Furniture City faced problem with its orders for kitchen sets due to stock outs. Mr. Daniel Holbrook, who is an expediter at the local warehouse, and Mrs. Brenda Sims, the saleswoman on the kitchen showroom floor identified that over 80% of customers are not satisfied. They realized that the firm required a new inventory policy in order to keep customers goodwill, increase the number of customer orders and avoid any delivery delays caused by stock outs.
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In this report we prepare an analysis of the stocking sets case for Furniture City. In order to achieve this, we find out an appropriate model that helps to achieve our target. Our aim is to find the optimal solution, which is the best combination of features and styles, requires for kitchen sets. To maximize the total number of kitchen sets and thus the number of customer orders, we use Excel Solver and we create a binary integer programming model using the information brought from Mr. Brenda.
Executive summary of recommendations
In this managerial report we prepare an analysis of the Furniture City Stocking Sets Case. Furniture City recently faced a problem due to the limited amount of warehouse space allocated to the kitchen department. As management consultants, our aim was to find the combination of features and styles that maximize the total number of kitchen sets.
In order to solve this problem we formulating it as a binary integer programming problem and we use the Excel Solver. The local warehouse could hold only a limited number of items, therefore we take into account these constraints and based on the assumptions we conclude that the maximum number of kitchen set is 4.
Specifically the style of features that each of these kitchen sets contained are:
Set 4: T3, W3, L3, C3, O3, S1, R1, D1
Set 11: T3, W1, L3, C3, O1, S1, R3, D1
Set 15: T3, W3, L1, C1, O1, S3, R3
Set 20: T2, W3, L1, C1, O2, S3, R4
Furthermore, we carry out further analysis in case of different situations. For example, if one of the departments discontinues then the warehouse space would reallocate. Consequently the total number of kitchen sets will increase by one more set. (see appendix 3). Additionally, in case some of the constraints change -more space provided- then the local warehouse could hold 6 kitchen sets. (see appendix 3)
At last we suggest some extensions and recommendations to Furniture City.
Statement of the problem situation
As we mentioned before, in the current problem, we have to find the optimal number of kitchen sets Furniture City stocks in the local warehouse. The information we use is from company’s records over the past three years and determined 20 kitchen sets. These 20 kitchen sets were consisting eight features in a variety of styles.
We have to bear in mind that there are some restrictions in the number of the sets as the warehouse can stored only a limited number of features.
Every kitchen set includes 20 square feet of tile and 5 rolls of wallpaper. The warehouse could hold only 50 square feet of tile and 12 rolls of wallpaper in the inventory bins. The inventory shelves could hold two light fixtures, two cabinets, three countertops and two sinks. Dishwashers and ranges are similar in size and the warehouse floor could hold a total of four dishwashers and ranges. All the features of each kitchen set are replenished immediately when a customer place an order.
We identify decision variables, objective function, and the set of constraints and by using Excel solver we have been able to analyze the situation problem and conclude to the optimal solution for Furniture City.
Assumptions
General assumption for LP models: Each problem can be realistically represented as a linear program if specific assumptions are valid. These assumptions are divided into four subcategories which are certainty assumption, proportionality assumption, additivity assumption and divisibility assumption. These assumptions are the parameter values are known, the objective function and constraints exhibit constant returns to scale, there are no interactions between the decision variables and decision variables are allowed to have any values that satisfy the constraints.
Specific Assumptions:
In order to find the optimal solution for Furniture City it is very important to take into account some assumption that they may cause limits to the planned model. Specific assumptions are statements that we assumed to be true and from which a conclusion can be drawn.
Every kitchen set contains specific features with different styles
7 Kitchen sets contains only 7 features ( sets 14 to 20 not include dishwasher)
Kitchen sets are incomplete if at least one its features is out of stock
The warehouse space is limited so is not possible to have in stock all the different styles of features for the 20 kitchen sets
The new inventory policy focuses on the most popular items and replenishes them immediately when sold. Therefore the majority of customers would receive their items without delays.
