Production with Multiple Retailers and Non-Linear Production Costs

Gilad Schwartz - M.Sc.student

Abstract:

Operations Management models typically assume that the production costs are proportional to the amount produced. One consequence of that assumption is that a (wholesale) price only contract is impractical since the only coordinated solution will leave the supplier with zero profit. But in the Production Economics literature, production costs are typically non-linear, and, indeed, the marginal costs are usually assumed to be increasing in the relevant range. When a supplier with non-linear costs sells to multiple retailers, the model is no longer separable by retailer, as non-linear costs create cost, and thus operational, dependencies. We thus wish to incorporate non-linear production costs into supply chains with multiple retailers which differ in their demand distributions and retail prices, whether exogenous or endogenous. There is no pooling of inventory - units are pushed to retailers in advance.

As a baseline, we start by analyzing a two-retailer centralized system. A generalization to more retailers will be straightforward in principle. For general production costs function and demand distribution, we derive the optimality conditions and perform comparative statics with respect to prices. We then provide additional insights by specializing the production costs to a power function (e.g., quadratic). We then consider a one-retailer price-setting firm for both additive and multiplicative demand uncertainty, and extend it to two retailers. To conclude our analysis we allow the firm to delay pricing, resulting in either holdback or market clearing.

העבודה נעשתה בהנחיית פרופ' יגאל גרציאק.

ההרצאה תתקיים ביום ה', 19.07.12, בשעה 14:00 בחדר 206, בנין וולפסון הנדסה, הפקולטה להנדסה, אוניברסיטת תל-אביב.