Trade-offs between multiple objectives via the ε-constraint method

In the research problem, due to different possibilities for inventory decisions, trade-offs occur among total cost, spoiled wastage and amount of CO2 emission from production and inventory operations. This means that decreasing expected spoiled wastage from warehousing or decreasing emission from production and inventory operations comes at a cost.

The objective of the firm is to choose an ordering policy that minimises its cost subject to the constraints on the amount of carbon emitted (this cap can reflect either government regulations imposed on the firm or a voluntary effort by the firm to reduce its emission by a specified amount) and the amount of food products spoiled. An evaluation of economic and environmental factors in the trade-off analysis assists managers in setting up sustainability targets. Managerial insights on improving sustainability of the analysed food supply chain can be obtained through determination of the cost of being sustainable

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from the point of reducing wastage or production and warehousing emission in the trade-off analysis (see Figure 7.2-7.5).

In problem 1, model results suggest that emissions can be reduced by having frequent replenishments. This is reasonable since the total emission from production and inventory operations will be lower for a smaller quantity of items produced and carried. However, this increase in the number of replenishments results in higher ordering costs.

In addition to the aforementioned LC and LE base cases, three additional instances are generated by lowering the value (limit on CO2 emission) by a certain percentage from the highest emission level at each instance. As this numerical example is a small scale problem, the value (limit on wastage) can be lowered only once which gives the same result as one of the lower emission limit cases. The derived Pareto frontier in Figure 7.2 represents the trade-off relationships between cost and emission for the problem in question. This is done to observe the dependency between the two objectives.

Figure 7.2 Trade-offs between total cost and CO2 emission in Problem 1 Given a certain percentage of the cost increase from the LC base case, the expected level of emission is reduced. For instance, one of the presented solutions can be selected for the analysed food SC. Suppose that the point around the emission level of 87% on the Pareto frontier in Figure 7.2 would be selected. This would ensure in approximate numbers an emission reduction of 13% in return of a cost increase of 9%. This indicates that the cost of being sustainable for this problem can be determined from the point of reducing warehousing emission.

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For problem 2, the 20 additional instances were generated by lowering the limit on the CO2 emission value by a certain percentage from the highest emission level at each instance for both centralised and decentralised decision making processes. Due to the non-stationary process of stochastic customer demand, there are more choices for the ordering policy. The derived Pareto frontiers in Figure 7.3A-7.3B represent the trade-off relationships between cost and emission under centralised (shared emission caps) and decentralised (individual emission caps) decision making processes of problem 2, respectively.

Figure 7.3 Trade-offs using -method for Problem 2 under (A) centralised and (B) decentralised controls

It can be observed that the behaviour of trade-offs under the decentralised decision making process in Figure 7.3B is cost overlapping. The model suggests a few alternatives that give approximately the same cost increase but differ in emission reduction. As shown in the figure, as the optimum total cost increases by about 6% from the LC base case, the carbon emission resulting from the SC is reduced by about 5%, 10% or 12% depending on the suggested solutions, for instance. This is owing to the choice of where in the SC and to what extent the limit is placed on emissions as well as a small scale of the problem itself.

Comparing the trade-offs between Figure 7.3A and 7.3B, the results clearly suggest the benefit of using centralised control over decentralised control. Figure 7.3A confirms that adopting a centralised decision making process will offer more economical assistance in improving the perishable food SC

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sustainability with up to a 12% carbon reduction in comparison with a decentralised one. A shared carbon cap provides the SC with the flexibility of having some firms emit more if they can be offset with less emission from other firms. This allows a firm that is more cost effective at reducing its carbon emission to take on a greater responsibility in meeting the carbon cap. The message is that the producer and its suppliers should look for ways to collaborate with each other in a manner as close to centralised control as possible.

For the replenishment plan of suppliers in example problem 3, the 14 additional instances are generated by lowering the limit on the waste value by a certain percentage from the highest expected waste level at each instance. It can be seen from Table 7-13 that the difference of emission generated when adopting LC and LE base cases is not significant so no further trade-off can be done. The derived Pareto frontier in Figure 7.4 represents the trade-off relationships between cost and waste. It can be observed from the impact of varying the waste limit/cap in Figure 7.4 that adjustments in order quantity in each period, could lead to reduction in perished raw material while not significantly compromising cost. As shown in the figure, as the total cost increases by about 1.2% from the LC base case, the perished items at the suppliers is reduced by about 19% due to an increase in replenishment from 4 to 5 orders of raw material , for instance.

Figure 7.4 Trade-offs between cost and waste using -method for Problem 3 for suppliers

For the production/replenishment plans of the SC after demand realisation in example problem 3, the derived Pareto frontier in Figure 7.5 represents the

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trade-off relationships between cost and emission. Given a certain percentage of the profit decrease, the expected level of emission is reduced. This indicates that the cost of being sustainable for this problem can be determined from an increase in rejected retailer orders such that emissions from SC activities are reduced. As shown in the figure, a sharp decrease of emission level from 99.5% to 97.5% with a profit reduction of 3.15% is resulted from a rejection of orders as twice as much comparing with an instance with 3.02% decrease in profit (i.e. an increase from 72 to 150 demands got rejected).

Figure 7.5 Trade-offs between profit and emission using -method for Problem 3 for the SC after accepted demand

With the resulting Pareto solutions from example problems discussed above, the final decision is made among them taking the total balance over all SC performances into account. This is a problem of value judgment of decision maker.