TY - JOUR
T1 - Optimal ordering policies in inventory systems with random demand and random deal offerings
AU - Gurnani, Haresh
N1 - Funding Information:
¢~ This research is partially supported by a DAG Grant from The Hong Kong University of Science and Technology.
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 1996/12/6
Y1 - 1996/12/6
N2 - In this paper, we determine the optimal order policies for a firm facing random demand and random deal offerings. In a periodic review setting, a firm may first place an order at the regular price. Later in the period, if a price promotion is offered by the supplier (with a certain probability), the firm may decide to place another order. We consider two models in the paper. In the first model, the firm does not share the cost savings (due to the promotion offered by the supplier) with its own customers, i.e. its demand distribution remains fixed. In the second model, the cost savings are shared with the final customers. As a result, the demand distribution shifts to the right. For both the models, in a dynamic finite-horizon problem, the order policy structure is divided into three regions and is as follows. If the initial inventory level for the firm exceeds a certain threshold level, it is optimal not to order anything. If it is in the medium range, it is optimal to wait for the promotion and order only if it is offered. The order quantity when the promotion is offered has an 'order up to' policy structure. Finally, if the inventory level is below another threshold, it is optimal to place an order at the regular price, and to place a second order if the promotion is offered. The low initial inventory level makes it risky to just wait for the promotion to be offered. The sum of the order quantities in this case has an 'order up to' structure. Finally, we model the supplier's problem as a Stackelberg game and discuss the motivation for the supplier to offer a promotion for the case of uniform demand distribution for the firm. In the first model (when the firm does not share the cost savings with its customers), we show that it is rarely optimal for the supplier to offer a promotion. In the second model, the supplier may offer a promotion depending on the price elasticity of the product.
AB - In this paper, we determine the optimal order policies for a firm facing random demand and random deal offerings. In a periodic review setting, a firm may first place an order at the regular price. Later in the period, if a price promotion is offered by the supplier (with a certain probability), the firm may decide to place another order. We consider two models in the paper. In the first model, the firm does not share the cost savings (due to the promotion offered by the supplier) with its own customers, i.e. its demand distribution remains fixed. In the second model, the cost savings are shared with the final customers. As a result, the demand distribution shifts to the right. For both the models, in a dynamic finite-horizon problem, the order policy structure is divided into three regions and is as follows. If the initial inventory level for the firm exceeds a certain threshold level, it is optimal not to order anything. If it is in the medium range, it is optimal to wait for the promotion and order only if it is offered. The order quantity when the promotion is offered has an 'order up to' policy structure. Finally, if the inventory level is below another threshold, it is optimal to place an order at the regular price, and to place a second order if the promotion is offered. The low initial inventory level makes it risky to just wait for the promotion to be offered. The sum of the order quantities in this case has an 'order up to' structure. Finally, we model the supplier's problem as a Stackelberg game and discuss the motivation for the supplier to offer a promotion for the case of uniform demand distribution for the firm. In the first model (when the firm does not share the cost savings with its customers), we show that it is rarely optimal for the supplier to offer a promotion. In the second model, the supplier may offer a promotion depending on the price elasticity of the product.
KW - Dynamic programming
KW - Gaming
KW - Inventory
KW - Promotion
KW - Purchasing
UR - http://www.scopus.com/inward/record.url?scp=0030572954&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0030572954&partnerID=8YFLogxK
U2 - 10.1016/0377-2217(95)00272-3
DO - 10.1016/0377-2217(95)00272-3
M3 - Article
AN - SCOPUS:0030572954
VL - 95
SP - 299
EP - 312
JO - European Journal of Operational Research
JF - European Journal of Operational Research
SN - 0377-2217
IS - 2
ER -