Optimal Production-inventory Policy Research Articles

Optimal production-inventory policy for products with time-dependent demand pattern and backlogged shortages

In this work, a production-inventory system for items with a time-dependent demand pattern is studied. Shortages are allowed and these are met with the arrival of the next production run. Fluctuations of the net inventory level are analysed and the costs related with the production and inventory management are calculated. The aim is to maximise the profit per unit time. That profit is equal to the difference between sale revenue and production-inventory costs. In the analysis of this system, different scenarios can occur. All these possible cases are studied in detail and, for each scenario, the optimal production-inventory policy and the maximum profit per unit time are determined. Moreover, several numerical examples to illustrate the solution methodology are presented. Finally, a sensitivity analysis of the optimal inventory policy with respect to several parameters of the system and some useful managerial insights derived from the results are given.

Optimal Production-Inventory Policy for a Periodic-Review Energy Buy-Back System over an Infinite Planning Horizon

This paper studies a periodic-review production-inventory control model under an energy buy-back program over an infinite planning horizon, in which a fixed setup cost and compensation levels corresponding to various market states are involved. The objective is to identify the manufacturer’s optimal production-inventory policy that can minimize his total discounted cost or long-run average cost. By using Veinott’s conditions, it is shown that such a state dependent optimal policy is of either an [Formula: see text], or partly an [Formula: see text] type.

Optimal production-inventory policy for the multi-period fixed proportions co-production system

Consider the multi-period production-inventory problem where a manufacturer purchases and processes a raw material into two products in fixed proportions when facing uncertain demands. In each period, the manufacturer first reviews the on-hand inventories of the products and then decides the purchase/processing quantity of the raw material. After processing the raw material into the end products, the demands of the two products are realized and satisfied by the available inventories. Any leftover inventories are carried to the next period while the unsatisfied demands are backordered. By proving the concavity and submodularity of the expected profit-to-go function, we establish that the one-dimensional produce-up-to policy is optimal. We also study the case where the raw material is seasonal and the manufacturer has only one chance to purchase. Modeling it as a dynamic program, we establish that the one-dimensional produce-down-to policy is optimal. Finally, we conduct numerical studies to examine the impacts of supply-demand balance and price fluctuation on the optimal policy, and derive managerial insights from the analytical findings.

Optimal production-inventory policy for closed-loop supply chain with remanufacturing under random demand and return

This paper presents a centralized production-inventory model for an infinite planning horizon of a two-echelon closed-loop supply chain (CLSC) consisting a retailer, manufacturer, and remanufacturer. The demand at the retailer is satisfied through the new and remanufactured products received from the manufacturer and remanufacturer, respectively. The proposed model considers demand at the retailer and return at the remanufacturer as random. The manufacturer and remanufacturer produce the products at a finite rate, and they deliver to the retailer alternatively in multiple batches. An algorithm is developed to find the optimal-lot sizing and shipment policies of each entity of the CLSC by minimizing the expected joint total cost of the system. The results show that the CLSC is more profitable than the forward supply chain when the remanufacturing cost of the returned product is significantly low compared to the manufacturing cost of the new product, the demand variation at the retailer is low, and the fraction of demand returned is close to 1.

Two-echelon closed-loop supply chain deterministic inventory models in a batch production environment

This paper considers a two-echelon closed-loop supply chain consisting of a manufacturer and a remanufacturer at the upper echelon and a retailer at the lower echelon. The retailer faces a constant demand from customers, which is satisfied through recovered and new products received from the remanufacturer and the manufacturer, respectively. The manufacturer produces the product with finite rate, whereas the recovery of returned product is instantaneous at the remanufacturer. We develop three models to determine the optimal production-inventory policy of the players for minimizing the joint total cost of the system. In the first model, the retailer receives the product in batches from the manufacturer and the remanufacture simultaneously, whereas in the second and third models, the batches are received alternatively. In the third model, however, the procurement of raw material at the manufacturer is also considered. Numerical illustration is presented to examine the impact of certain key parameters.

Optimal production-inventory policy for an integrated multi-stage supply chain with time-varying demand

An integrated multi-stage supply chain with time-varying demand over a finite planning horizon is considered in this paper. The objective is to devise the optimal production-inventory policy to minimize the total operational cost. The model is formulated as a mixed integer nonlinear programming problem. The problem is represented as a weighted directed acyclic graph. The global minimum total operational cost is computed in polynomial time by the developed algorithm. Two numerical examples of a seasonal product and a product over its life cycle are studied to illustrate the results. A sensitivity analysis of the system parameters is conducted to assist the supply chain decision makers.

An integrated production-inventory model for the singlevendor two-buyer problem with partial backorder, stochastic demand, and service level constraints

This paper presents an integrated single-vendor two-buyer production-inventory model with stochastic demand and service level constraints. Shortage is permitted in the model, and partial backordered partial lost sale. The lead time demand is assumed follows a normal distribution and the lead time can be reduced by adding crashing cost. The lead time and ordering cost reductions are interdependent with logaritmic function relationship. A service level constraint policy corresponding to each buyer is considered in the model in order to limit the level of inventory shortages. The purpose of this research is to minimize joint total cost inventory model by finding the optimal order quantity, safety stock, lead time, and the number of lots delivered in one production run. The optimal production-inventory policy gained by the Lagrange method is shaped to account for the service level restrictions. Finally, a numerical example and effects of the key parameters are performed to illustrate the results of the proposed model.

