An optimisation model for the design of global multi-echelon supply chains under lead time constraints

This article presents a mixed integer programming model for the design of global multi-echelon supply chains while considering lead time constraints. Indeed, we impose that the delivery lead time that can be promised by the company must be smaller than the lead time required by the customer. The delivery lead time is calculated based on the lead times of purchasing, manufacturing and transportation that are triggered by the customer order while considering the stock levels of purchased, intermediate and final products that must be kept at the different facilities. Computational studies are conducted in order to analyse the impacts of including lead times on the supply chain design decisions and to prove the solvability of the model.     

Supply chain design to guarantee quoted lead time and inventory replenishment: model and insights

Do lead time constraints only lead to re-think and re-optimise the inventory positioning along the supply chain or can they impact on the design of the supply chain itself? To answer such a question, we integrate the lead time constraints in a multi-echelon supply chain design model and challenge the difficulty of combining in the same model the long-term decisions (facility location, supplier selection) with the midterm decisions (inventory placement and replenishment, delivery lead time). The model guarantees the respect of the quoted lead time associated with each customer order and the replenishment of the different stocks (raw materials, intermediate and final products) in the different stages of the supply chain between any pair of consecutive orders. We use the model to investigate the impact of the quoted lead time and customer’s order frequency on supply chain design decisions and costs. Some of our results indicate that the lead time constraints can lead to bringing the sites of manufacturing and distribution close to the demand zone and to select local suppliers in spite of their higher cost.     

The effect of human factors on the performance of a two level supply chain

Many studies have addressed the issue of coordination in a supply chain. Coordinating mechanisms such as joint lot sizing models, quantity discounts and delay in payments have been used to achieve coordination in a supply chain. An important omission in this literature is the role of human factors, in particular inspection errors and learning, as a tool to improve coordination in a supply chain. In this paper, two coordination mechanisms found in the literature are integrated into a model for a two-level supply chain in which the incoming quality level of raw materials provided to a vendor by a set of suppliers is not perfect. The model addresses supply chain coordination by specifically investigating the role of different human factors on the total cost of the supply chain. These factors are: (a) type I and type II inspection errors; (b) learning in the production process; and (c) learning in quality at the suppliers’ end. Numerical examples are used to compare the costs of the three extensions with the base model (with no defectives).     

A supply chain model with vendor-managed inventory,consignment, and quality inspection errors

This paper considers the integration between quality control and production inventory control in supply chain management. Specifically, we study the effect of inspection errors on the costs incurred in a supply chain system with a single vendor and multiple buyers. In this system, the vendor enters into a vendor-managed inventory (VMI) and a consignment stock (CS) partnership with several buyers. We assume that the items made by the vendor are not in perfect quality, but they contain a given proportion of defective units. We also assume that quality inspection of these items by the buyers is subject to sampling errors. Three cases indicating to different levels of supply integration are considered: VMI–CS system, traditional system and integrated system. For each case, a mathematical model is formulated, an optimum solution is developed, and a numerical example is solved.     

A note on a study of an integrated inventory with controllable lead time

Pan and Yang (Pan, C.H. and Yang, J.S., 2002. A study of an integrated inventory with controllable lead time. International Journal of Production Research, 40 (5), 1263–1273.) proposed the paper about integrated inventory with controllable lead time. The vendor produces the item in the quantity of mQ, and the purchaser would receive it in m lots, with which each having a quantity of Q. In practice, the vendor manufactures the product in the quantity of mQ with a finite production rate P at one set-up. Based on the practical fact, a modified model is proposed in this note. The proposed model takes the crashing set-up time into account. Numerical examples are presented to illustrate the procedures and results of the proposed algorithm. The modified model is shown to provide lower total costs and shorter lead time compared with those of Pan and Yang.     

Model predictive control for inventory management in biomass manufacturing supply chains

This paper presents a centralised model predictive control strategy applied to biomass inventory control in sugarcane industries. Sugarcane industries are important renewable energy producers and an adequate inventory control of their feed material (biomass) can improve energy production. Simple linear discrete-time models with dead-time are developed to predict the controlled variable behaviour. Two layers are used in the controller, in the upper one performance is optimised by an linear programming (LP) algorithm and a multivariable generalised predictive controller (GPC) or multivariable generalised predictive controller with dead-time compensation (DTC-GPC) is used in the lower level. Simulation results in general show that the proposed controllers globally optimise the system behaviour and find an optimal ordering amount for keeping stock levels. In cases of plant/model mismatch DTC-GPC can have a significant and positive impact on the control of stock levels adding one more parameter for achieving minimised oscillatory performances (bullwhip effect).     

