In this study, a fuzzy mathematical programming for an inventory system with defective items is considered. The system consists of a single machine that requires maintenance to enhance its efficiency, performance and lifespan. Due to the environmental uncertainties, uptime is estimated based on the linguistic variables, i.e., experts' opinions. So, the inherited uptime is a fuzzy number in trapezoid form, i.e., machine works certainly up to a time and it fails with an optimistic and pessimistic estimation. Moreover, machinery should go through a preventive maintenance procedure during downtime. The proposed model helps production managers to reduce system costs by improving machine efficiency and performance employing appropriate maintenance policies. To solve the proposed problem, we optimise system costs by calculating optimum production cycle using an algorithm to calculate upper and lower bounds of inherited crisp problem. Finally, a numerical example is represented to investigate the effectiveness of the proposed algorithm.

This research presents an inventory system with partial backordering and imperfect process with a stochastic numbers of products that are defective per order. This problem is known and there are some customers that do not wait for their orders to be fulfilled so a particular proportion of backordered items become lost sales. This paper considers both mentioned situations simultaneously while the number of defective items follows a uniform distribution and the proportion of backordering is constant. This condition is modelled. The cost function of this inventory model includes order cost, holding cost and two types of shortage costs, one of them is related to backordered items and the other one is related to lost sales. This paper also provides a solution method to obtain optimum values for the decision variables, order quantity and total shortage, then we derive the value of the total cost function according to the optimum values obtained for the decision variables. Finally, some numerical results and diagrams are provided to show how some parameters affect the values of the decision variables and the cost function.

Fresh agri-food products, like fruits and vegetables (F&Vs), are perishable products having a very short shelf life. They are different from non-perishables in managing their inventories as customers are more concerned about the nutritious value and shelf life. Customers are becoming strategic and planning their purchase based on the markdown and other promotional activities. Retailers are finding it difficult to a trade-off between the prices and remaining shelf life for offering markdown. Therefore, decisions depending upon the value and timing of such markdowns for 'not so fresh' F&V are important. This paper attempts to address these issues based on previously published studies which suggested a simple procedure to identify the quantum and time of markdowns for perishable products inside a retail store. Extending the approach, Monte Carlo simulation is applied in order to generate randomness in probability of sales and demand for F&V. A questionnaire is used in order to get the primary data from 89 retailers from Delhi/NCR, India. Organised retail of F&V is still at starting stage in India and no such study has been attempted before.

The focus of this study is on tactical-level capacity management which refers to the determination of in-house workforce production capacity in an optimal cost-efficient manner in a multi-period mode. Two options for capacity planning are investigated for rapid prototyping with the help of a mixed-integer linear optimisation model: smoothing the capacity utilisation over time vs. a higher level of capacity availability. A sensitivity analysis based on real empirical data in Siemens AG is used for the revealing the impact of workforce and capacity flexibility on operational performance. The results suggest that the number of workers decreases if production orders have not to be completed within only one week. On the contrary, if the binary restriction on the order fulfilment within one week is released, the production orders can be split into different weeks and this results in a higher smoothing rate and thus in a higher capacity utilisation degree.

In this article, we consider a perishable inventory system with postponed demand and single server. The server is allowed to take multiple vacations during stock out period. The demands that arrive during a stock out period or server vacation period either postponed their demand or considered to be lost according to a Bernoulli distribution. The postponed demands are sent to a place called pool and its capacity is finite. When the server is not in vacation and the inventory level is above s, the demands in the pool are selected one by one with FCFS discipline. The waiting time distribution for demands in the pool is derived for both (s, S) and the variable ordering policy. System performance measures for model with variable ordering policy and (s, S) policy are also computed under steady-state case. And these performance measures are used to calculate the total expected cost rate for both policies. Finally, using numerical results, we compare the optimal total cost rate corresponding to two policies and also we compare the expected waiting time of the pooled demands.

This paper describes an optimisation algorithm that minimises the total inventory investment of a one warehouse and an m non-identical retailer's inventory system using reorder point and order quantity (R, Q) policies. The inventory system is subject to constraints on the average ordering frequency and number of backorders. The system is decomposed by echelon and location, and analytical expressions are derived for the inventory policy parameters. Sets of computational experiments illustrate the effectiveness of the heuristic over a wide range of problem instances. Experimental results indicate that the heuristic optimisation algorithm is an effective procedure for optimising the sampled inventory systems regarding both the quality of the solutions and the computational times. This research provides approximations and a heuristic optimisation procedure for a two-echelon inventory system for the non-identical retailer's case.

In a decentralised supply chain, the presence of initial inventory at the retailer is believed to cause the manufacturer to set a lower wholesale price than otherwise. But is such always the case? The importance of that question also derives from a multi-period setting where the manufacturer chooses a wholesale price in each period based on initial inventory at retailer. As the wholesale price is decreasing in inventory level, goes the argument, the retailer will 'overstock', referred to as holding 'strategic inventory'. We show that the optimal wholesale price may increase in initial inventory. We initially assume fixed retail price, and later consider a model with price-sensitive demand. We then outline other price-sensitive models based on different demand functions.

This paper assesses the impact of tail dependence on the consolidation effect. Based on different R packages, it was not only possible to use copulas for modelling the dependence structure between decentralised demands, but also to randomly generate and optimise different scenarios for various product characteristics, thus finding the best pooling policy: inventory centralisation, regular transshipment, or independent systems. Results suggest a different pattern for the decision-making rationale involving correlation and inventory holding costs. While independent systems and regular transshipments seem to compensate for strong upper tail dependence structures, centralisation seems to compensate for strong lower tail ones.

A game theoretic approach is used to analyse an inventory problem with two products, stochastic demand, and uncertain supply. The supply chain analysed includes two competing retailers selling two substitutable products and those retailer’ suppliers. Retailers face stochastic demand and replenish the inventory from the suppliers. However, both suppliers provide an indeterminate fraction of the quantity requested, due to randomness in capacity and quality. Some customers with unmet demand will substitute that product with one sold by the other retailer. We assume that the retailers are rational players with conflicting objectives. We model the retailers’ single period expected payoffs and identify the ordering decisions using Nash strategy. We prove the existence and uniqueness of the Nash solution, and provide results for numerical examples. We analyse the combined impact of product substitution and supply uncertainty on the retailers. Results suggest that supply uncertainties do not always hurt retailers’ expected payoffs.

In this study we consider a simple two level supply chain consisting of an assembler and a group of suppliers producing a single product for a constant external demand rate. Suppliers manufacture the product’s components at unequal rates. When all components are available, they are assembled to a finished product. The determination of the lot sizes of the product and its components depends on whether one seeks system optimality, corresponding to a coordinated system, or whether the assembly firm dictates to the suppliers the lot sizes it prefers. We develop a model to compare the effects of coordinated and decentralised decisions on the total cost of the system.