# Optimizing Insurance Contract for a two-level two-period Supply Chain

Document Type : Research Paper

Authors

1 Industrial Engineering Department, Yazd University, Yazd, IRAN

2 Industrial Engineering Department, Yazd University, Yazd, Iran

Abstract

We can apply any method for organizing a supply chain, but contracting is more viable. Among many contracts that does so, the Insurance contract is more efficient. The problem is tuning the contract's parameters (for a two-level two-period supply chain with one supplier and one retailer) to achieve the optimum point where there is more gain for everyone separately, and the predictable risks all have been covered. The insurance contract covers every predictable risk that the downstream is facing. Instead, the retailer gives the supplier some money as a side payment (Premium). So, it has two main parameters, first, the fraction ($\beta$) of every predictable loss by the retailer, which the supplier must pay, and second, the side payment (M), which the retailer must pay. We will find the best $\beta$ for a one-supplier one-retailors supply chain with two main sale periods. But for reaching the optimum state of all the insurance contract's possible forms, we designed some mathematical models based on scenarios. Then we optimize these stochastic models to find the best contract possible for 1000 initial scenarios. Every scenario indicates one possible number for price and one for demand in each period (generating 4000 possible numbers for the independent demand and price). We needed to know the maximum possible profit for the whole supply chain. First, we designed a centralized supply chain where the maximum profit is possible, then a decentralized supply chain to know the minimum of what's possible. When we have the ends of our range, we can design the final model with an insurance contract applied. In this model, we insert the $\beta$ and M into the model as the insurance contract does. First, we reduce the number of scenarios to 20 with a novel method. Then we find the optimum point by solving the final model for each $\beta$. The result was better at $\beta$=0.25. In the next step, by supposing equal negotiating power for the sides, we split the extra money into two equivalent sizes, and the M amount was measured as half of the extra money that the contract can reach. The extra money was at 0.9893 of our range means the contract earns 99.97\% of what is possible.

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