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In this paper, realistic production-inventory models with shortages for a deteriorating item with imprecise preparation time for production (hereafter called preparation time) has been formulated and an inventory policy is proposed for maximum profit in a finite time horizon. Here, the rate of production is constant, demand depends on selling price, marketing cost, and inventory level, and setup cost depends on preparation time. The imprecise preparation time is assumed to be represented by a fuzzy number and is first transformed to a corresponding interval number and then following interval mathematics, the objective function for total profit over the finite time horizon is changed to respective multi-objective functions. These functions are maximized and solved for a set of Pareto optimal solution with the help of the weighted sum method using the generalized reduced gradient technique. Different case studies have been made depending upon the occurrence of shortages. The models have been illustrated by numerical data. Pareto-optimal solutions for different weights are obtained and presented in tables and graphs.

This paper presents a stylized model to determine the optimal strategy for the integrated supplier-retailer inventory model under the condition that both the supplier and retailer have adopted a trade credit strategy. By analyzing the total channel profit function, we develop an algorithm to simultaneously determine the retailer's optimal order quantity and the number of shipment per production run from the supplier to the retailer. Our results demonstrate that the trade credit strategy is effective to supply chain system performance when customers are sensitive to the credit period length offered by the retailer. Moreover, when customers are sensitive to the credit period, if the retailer conveys partial advantage gained from the trade credit offered by the supplier to customers by suitably adjusting the customer's credit period then the entire system and every channel partner can benefit.

A single item, single cycle economic production quantity model for perishable products is proposed where the demand is two-component and stock dependent. The production inventory scenario of products like cake, bread, fast foods, fishes, garments, cosmetics etc in the festival season is considered. The profit function is formulated under the assumption that the time period of the festival seasons is fixed and the display capacity of the produced item is limited. In the formulation process, to introduce more flexibility, a goal programming technique is incorporated to achieve the producer's desired profit and stock of as much inventory as possible below the display capacity level. A numerical example is presented to illustrate the proposed model. A sensitivity analysis of the model is also carried out.

Many companies are facing the challenges of dynamic market and capital shortage. To overcome these challenges, we examine the case in which the company develops early sales strategy that entices customers to commit to their orders at a discount price prior to the selling season. The time between payment and fulfillment of these pre-committed orders provides an opportunity for the company to "lock" part of market demand and relieve the company's procurement budgetary constraint. This paper evaluates the benefits of the early sales strategy. Firstly, we provide a novel method to compute the optimal discount rate of the early sales strategy; comparative static analysis of parameters (e.g., market size, sensitivity level of the market responding to price change, and the probability of a customer purchasing the company's product) toward the optimal discount rate is also investigated. Secondly, we investigate the model of the early sales where the company is with procurement budgetary constraint. It is theoretically proved that the optimal discount rate in the model is larger than that without the constraint. Computational study demonstrates that early sales can significantly relieve the budgetary shortage, and substantially increase the expected profit.

This paper studies the joint stock and production capacity rationing polices for a make-to-stock system with two partially substitutable products manufactured at two factories, respectively. Customers are classified into three types with each type further segmented into multiple classes. Type I and Type II customers are selective and accept their favorite products only. Type III accepts either of the two products and hence its demand is regarded as the flexible demand. The management has to decide whether to run or stop production and whether the various classes of demand for each type of customers have to be satisfied from available inventory or not — in which case demand is lost — in order to minimize the firm’s inventory and production costs. We formulate the problem as a make-to-stock queue system and characterize the optimal joint stock and production rationing policies as monotone switching curves. Numerical examples are given to illustrate the optimal policies and demonstrate the value of flexible demand. Moreover, we develop a simple heuristic policy and compare the costs associated with the optimal and heuristic policies for different parameters.

This paper focuses on the impact of ‘cap-and-trade’ mechanism and customer’s environmental awareness on emission-dependent manufacturer. Carbon emission cap from the perspective of government will be confirmed. In the ‘cap-and-trade’ system, emission permit becomes one of the key factors of production for emission-dependent firms. If the cap is insufficient to satisfy the target production, extra permit should be purchased via trading, otherwise, the remaining permit will be sold to other firms. Since the product demand has been influenced due to the consideration of customer environmental awareness, the production will be decided by analyzing the produced decision-making process of the emission-dependent firm in this case. Base on the consideration of improving environment benefits, carbon emission cap of this kind of manufacturer will be determined. Additionally, numerical analysis is considered. We found that it is profitable for the manufacturer investing; meanwhile, the emission intensity of this manufacturer is ameliorative. And emission reduction investment should be encouraged by the environmental administration in some way of preferential policy.