Delivery delays have negative impact to the customer satisfaction and company’s reputation.
If any feature is damaged then it could not included in the kitchen set and must replenished
When a customer orders a kitchen set, all the particular items composing that kitchen set are replenished at the local warehouse immediately.
If any of the warehouse departments discontinued, then the space has to reallocate. As a result the new space allows us to stock more features.
Major steps of analysis
Developing the suitable model: We decide to develop a binary integer programming model in order to conclude to the optimal solution for the company’s situation, taking into account the restrictions which limiting our choices and all the assumptions stated above. We also identify decision variables, objective function, a set of constraints, non-negative and binary variables.
Formulating the problem: In the first step, we identify the decision variables, objective function and the constraints. In case of our situation, the decision variables are the features and styles that each kitchen consists. The objective function is to maximize the total number of kitchen sets, and thus the number of customers’ orders, that the company stocks in the local warehouse. Additionally since the amount of warehouse space allocated to the kitchen department is limited we have some constraints regarding the number of features and styles. We also set us binary variables the number of kitchen sets. For example if all the features of a specific kitchen set are available in the warehouse then the answer is 1, otherwise is 0 (see appendix 1 for the mathematical formulation) .
Sensitivity analysis: Carrying out a sensitivity analysis was necessary in this type of problems so as to understand whether a better decision was to be taken when some conditions of the problem situation changed. It is very important and useful technique because it gives us the opportunity to observe how the new values affect the whole inventory policy. In case of our problem, we assume changes regarding the warehouse space.
Major of findings
By using Excel Solver we conclude to the optimal solution, which in this case is the number of kitchen sets Furniture City stocks in the local warehouse.
Table 1
In the above table (table 1) we summarize the results. The total number of kitchen sets that the company we would stock in the local warehouse is 4. Specifically the four kitchen sets are Kitchen set 4, 11, 15 and 20.
Sensitivity analysis: We additionally carry out further analysis in case of different situations. Firstly, in case Furniture City decide to terminate carrying one of its department and divide the remaining space to the rest departments. Therefore, the number of inventory that the warehouse could hold increased. By following the same steps we investigate how the optimal number of sets in the kitchen department affected. The total number of kitchen sets would be 5 and specifically the complete sets are 4, 8, 11, 15, 20 (see appendix 3).
Secondly, Mrs. Brenda Sims suggest to the management department to provide all the extra space left from the terminated department, as a testing ground for future inventory policies. In case management accepts this suggestion, the kitchen department would have the opportunity to store even more features than in the first situation. The inventory policy would also change in this situation and the total number of sets would be 6 and the complete sets are 4, 7, 10, 11, 15, 16 (see appendix 3).
Conclusion – Extensions and improvements
The purpose of this managerial report was to determine the number of kitchen sets we can obtain taking into account the limit space in the company’s warehouse. It was necessary to formulate and solve the given problem by using Excel Solver and binary integer programming. We conclude in the optimal solution considering all the aspects in our situation and the constraints.
Moreover, after the analysis of this problem we are able to make suggestions for further improvements.
Immediate replenishment: The immediate replenishment is necessary and very important for Furniture City. If the items composing a kitchen set could not be replenished immediately the inventory policy would be affected. For example when a customer asks for a specific item, the rest features composing the kitchen set would stay unused in the warehouse. If this item not replenished then the kitchen set and generally the kitchen sets are having this item could not be sold, as would be incomplete. Due to that, the incomplete sets would hold the space inefficient. Furthermore, the customers who willing to buy these kitchens they have to wait until the item replenish (delivery delays) and might be change their minds and cancel their order.
We recommend that Furniture City should reduce its kitchen sets and offer to its customers only the most popular. In our solution we conclude that the company, with the existing warehouse space, could hold only four out of twenty sets. Since the warehouse could not stock all the sets, is better to reduce them. These will satisfy more customers and the company would avoid complaints for the stock outs and delivery delays.
