Number Of Outstanding Orders Research Articles

Synchronization in a two‐supplier assembly system: Combining a fixed lead‐time module with capacitated make‐to‐order production

AbstractA high‐tech manufacturer often produces products that consist of many modules. These modules are either sourced from one of its suppliers or produced in‐house. In this paper, we study the common case of an assembly system in which one module is sourced from a supplier with a fixed lead‐time, while the other module is produced by the manufacturer itself in a make‐to‐order production system. Since unavailability of one of the modules has costly consequences for the production of the end‐product, it is important to coordinate between the ordering policy for one module and the production of the other. We propose an order policy for the lead‐time module with base‐stock levels depending on the number of outstanding orders in the production system of the in‐house produced module. We prove monotonicity properties of this policy and show optimality. Furthermore, we conduct a computational experiment to evaluate how the costs of this policy compare to those of a policy with fixed base‐stock levels and show that average savings of up to 17% are attained.

A two-stage stochastic programming model for periodic replenishment control system under demand uncertainty

The inventory control system consists of defining strategies to manage inventory replenishment such that costs involved in ordering, holding, and meeting the demands are optimized. Although several methods for inventory management are proposed in the literature, the assumptions made necessary can hinder their applicability in practice. Motivated by this fact, we propose a methodology for determining the optimal parameters of an inventory control system for single-item one-echelon supply chains using two-stage stochastic programming, considering periodic review and uncertain demand. The proposed approach is flexible enough to consider backlogs or lost sales cases without limitations on the number of outstanding orders and allows the consideration of uncertainties in a more comprehensive manner when compared to currently available methods. The optimal review periodicity and the inventory target level are determined using a nonlinear mixed-integer programming model, which takes into account the uncertain nature of the item demand levels through a finite set of scenarios. We present how this model can be reformulated as a deterministic equivalent mixed-integer linear programing model and how the Sample Average Approximation method can be used to incorporate the uncertainty into it. To validate the proposed approach, we perform a simulation-based sensitivity analysis in the neighborhood of the solutions obtained. We also compare them with those obtained applying the Hadley-Whitin method, considering the premises that are necessary for the later. Further, we present results from a case in which the stochastic demand is not stationary. The results obtained provide strong evidence of the potential of the proposed approach.

Supply management of high-value components with a credit constraint

Due to rapid increases in the automotive markets in emerging economies, leading car manufacturers rapidly expand their manufacturing capacity in countries such as China. A certain portion of key performance components however continue to be sourced from developed countries. We study such a manufacturer that imports high-value components from a developed country. There are two available transportation modes: a slow mode with low cost and long and stochastic lead time, and a fast mode with high cost and short and deterministic lead time. Moreover, the manufacturer is subject to a credit constraint that bounds both the in-warehouse inventory and the number of outstanding orders (because it needs to pay for the components in advance). Consequently, the cheapest hedge against demand and supply uncertainty—inventory—is only available to a limited extent and the decision maker must turn to using the fast transportation mode for a much larger share of the orders. We model the manufacturer’s ordering policy and study its performance using simulation. Our study shows the adverse effects that the credit limit has on the growth opportunities of such companies in developing countries that import high-value components or other goods from developed countries. We show that especially the reduction in lead time variability can substantially reduce these adverse effects. Realizing that this variability is primarily caused by the import customs procedures, governments in developing economies have a means to assist their local manufacturers.

Ranking of generalised multi-stage KANBAN policies

We consider KANBAN type batch-ordering policies in a multi-stage production–inventory system. KANBAN policies and various modifications of such policies may be interpreted as installation stock ( Q, r)-policies with constraints on the number of outstanding orders. If the same constraints are applied also to MRP and echelon stock ( Q, r)-policies, the ranking lists established by Axsäter and Rosling (Axsäter, S., Rosling, K., 1993. Management Science 39, 1274–1280; Axsäter, S., Rosling, K., 1994. European Journal of Operational Research 75, 405–412) for such policies remain valid. The result is based on new definitions of the inventory positions, and suggests new classes of generalised KANBAN type batch-ordering policies with potentially improved performance.

The{Q,r)Inventory System With An Unreliable Supplier

AbstractThis paper examines the impact on operating costs of having an unreliable supplier in a continuous review, fixed order quantity (Q) — reorder point (r) inventory system. We assume Poisson demand and exponentially distributed lengths of the supplier’s on and off periods. On (off) periods represent time lengths during which the supplier is able (unable) to fill new orders. Any unsatisfied demand is assumed to be lost. We analyze two situations. The first has a negligible lead time but allows the number of outstanding orders, each of a fixed size Q, to be arbitrary. The second situation, on the other hand, has a constant lead time but there the number of outstanding orders is restricted to at most one. In each case, exact expressions necessary to find the average cost minimizing (Q, r) pair are developed and several numerical examples are solved. Computational results show the cost function to be well behaved and suggest that ignoring supply uncertainty or approximate modeling can be relatively very ...

Continuous-Review (s, S) Inventory Models with State-Dependent Leadtimes

This paper describes the development of a continuous-review (s, S) inventory model with complete backordering and state-dependent, stochastic leadtimes. The demand on the inventory system is assumed to be a Poisson process, and the order-filling portion of the replenishment leadtime is allowed to depend on the number of outstanding orders (i.e., to be state dependent). The inventory state probabilities which are required in order to optimize the cost function with respect to s and S can be obtained via a queuing analysis on the order-filling process. Orders are assumed to arrive at a single-channel service facility, where the service may be state dependent in either one of two ways: (1) the instantaneous probabilities at an arbitrary point in time of an order being filled (i.e., a service completed) in an infinitesimal interval of length Δt is μ(m)Δt + o(Δt), where m is the number of outstanding orders (instantaneous state dependence); and (2) the order-filling time is an exponentially distributed random variable with distribution function Bn(t) = 1 − e−μ(n)t, where n is the number of outstanding orders just after the previous order has been filled (departure-point state dependence). The μ(·) used to illustrate the methodology is two state; that is, μ(·) = μ1 if only one order is outstanding and μ if more than one is outstanding. The appropriate queuing model describing the ordering process turns out to be a Poisson input, batch-service model with batch size Q = S − s. The instantaneous state-dependent model is analyzed using a Chapman-Kolmogorov approach, while the departure-point state-dependent model utilizes an imbedded-Markov-chain approach. The computational aspects of the models are illustrated for a specific set of values of the appropriate parameters.

Stochastic inventory models with bulk demand and state-dependent leadtimes

This paper describes two one-for-one ordering (S − 1, S) inventory models in which the time required for order replenishment is state-dependent. The demand is assumed to follow a compound Poisson distribution, and that portion of the leadtime corresponding to the actual filling of orders is assumed to depend on the number of outstanding orders. Since the orders placed are assumed to go into a single-server queue, queuing results are used to obtain the expected inventory cost as a function of S in order to obtain an optimal value of S.

Stochastic inventory models with bulk demand and state-dependent leadtimes

This paper describes two one-for-one ordering (S − 1, S) inventory models in which the time required for order replenishment is state-dependent. The demand is assumed to follow a compound Poisson distribution, and that portion of the leadtime corresponding to the actual filling of orders is assumed to depend on the number of outstanding orders. Since the orders placed are assumed to go into a single-server queue, queuing results are used to obtain the expected inventory cost as a function of S in order to obtain an optimal value of S.