problem where two critical components are required for assembly of the final product, the demand for which is stochastic. The components can be ordered separately from individual suppliers or in a set (a set refers to the components in the required ratio) from a joint supplier. We consider the case where the assembly stage is free, i.e., the firm procures and stores the components and sells complete sets. The supplier delivery process may be random owing to uncertainty in the production process (e.g., semiconductor industries). We assume that a supplier, with probability beta (say), supplies 100\% of the order quantity in the current period, and with probability (1-beta) supplies nothing. If there is no delivery during this period, the order is delivered in the next period. The added complexity of coordinating shipments of different components requires careful planning in placing the orders. In the single-period problem, if no order is placed with the joint supplier, the order quantities from the individual suppliers follows an order-up-to policy structure with identical order levels. However, it is optimal to diversify (i.e., order from the joint supplier as well) when the inventory level is below a certain threshold (determined in this paper). With lower initial inventory levels, the firm cannot risk the cost of stockouts if the individual supplier(s) fail to deliver in the current period. With certain conditions on the cost and delivery parameters of the suppliers, we show that the policy structure for the multi-period problem is similar to that of the single-period problem, except that the order up-to-levels are not the same. Intuitively, it might be optimal to order extra components for use in the future. This is a direct consequence of the uncertainty in the delivery timing of the suppliers. Finally we conduct a computational study of the two-period problem and determine the effect of supplier costs and the probability of

This paper addresses the issue of location of inspection stations along a serial production line. As a function of inspection site, the capacity required to test and repair the parts would vary. The production-inspection model developed provides management with information on such capacity planning issues. It integrates the issues of inspection location, inspection capacity, and production capacity. We consider a two-stage production line and evaluate cases when there are inspection sites after each production stage and when inspection is carried out after the final stage. In the latter case, we find the conditions when the safety stock required to meet the demand is higher, This has managerial implications because the inventory level is not only higher, it is held after the final stage, i.e. has more value added onto it. However, if there are inspection stations after each stage, the capacity required to test and repair the parts is higher. The intent of this work is to provide insights into designing production-inventory systems for the serial model that we consider. We also discuss the generalization of the scope of the two-stage model to an N stage production line. In an extension to the problem, we consider the situation when not all the defectives can be repaired. We extend the basic model by considering the effect of partial scraping of the defectives.

This paper addresses the issue of location of inspection stations along a serial production line. As a function of inspection site, the capacity required to test and repair the parts would vary. The production-inspection model developed provides management with information on such capacity planning issues. It integrates the issues of inspection location, inspection capacity, and production capacity. We consider a two-stage production line and evaluate cases when there are inspection sites after each production stage and when inspection is carried out after the final stage. In the latter case, we find the conditions when the safety stock required to meet the demand is higher, This has managerial implications because the inventory level is not only higher, it is held after the final stage, i.e. has more value added onto it. However, if there are inspection stations after each stage, the capacity required to test and repair the parts is higher. The intent of this work is to provide insights into designing production-inventory systems for the serial model that we consider. We also discuss the generalization of the scope of the two-stage model to an N stage production line. In an extension to the problem, we consider the situation when not all the defectives can be repaired. We extend the basic model by considering the effect of partial scraping of the defectives.

In this paper we consider an assembly problem where two critical components are required for assembly of the final product, the demand for which is stochastic. The components can be ordered separately from individual suppliers or in a set (a set refers to the components in the required ratio) from a joint supplier. We consider the case where the assembly stage is free, i.e., the firm procures and stores the components and sells complete sets. The supplier delivery process may be random owing to uncertainty in the production process (e.g., semiconductor industries). We assume that a supplier, with probability beta (say), supplies 100\% of the order quantity in the current period, and with probability (1-beta) supplies nothing. If there is no delivery during this period, the order is delivered in the next period. The added complexity of coordinating shipments of different components requires careful planning in placing the orders. In the single-period problem, if no order is placed with the joint supplier, the order quantities from the individual suppliers follows an order-up-to policy structure with identical order levels. However, it is optimal to diversify (i.e., order from the joint supplier as well) when the inventory level is below a certain threshold (determined in this paper). With lower initial inventory levels, the firm cannot risk the cost of stockouts if the individual supplier(s) fail to deliver in the current period. With certain conditions on the cost and delivery parameters of the suppliers, we show that the policy structure for the multi-period problem is similar to that of the single-period problem, except that the order up-to-levels are not the same. Intuitively, it might be optimal to order extra components for use in the future. This is a direct consequence of the uncertainty in the delivery timing of the suppliers. Finally we conduct a computational study of the two-period problem and determine the effect of supplier costs and the probability of

This paper addresses the issue of location of inspection stations along a serial production line. As a function of inspection site, the capacity required to test and repair the parts would vary. The production-inspection model developed provides management with information on such capacity planning issues. It integrates the issues of inspection location, inspection capacity, and production capacity. We consider a two-stage production line and evaluate cases when there are inspection sites after each production stage and when inspection is carried out after the final stage. In the latter case, we find the conditions when the safety stock required to meet the demand is higher, This has managerial implications because the inventory level is not only higher, it is held after the final stage, i.e. has more value added onto it. However, if there are inspection stations after each stage, the capacity required to test and repair the parts is higher. The intent of this work is to provide insights into designing production-inventory systems for the serial model that we consider. We also discuss the generalization of the scope of the two-stage model to an N stage production line. In an extension to the problem, we consider the situation when not all the defectives can be repaired. We extend the basic model by considering the effect of partial scraping of the defectives.

In this paper we consider an assembly problem where two critical components are required for assembly of the final product, the demand for which is stochastic. The components can be ordered separately from individual suppliers or in a set (a set refers to the components in the required ratio) from a joint supplier. We consider the case where the assembly stage is free, i.e., the firm procures and stores the components and sells complete sets. The supplier delivery process may be random owing to uncertainty in the production process (e.g., semiconductor industries). We assume that a supplier, with probability beta (say), supplies 100\% of the order quantity in the current period, and with probability (1-beta) supplies nothing. If there is no delivery during this period, the order is delivered in the next period. The added complexity of coordinating shipments of different components requires careful planning in placing the orders. In the single-period problem, if no order is placed with the joint supplier, the order quantities from the individual suppliers follows an order-up-to policy structure with identical order levels. However, it is optimal to diversify (i.e., order from the joint supplier as well) when the inventory level is below a certain threshold (determined in this paper). With lower initial inventory levels, the firm cannot risk the cost of stockouts if the individual supplier(s) fail to deliver in the current period. With certain conditions on the cost and delivery parameters of the suppliers, we show that the policy structure for the multi-period problem is similar to that of the single-period problem, except that the order up-to-levels are not the same. Intuitively, it might be optimal to order extra components for use in the future. This is a direct consequence of the uncertainty in the delivery timing of the suppliers. Finally we conduct a computational study of the two-period problem and determine the effect of supplier costs and the probability of