An optimal consignment stock production and replenishment policy with controllable lead time

This paper considers a single-vendor and single-buyer production system in which the lead-time is controllable with an extra investment under a long-term agreement between the two trading partners. The vendor produces at a finite rate, ships the outputs in lots of equal size within a production cycle, and delays those shipments for a certain period when the buyer’s inventory approaches the capacity limits. Therefore, the arrival of these shipments does not lead to an increase in the buyer’s inventory. Meanwhile, the buyer holds the payment until the complete consumption of the products. The holding cost consists of a storage component and a financial component. A joint EOQ/EPQ model is then established under cases where the buyer’s unit storage holding cost might be greater or less than that of the vendor to jointly determine the number of shipments, the size of each shipment, the number of delayed shipments, and the lead time that minimise the yearly joint total expected cost (JTEC) of the system. An efficient solution procedure is provided to solve the non-linear integer optimisation model that defined the system under consideration. A method to determine the integer global optima from the real global optima is also presented. Two numerical experiments are conducted to illustrate the procedure and the results show that considering the combined effect of adopting a consignment stock policy and lead time crashing opportunities may lead to a better result than any of these two policies considered separately.     

Multi-item inventory model with variable backorder and price discount under trade credit policy in stochastic demand

In this paper, a two echelon supply chain with one manufacturer and one retailer is developed for multi products. The retailer faced with the uncertain demand for all products which follows a normal distribution. The production process is assumed to be imperfect, and the defectiveness is assumed to follow a beta distribution. The manufacturer produces and delivers the products in a number of equal-sized batches to the manufacturer's warehouse, and thereby it is delivers in a number of equal batches to the retailer's warehouse. Shortages are allowed to occur, at the retailer side, and it is backordered partially. The retailer offers a price discount for backordered items to his customers. Both the lead time crashing cost and the partial backorder ratio are considered as the inverse function of lead time. Under these assumptions, there are three inventory models proposed in this paper, one with non-integrated approach, the other with an integrated approach without trade credit and finally an integrated approach with trade credit. A new iterative algorithmic procedure has been developed to minimise the total cost. Finally, numerical examples are given to illustrate the models and the sensitivity analysis is conducted over various model parameters.     

Grammatical evolution in developing optimal inventory policies for serial and distribution supply chains

Recently, there has been a growing literature on biologically inspired algorithms, particularly genetic algorithms and genetic programming, applied to supply chain modelling and inventory control optimisation. Due to the rigidity of the genetic algorithms approach, it is difficult to change the underlying model logic and add richness to the supply chain. While genetic programming provides a more flexible approach than that provided by genetic algorithms, to date its application has been limited to small supply chain modelling problems in relation to optimal inventory policies. This research applies Grammatical Evolution, a relatively new biologically inspired algorithm, to the field of supply chain optimisation, employing human readable rules called grammars. These grammars provide a single mechanism to describe a variety of complex structures and can incorporate the domain knowledge of the practitioner to bias the algorithm towards regions of the search space containing better solutions. Results are presented showing Grammatical Evolution is at least competitive in cost terms, and superior in flexibility, with these methods applicable to any supply chain of the serial or distribution type. Furthermore, Grammatical Evolution shows an adaptive ability that augurs well for supply chains in dynamic environments, such as disruption.     

A strategic and tactical model for closed-loop supply chains

In this paper, a strategic location-allocation model is developed for the simultaneous design of forward and reverse supply chains. Strategic decisions such as network design are accounted for together with tactical decisions, namely, production, storage and distribution planning. The integration between strategic and tactical decisions is achieved by considering two interconnected time scales: a macro and a micro time. At macro level, the supply chain is designed in order to account for the existing demands and returns, whose satisfaction is planned simultaneously at the micro level where tactical decisions are taken. A Mixed Integer Linear Programming formulation is obtained which is solved to optimality using standard Branch & Bound techniques. Finally, the model accuracy and applicability is illustrated through the resolution of a case study.     

