Mohammed A. Darwish

Vendor managed inventory model for single-vendor multi-retailer supply chains

Vendor managed inventory is an integrated approach for retailer-vendor coordination, according to which the vendor decides on the appropriate inventory levels within bounds that are agreed upon in a contractual agreement between vendor and retailers. In this contract, the vendor usually incurs a penalty cost for items exceeding these bounds. The purpose of this paper is to develop a model for a supply chain with single vendor and multiple retailers under VMI mode of operation. This model explicitly includes the VMI contractual agreement between the vendor and retailers. The developed model can easily describe supply chains with capacity constraints by selecting high penalty cost. Theorems are established to alleviate the complexity of the model and render the mathematics tractable. Moreover, an efficient algorithm is devised to find the global optimal solution. This algorithm reduces the computational efforts significantly. In addition, numerical experiments are conducted to show the utility of the proposed model.

Optimal selection of process mean for a stochastic inventory model

It is very common to assume deterministic demand in the literature of integrated targeting – inventory models. However, if variability in demand is high, there may be significant disruptions from using the deterministic solution in probabilistic environment. Thus, the model would not be applicable to real world situations and adjustment must be made. The purpose of this paper is to develop a model for integrated targeting – inventory problem when the demand is a random variable. In particular, the proposed model jointly determines the optimal process mean, lot size and reorder point in (Q,R) continuous review model. In order to investigate the effect of uncertainty in demand, the proposed model is compared with three baseline cases. The first of which considers a hierarchical model where the producer determines the process mean and lot-sizing decisions separately. This hierarchical model is used to show the effect of integrating the process targeting with production/inventory decisions. Another baseline case is the deterministic demand case which is used to show the effect of variation in demand on the optimal solution. The last baseline case is for the situation where the variation in the filling amount is negligible. This case demonstrates the sensitivity of the total cost with respect to the variation in the process output. Also, a procedure is developed to determine the optimal solution for the proposed models. Empirical results show that ignoring randomness in the demand pattern leads to underestimating the expected total cost. Moreover, the results indicate that performance of a process can be improved significantly by reducing its variation.

An integrated single-vendor single-buyer targeting problem with time-dependent process mean

The inventory/production decisions in single-vendor single-buyer supply chain are integrated with the targeting problem in this paper. Traditionally, the process mean is assumed to be constant over time. However, it is common that production processes deteriorate with time and constant process mean assumption is not appropriate in this situation. In the proposed model, this restrictive assumption is relaxed and the process mean is considered to drift with time. Also, solution method is discussed and sensitivity analysis on the model’s key parameters is conducted. In particular, the effect of the shift in the process mean and the variation in the filling process are examined.

Optimal production and inventory decisions for supply chains with one producer and multiple newsvendors

This paper considers a supply chain with a single manufacturer supplying a newsvendor-type item to multiple retailers (newsvendors). The manufacturer produces the item in batches at a finite rate and ships the output to the retailers. The retailers then have to satisfy a stochastic demand which follows a general probability distribution. The objective is to view the system as an integrated whole and determine the production and shipment schedule which maximises the expected total profit in a selling period. The concavity of the expected total profit function is established, the global optimal solution is derived, and a simple but efficient algorithm is set out. Two special cases are considered, the first of which is for fast-moving items and the other for slow-moving items.

Stochastic inventory model with finite production rate and partial backorders

One of the most widespread stochastic inventory models is the classical stochastic continuous review inventory control (Q, R) model. However, there are some restrictive assumptions in deriving this model. One of these assumptions is that the production rate is infinite which has motivated many researchers to develop (Q, R) models with finite production rate. In these models, the randomness of demand is indirectly introduced in the models by assuming that the safety stock is equal to a safety factor multiplied by the standard deviation of lead time demand. In this paper, the classical stochastic continuous review inventory control (Q, R) model is generalised for the case when the production rate is finite and unmet demand is partially backordered. Unlike the models presented in the literature, the probabilistic nature of the demand is reflected directly in the formulation of the proposed model. Furthermore, the optimal lot size and reorder point are determined for this model. Two types of items are investigated; fast-moving and slow-moving items. Also, the effect of the production rate on the optimal solution is studied through numerical examples. The results show that the production rate impacts the inventory and production decisions significantly.