Regarding the delivery delays, the company could find some alternative solutions so as to offer express delivery to its local warehouses. For example, it could hire more employees or have more delivery vans available for immediate replenishment. In addition, another efficient recommendation would be to increase the space of the warehouse. We definitely believe that if Furniture City can rent a new place near the warehouse or extend its existing building it will has the opportunity to stock more items and more complete kitchen sets. Obviously, these two recommendations will add extra costs to the company but it will offer better customer services.
We conclude on the combination that maximizes the number of the kitchen sets can be stock in the warehouse. Finally, we are able to explain any misunderstanding point in this report and we are also be available to provide advices for any further problems may the company face in the future.
Appendix 1
Mathematical formulation
Maximize
Z= X1+X2+X3+X4+X5+X6+X7+X8+X9+X10+X11+X12+X13+X14+X15+X16+X17+X18+X19+X20
Constraints
Kitchen sets are binary (0,1)
Let X be the number of kitchen sets
X1=1 if you choose kitchen set 1, 0 otherwise
X2=1 if you choose kitchen set 2, 0 otherwise
Similarly for the other kitchen sets possible
Features and styles are binary (0,1)
Let T1,2,3,4 be the no. of different styles of Floor Tile
W1,2,3,4 be the no. of different styles of Wallpaper
L1,2,3,4 be the no. of different styles of Light Fitting
C1,2,3,4 be the no. of different styles of Cabinets
O1,2,3,4 be the no. of different styles of Countertop
D1,2, be the no. of different styles of Dishwasher
S1,2,3,4 be the no. of different styles of Sink
R1,2,3,4 be the no. of different styles of Ranges
T1,2,3,4 =1 if you choose this style of Floor Tile, 0 otherwise
W1,2,3,4 =1 if you choose this style of wallpaper, 0 otherwise
Similarly for the other Features and styles
Kitchen sets
For example we get kitchen Set 1 if we have features T2, W2, L4, C2, O4, D2, S2, and R2
Set 2 if we have T2, W1, L1, C4, O4, D2, S4 and R2 etc.
Therefore
Set 1 > = 1 IF (T2+W2+L4+C2+O4+D2+S2+R2)/8 >=1
Set 1 <= (T2+W2+L4+ C2+O4+D2+S2+R2)/8
Set 2 >= 1 IF (T2+W1+L1+C4+O4+D2+S4+R2)/8 >=1
Set 2 <= (T2+W1+L1+C4+O4+D2+S4+R2)/8
Set 3 >= 1 IF (T1+W3+L2+C1+O1+D1+S3+R3)/8 >=1
Set 3 <= (T1+W3+L2+C1+O1+D1+S3+R3)/8
Set 4 >= 1 IF (T3+W3+L3+C3+O3+D1+S1+R1)/8 >=1
Set 4 <= (T3+W3+L3+C3+O3+D1+S1+R1)/8
Similarly for the other sets 5-13. Due to, sets 14-20 do not contain one of the features- dishwashers – the constraint is divided by 7 instead of 8.
For example for Set 14:
Set 14>=1 IF (T4+W4+L4+C1+O3+S1+R1)/7 >= 1
Set 14<= (T4+W4+L4+C1+O3+S1+R1)/7
Warehouse space limitations
The inventory shelves could hold limited number of Features:
L1+L2+L3+L4<= 2 (Light Features)
C1+C2+C3+C4<= 2 (Cabinets)
O1+O2+O3+O4<= 3 (Countertops)
S1+S2+S3+S4<= 2 (Sinks)
Every kitchen set includes exactly 20 square feet of tile (T) and 5 rolls of wallpaper (W), The warehouse could hold:
T1+T2+T3+T4<= 2 (50 square feet so 50/20= 2,5)
W1+W2+W3+W4<=2 (12 rolls so 12/5= 2,4)
Appendix 2
In Kitchen set 1 to 13 we multiply sumproduct by 8 and sets from 14 to 20 we multiply them by 7 because the features are 7.
Appendix 3
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