Consignment and vendor managed inventory in single-vendor multiple buyers supply chains

In this paper we model a consignment (CS) and vendor-managed inventory (VMI) policy for a single vendor and multiple buyers supply chain with known demand. We study three vendor–buyers partnerships: (i) the vendor and the buyers act independently, (ii) the vendor enters in a vendor-managed inventory consignment (VMI&CS) partnership with the buyers and (iii) the vendor and the buyer belong to a vertically integrated firm where a single decision maker decides about the ordering policies. We use relationships (i) and (ii) to study the benefits of the VMI&CS agreement. We provide analytical and numerical results. We find that such an agreement is more beneficial when the vendor has a flexible capacity. It is also more attractive to buyers when they have significant order costs and the vendor's setup cost is not large. Finally we find that under VMI&CS the vendor will tend to make more frequent shipments with smaller lots.     

A closed-loop supply chain with stochastic product returns and worker experience under learning and forgetting

This paper addresses a single-manufacturer single-retailer closed-loop supply chain with stochastic product returns considering worker experience under learning and forgetting in production and inspection of returned items at the manufacturer. Customer demand is assumed to be dependent linearly on the retail price, and it is fulfilled by using both manufactured and remanufactured products. The manufacturer delivers the buyer’s order quantity in a number of equal-sized batches. The optimal number of shipments, the shipment size and the retail price are determined by maximising the average expected profit of the closed-loop supply chain. It is observed from the numerical study that high learning effects in production and inspection lead to high recovery rates of used products, which, besides an economic advantage, may have a positive effect on the environment. Even though forgetting has an adverse effect, the average expected profit of the closed-loop supply chain is much higher than that of the basic model which ignores worker learning.     

Coordination of pricing,inventory, and production reliability decisions in deteriorating product supply chains

In this article, we study a two-level supply chain model for deteriorating items, in which the supplier’s production system is unreliable and the retailer’s demand is price-sensitive. The supplier’s production line may randomly shift from the in-control state to the out-of-control state. When the production line is in the out-of-control state, a proportion of the produced products will have bad quality. To mitigate the out-of-control risks, the supplier can improve the production line reliability by investing in high-quality machines, highly skilled workers, or advanced maintenance technologies. We start with the study of pricing and inventory problems concerning endogenous reliability in the integrated and decentralised scenario. To better illustrate the proposed models, two applicable algorithms are designed to determine the optimal production reliability, ordering quantity, and prices. Then, a cooperative reliability investment and revenue-sharing contract is proposed to coordinate the supply chain. Numerical examples and sensitivity analysis of the equilibrium strategies and coordinating results on key system parameters (e.g. deterioration rate, production rate, etc.) are given to verify the effectiveness of the contract, and meanwhile get some managerial insights.     

Mathematical programming model for centralised master planning in ceramic tile supply chains

The object of this article is to develop a centralised replenishment, production, and distribution model for ceramic tile supply chains. These supply chains are assumed to be multi-item, multi-supplier, multi-facility, multi-type and multi-level distribution centres. The model deals with multi-period master planning where sourcing considerations for replenishments, production facilities, and distribution centres are important to maximise an objective function involving the total net profit. This model is deterministic and has been formulated as a mixed-integer linear programming (MILP) model. An example based on modifications of real-world industrial problems is presented.     

Safety stock or safety lead time: coping with unreliability in demand and supply

Safety stock and safety lead time are common measures used to cope with uncertainties in demand and supply. Typically, these uncertainties are studied in isolated instances, ignoring settings with uncertainties both in demand and in supply. The current literature largely neglects case study based contexts and, often, single product situations are investigated in which machine set-ups are not considered. Based on the problems and findings in a case study, we investigate the effects of safety stock and safety lead time on delivery performance in a multi-product setting. The outcomes of the extensive simulation study indicate that utilising a safety lead time results in a higher delivery performance where there is a variable supply, whereas having a safety stock results in a higher delivery performance where there is unreliable demand information. In contrast to earlier findings in the single product situation, this study shows that managers facing the combination of unreliability in demand information and supply variability in a multiple product situation should opt for a safety lead time as the most effective way of improving their delivery performance.     

