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This paper investigates a supply contract design by a dominant manufacturer who faces a stochastic demand during a selling season. The manufacturer has several estimations of the supplier's cost with corresponding probabilities, that is, asymmetric cost information. The manufacturer designs a menu of call option contracts that include three variables: a supply order, an option, and an exercise price. We determine the optimal negative correlation between option and exercise prices as well as closed-form formulas for the optimal supply orders. The results show that in the optimal menu of contracts either the option or the exercise price may be omitted from the menu, whereas the supply orders should always be customized for each supplier type. We show that in this problem, optimal profit assignment between contract partners under put and bidirectional option contracts is the same as call option contract studied. Numerical analysis including managerial insights is presented.

a b s t r a c tDifferent models have been proposed in the field of preventive maintenance planning for finding optimal age replacement policies. While previous studies have focused mainly on classical cost objectives, this paper presents a novel multi-objective model for preventive replacement of a part over a planning horizon. The proposed model considers different objectives and practical issues, such as corrective replacement and its consequences, residual lifetime objective, and kind of productivity index. Also, the model determines number of spare parts, required for replacement with the defected part, to be provided at the beginning of the planning horizon. The multi-objective model is applicable for machines or equipments which are repaired through replacing their defected part with new spare part.For solving the multi-objective model, regarding to ability of e-constraint method to generate different pareto-optimal solutions, a procedure is developed based on this method.The procedure shows how the e-constraint method can be used for finding preferred solution in situations where there is no access to decision maker. The model and solution procedure are illustrated by a numerical example.

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In competitive conditions, demand depends on the price and retailers with lower prices sell more. In this paper a dynamic model is developed in which demand is price-dependent and the price is determined by the retailer based on its inventory level. The retailer can offer discounts to customers, regarding its inventory level, based on different scenarios such as linear, total or increasing scenarios. Simulations show that each scenario has different effects on the long-term chaotic behavior of the inventory level, and is able to control aperiodic behavior of inventory level under specific initial conditions. It is established that in order to secure inventory stability, the discount scenario should consider the incoming shipments to the retailer and the potentially maximum demand, instead of the inventory level.

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