Supply Risk in a Multiple-sourcing Supply System

In a single-period, single-item, single-site inventory system, we address the issue of selecting suppliers from multiple unreliable suppliers and allocating orders among them to satisfy uncertain demand and minimize total cost from the view of retailers. The suppliers may have different fixed order costs, item costs, and/or restrictions on minimum and maximum order sizes. Supplier reliability is modeled as the probability of on-time delivery, which implies that with a certain probability, the supplier fails to fulfill the entire order. Total cost consists of item costs (proportional to delivered quantities), end-of-period costs (including disposal and penalty costs), and in some of our models, fixed ordering costs.;In the supply-risk literature, most multiple-sourcing inventory models make the assumption that fixed ordering costs are incurred and demand is deterministic, or that there is no fixed cost and demand is stochastic. However, in practice, demand is stochastic and there is also overhead associated with generating or receiving an order. We solve the problem of determining the optimal order policy under such circumstances. In most of our models, fixed cost is incurred when an order is placed, which complicates the problem in that order cost is not proportional to the order quantity. Fixed cost is not directly incurred in some models, but there are minimum order size constraints for those problems, which reflect fixed costs indirectly. Suppliers’ binomial delivery probability complicates the problem because the optimal order quantity allocation is more difficult to determine compared with order quantity allocation problems with perfectly reliable suppliers or unreliable suppliers delivering a random percentage of an order (random yield).;Due to fixed cost and/or minimum order size constraints, the expected total cost is nonconvex, which is analyzed by considering several cases separately. Within each case, the cost function is proven to be convex and can be optimized. These cases are compared with each other to determine optimal policies. Properties of this problem are examined so that some comparisons are unnecessary, which makes the process more efficient computationally. We consider three types of models based on different assumptions about the number of suppliers and the initial inventory level.;Model I assumes two unreliable suppliers with zero initial inventory level. The optimal policy structures as a function of reliability level are derived for the identical-supplier model with different fixed cost scenarios. The effects of cost parameters, reliability levels, and demand distributions on optimal policy structures and order quantities are investigated. Models with different assumptions about item costs or reliability levels are also discussed and the corresponding optimal policy structures are provided. An approximation method to compute the optimal order quantities and corresponding computational results are presented.;Model II lies between the single-period model (Model I) and a multiple-period model by making the assumption of an arbitrary initial inventory level. We prove that there are ten possible optimal policy structures as a function of initial inventory level. Two special models are considered. One assumes that the more expensive supplier is perfectly reliable and the other assumes that the two suppliers are identical. Numerical experiments are carried out to compare the costs of implementing optimal single-period policies in three-period problems with the optimal costs resulting from a Markov Decision Process formulation. The conditions under which the optimal single-period policies are good approximations for multiple-period problems are investigated. A heuristic method is proposed to reduce the approximation errors.;Model III extends Model I by assuming that the number of suppliers is more than two. Fixed order costs are dropped from this model. Instead, order size constraints are added to represent minimum order size requirements and suppliers’ capacities. This model is divided into two problems: (1) the master problem which involves selection of a set of suppliers and (2) a subproblem which involves determination of the order quantity allocation to a given set of suppliers. Five methods are proposed to solve subproblems and four methods are proposed to solve master problems. Combinations of these methods are discussed and implemented in numerical experiments to show their performance. The effects of various problem parameters on the supplier selection decision are presented.