Stochastic inventory model for imperfect production processes

Production/inventory decisions for imperfect production process are considered in this paper. The process is in the in-of-control state when it starts a production run. However, it may shift to the out-of-control state at any point in time during the production cycle. The time until the shift from the in-control state to the out-of-control state is modelled by a Weibull random variable with increasing hazard. It is assumed that when the process is in the out-control state, it stays in that state until the next setup where it is brought to as-good-as new conditions. While in the out-of-control state, the process produces a fixed fraction on non-conforming items which are scrapped with no salvage value. Unlike the existing models in the literature, the demand is stochastic and is modelled by a normal probability distribution. Two cases are considered, the first of which is for a predetermined service level case. The other case is when the service level is a decision variable. The cost function is developed and minimised to find the optimal lot size using a simple and efficient algorithm.

Service level enhancement in newsvendor model

This paper considers a decision rule for newsvendor model with emergency order.The model involves service level revision during the consumption period of the item.Emergency order is placed if service level is dropped to a certain value. Nowadays, competition in global market forced companies to offer high service levels for customers with high expectations. An important type of service levels that businesses usually use in controlling inventory systems is the fill rate. Typically, in such businesses, a vendor orders a batch at the beginning of an inventory cycle such that a certain expected fill rate is met. An obvious shortcoming of this method of ordering is that the expected fill rate may drop to an unacceptable value during consumption period. This disruption in expected fill rate may lead to significant losses to a business. We, thus, propose a newsvendor model which allows the vendor to place an initial order that satisfies a predetermined fill rate. When the expected fill rate drops to a specific value during consumption, another order is placed to increase the expected fill rate. Propositions are developed to reduce the difficulty of the model and we devise a simple solution method which determines the initial optimal lot size, optimal lot size of the second order, and the reorder point.

Integrated location model with risk pooling and transportation mode selection

Location model with risk pooling and mode selection problems are integrated in this paper. Specifically, we consider a supply chain consisting of one supplier, distribution centres, transient points, and retailers who observe random demand that follows a certain probability distribution. Supplier dispatches the product to distribution centres using one mode of transportation while a given distribution centre may serve a retailer directly using one mode of transportation or through a transient point using two modes of transportation. The model is expected to determine facility location decisions, inventory decisions, and intermodal transportation decisions. The set of retailers who are assigned to a particular distribution centre are not known a priori. The derived model is large-scale and non-linear mixed integer programme. The difficulty of the model is reduced by adding a redundant constraint which made the solution procedure attainable. Also, Lagrangian relaxation approach is used to develop lower and upper limits on the optimal solution.

Vendor managed inventory models for single-vendor multi-retailer supply chains with quality consideration

In this paper, efficient algorithms are devised to solve two VMI models for a single-vendor multi-retailer supply chain. The first model is for a decentralised supply chain where the vendors expected profit is maximised. The other model, however, is for a centralised supply chain where the expected system profit is maximised. It is assumed that the lot received by vendor contains a random number of non-conforming items and, thus, inspection is performed on the incoming lot before it is delivered the retailers. In addition, we assume that non-conforming items are sold as a single batch to a secondary market at a reduced price. We also assume that the inspection process is perfect and is performed at a finite rate. In the proposed models, we incorporate a VMI contract which includes an upper limit on retailers inventory level. In order to encourage cooperation between vendor and retailers, we propose a scheme that distributes the extra profit obtained by the integrated solution between the vendor and retailers.

Optimal wholesale price for producer in supply chain under newsboy environment

The lifecycles of technology-based products are rapidly becoming shorter through endless technological innovation. As a result, researchers and practitioners paid much attention on operations management issues for newsvendor-type products. However, due to the globalisation of market and keen competition, optimising supply chain decisions becomes very important and many researchers have turned their attention to the supply chain management for newsvendor-type products. In this paper, a model for supply chain with one producer and multiple retailers is considered. The retailers order quantities of the product based on newsvendor rule and the producer adjusts the production run accordingly. The purpose of the developed model is to find the optimal wholesale price which maximises the expected profit of the producer.