Incentives for quality improvement efforts coordination in supply chains with partial cost allocation contract

In this paper, we consider quality improvement efforts coordination in a two-stage decentralised supply chain with a partial cost allocation contract. The supply chain consists of one supplier and one manufacturer, both of which produce defective products. Two kinds of failure cost occur within the supply chain: internal and external. The supplier and the manufacturer determine their individual quality levels to maximise their own profits. We propose a partial cost allocation contract, under which the external failure cost is allocated between the manufacturer and the supplier at different rates based on information derived from failure root cause analysis. If the quality levels of the supplier and the manufacturer are observable, we show that the partial cost allocation contract coordinates the supply chain, provided that the failure root cause analysis does not erroneously identify the manufacturer’s fault as the supplier’s, and the supplier does not take responsibility for the manufacture’s fault. In the single moral hazard model, where only the quality level of the supplier is unobservable, the optimal share rates require the supplier to take some responsibility for the manufacture’s fault. However, in the double moral hazard model, where quality levels of the supplier and the manufacturer are unobservable to each other, the optimal share rates require the supplier not to take responsibility for the manufacturer’s fault. It is noted that the root cause analysis conducted by the manufacturer may have its disadvantage in attributing the fault to the supplier when both sides are at fault. We also propose a contract based on the dual root cause analysis to reduce the supplier’s penalty cost. Numerical results illustrate that the partial cost allocation contract satisfies the fairness criterion compared with the traditional cost allocation contract.     

Integrated planning in supply chains with buy-side and sell-side marketplaces

In this paper we develop a quadratic programming model for partner selection and planning in integrated supply chain networks embedded with both sell-side and buy-side electronic marketplaces. Such a scenario arises in several practical applications. In particular, we consider a contract manufacturer who procures components from suppliers through a component marketplace and sells its manufactured sub-assemblies to original equipment manufacturers (OEMs), through a sub-assembly marketplace. In these web-enabled supply chains, embedded with upstream and downstream electronic marketplaces, we need methods for online supply-chain partner selection based on pricing and delivery schedules. In this paper, we develop and present such a model that selects partners, synchronizes supply chain activities and optimizes the profit through optimal revenue pricing and cost minimization.     

Entropy-based model for the ripple effect: managing environmental risks in supply chains

Due to increasing diversity and growing size of modern industrial supply chains, today problems of identification, assessment and mitigation of disruption risks become challenging goals of the supply chain risk management. In this paper, we focus on environmental (ecological) risks in supply chains which represent threats of adverse effects on living organisms, facilities and environment by effluents, emissions, wastes, resource depletion, etc. arising due to supply chain’s activities. Harmful environmental disruptions may ripple through the supply chain components like a wave. The paper presents the entropy-based optimisation model for reducing the supply chain model size and assessing the economic loss caused by the environmental risks subject to the ripple effect. A main advantage of the suggested entropy-based approach is that it permits to essentially simplify the hierarchical tree-like model of the supply chain, at the same time retaining the basic knowledge about main risk sources.     

Bullwhip and anti-bullwhip effects in a supply chain

The anti-bullwhip effect, coined by Li et al. in 2005 based on the findings in a simulation study, is the contrary effect of the well-known bullwhip effect. Although there is ample empirical evidence that suggests both effects exist, current literature has not yet provided an integrated framework to address how the two effects are related with each other. By extending the classic work of Lee, Padmanabhan, and Whang of 1997 to a multi-stage supply chain, we derive closed-form formula to analytically describe how the two effects originate initially and then evolve over time and space in the supply chain. Our results show both the bullwhip effect and the anti-bullwhip effect can occur when facing different end-customer demands. However, the magnitude of these effects gradually decreases when moving upstream. We also show the impact of long lead-time on increasing the magnitude of information transformation at the next stage and simultaneously decreasing the magnitude at higher stages. These analytical results provide a theoretical explanation to most simulation findings of Li et al.'s 2005 work and can be used by researchers and practitioners to examine the empirical data and design innovate marketing strategies to convert the unwelcome bullwhip effect into the anti-bullwhip effect.