Production-inventory model for two-echelon closed-loop supply chain with finite manufacturing and remanufacturing rates

ABSTRACTThis research develops a two-echelon closed-loop supply chain production-inventory model consisting of a manufacturer, a remanufacturer and a retailer. The retailer faces a constant demand from the customers, which is satisfied by new and remanufactured product received from the manufacturer and the remanufacturer, respectively. The manufacturer and remanufacturer produce the product in batches with finite production rate. The manufacturer procures raw material in batches from outside supplier, and the remanufacturer receives the used product from the customers at a constant return rate. Many studies in the area of forward supply chain have established that the centralised production-inventory control models provide better results than the decentralised models. Hence, with synchronised activities of the supply chain players, this research proposes to find an optimal production-inventory policy of the players by minimising the joint total cost of the two-echelon closed-loop supply chain. Numerical illustration is presented to demonstrate the solution procedure and a sensitivity analysis is carried out to examine the impact of key parameters of the problem. Also, the total cost of closed-loop supply chain model is compared with the total cost of the corresponding forward supply chain model.

A coordinated two-phase approach for operational decisions with vehicle routing in a single-vendor multi-buyer system

This study considers a two-echelon system in which a vendor produces a product at a finite production rate and supplies it to several buyers facing independent normally-distributed demands. The product is delivered to the buyers using a set of different speed vehicles with identical capacity and different operating costs. The issues of lead time reduction and the service level constraint on the buyers have been incorporated in the model. A model is formulated to determine the optimal production–inventory policy, vehicle routes and vehicle type for each route by minimising the related production, inventory, lead time crashing and transportation costs of the system while satisfying the service level constraint on each buyer. A coordinated two-phase iterative approach is proposed to solve the model. Finally, a numerical example is included to describe the solution approach and illustrate the results.

Single-vendor multi-buyer integrated production-inventory model with controllable lead time and service level constraints

This paper presents an integrated production-inventory model where a vendor produces an item in a batch production environment and supplies it to a set of buyers. The buyer level demand is assumed to be independent normally distributed and lead time of every buyer can be reduced at an added crash cost. The buyers review their inventory using continuous review policy, and the unsatisfied demand at the buyers is completely backordered. A model is formulated to minimize the joint total expected cost of the vendor–buyers system to determine the optimal production-inventory policy. Since it is often difficult to estimate the stock-out cost in inventory systems, and so instead of having stock-out cost component in the objective function, a service level constraint (SLC) corresponding to each buyer is included in the model. A Lagrangian multiplier technique based algorithmic approach is proposed, which evaluates a very limited number of combinations of lead time of the buyers to find simultaneously the optimal lead time, order quantity and safety factor of the buyers and the number of shipments between the vendor and the buyers in a production cycle. Finally, a numerical example and effects of the key parameters are included to illustrate the results of the proposed model.

Optimal production-inventory policy for make-to-order versus make-to-stock based on the M/Er/1 queuing model

This paper analyzes a multi-product production / inventory system where demands for each item arrive according to a Poisson process and the production time for each product has an Erlang distribution. The paper proposes an optimality condition that specifies whether each product should be produced make-to-stock or make-to-order. In the event a product should be produced make-to-stock, an approach for computing the optimal base-stock level is proposed. Numerical examples are given for illustrative purpose.

Determining the optimal production–maintenance policy with inspection errors: using a Markov chain

Lee and Park examine the effects of an imperfect production process on the optimal production-inventory policy. They consider an imperfect production process which can go out of control after an exponentially distributed production time and then produce some proportion of defective items. The defective item cost is equivalent to the reworking cost and the warranty cost. Some maintenance-inspection mechanisms are introduced to monitor and restore the process to enhance process reliability and thereby lower the number of defective items produced. However, in many situations, a deteriorating production system possesses an increasing failure rate. In general, such a process will not be as good as new after maintenance but will be younger than its real age. Besides, Lee and Park did not investigate the possibility of imperfect inspection based on consideration of type I and type II errors. In this paper, we consider the effects of general time to shift distributions, two types of process inspection errors and general repair policy on the optimal production/inspection/maintenance policy. A mathematical model representing the expected average cost is developed using a Markov chain to jointly determine the production cycle, process inspection intervals, and maintenance level. An optimal production/inspection/maintenance policy is determined by minimizing the expected average cost. A numerical example is given to illustrate the use of the method. Based on this proposed Markov structure model, some process-related assumptions such as maintenance that can cause the system to go out of control and that the random results of general repairs can also be easily relaxed, and they are described in the section of model extensions. An extended production–maintenance model for a deteriorating production system is established. Scope and purpose There are numerous production situations which may cause a production facility to shift from an “in-control” state to an “out-of-control” state due to aging of equipment. Once the process shifts to an “out-of-control” state, an increased number of defective items will be produced until a maintenance–inspection is performed to return the process to an “in-control” state. To reduce the risk that a shift to an out of control state will occur, lot sizing, periodic inspection and maintenance of the process are needed. These tasks also enhance the economical operation of the system. In this study, we investigate a production/inspection/maintenance model under the assumptions that the production process is subject to random deterioration, and that the process can be monitored through inspections, so that the lot size, inspections and maintenance policy are subject to control. Uncertainty probabilities associated with inspections are also considered, i.e., inspection is assumed to be imperfect. Our objective is to determine the optimal production/inspection/maintenance policy under the effect of process inspection errors. A mathematical model which presents the expected average cost is developed. An optimal production/inspection/maintenance policy is found by minimizing the expected average cost. Since this problem arises in many practical situations, the results may be helpful to production managers in developing approaches to control production systems economically.