Business Finance Homework Help

Section 1 – Production Planning

An Italian confectionery SME produces four types of sugared almonds (classic, double milk, chocolate, lemon delight) using five ingredients (sugar, almond, milk, chocolate, lemon) that are purchased externally. The table below shows, for each kilo of sugared almonds, the quantities (in litres for milk and in kilograms for other ingredients) of ingredients needed to produce that type of product. In addition, both the maximum quantity of each ingredient that can be purchased monthly and the price of purchase are also indicated.

	Sugar	Almonds	Milk	Chocolate	Lemons
Classic	0.4	0.7	0	0	0
Double milk	0.2	0.5	0.5	0	0
Chocolate	0.1	0.1	0.3	0.4	0
Lemon delight	0.3	0.2	0	0	0.7
Maximum quantity (kg)	700	1200	500	200	350
Purchasing price (€/unit)	0.70	7	1.50	4.50	2.10

Based on the sales from the previous year, minimum quantities (in kg) of different types of sugared almonds to be produced monthly are reported below.

	Minimum monthly production quantity (kg)
Classic	40
Double milk	25
Chocolate	50
Lemon delight	15

In order to obtain a finished product ready to be sold, the manufacturing process requires different hours of labour input depending on the type of product. The following table reports the equivalent number of labour hours per kilogram of product, across the whole production range. Also, selling prices are reported.

	Classic	Double Milk	Chocolate	Lemon Delight
Labour hours	0.4	0.7	1.1	1.3
Selling price	14	19	27	36

The processing of the sugared almonds is carried out by 5 workers who work for 8 hours a day, 22 days a month, receiving a monthly pay of 1350 euros.

Build a PL model that allows you to plan the company’s monthly production, determining, for each type of sugared almond, the kilos to be produced to maximize profit.

The director of the confectionery company asked for our help to define the production plan that maximizes the monthly profit but also to have answers to the following questions:

• Which resources are scarce and which ones are abundant?
• How much does the company’s profit increase if the almond availability is increased by 20kg? What if the chocolate availability is increased by 20kg?
• Which resource guarantees a higher rate of profit growth?
• How much would the profit increase if the company hired another worker?
• The company wants to evaluate the possibility of producing an almost sugared almond completely made of almond. Knowing that the production of 1Kg of this product requires 0.3 kg of sugar and 0.9 kg of almond and that it takes 1 hour of workmanship, what is the selling price that makes this production cost-effective?
• What are the ranges of variability of the selling prices of the products which will not alter the optimal solution?
• What are the ranges of variability of the raw materials availability which will not alter the optimal solution?

Section 2 – Demand Forecasting

The Planning Department of a large distribution centre operating in Barnsley is interested in determining the number of pallets, which will be handled throughout the centre in the 2022 year, for staffing and dimensioning purposes. A historical series of the goods handled in latest years is available.

Based on the data shown below, develop a reliable forecast for the 2022 year, employing a method of your choice, justifying such choice and reflecting on its performance.

Also, develop some qualitative considerations about the reliability of this forecast, explaining which additional factors should be taken into account.

	2013	2014	2015	2016	2017	2018	2019	2021	2021
January	31,292	33,193	33,214	28,051	30,061	32,595	35,797	35,150	38,150
February	31,769	32,828	32,132	28,198	29,957	36,337	33,877	36,223	46,223
March	38,452	39,334	40,340	36,911	37,973	41,229	42,394	46,964	49,964
April	42,973	49,597	50,675	46,890	50,880	56,293	55,316	67,557	69,544
May	53,710	54,990	56,564	54,107	58,726	63,858	66,954	83,020	87,221
June	53,917	54,766	58,489	55,327	59,435	60,121	68,472	89,261	94,352
July	59,805	60,819	61,941	57,816	63,667	65,322	77,932	100,910	108,816
August	63,664	63,887	64,011	60,670	70,599	78,045	80,496	112,022	125,012
September	58,385	59,551	60,693	56,052	62,291	62,172	73,867	94,611	98,241
October	53,451	54,676	55,177	57,859	56,324	56,737	65,668	84,101	89,232
November	37,462	38,188	34,399	35,385	37,185	33,586	39,724	58,494	66,321
December	37,234	37,044	33,201	34,156	39,937	35,893	42,391	59,214	62,334

Section 3 – Sheffield City Region Location Analysis

Exhibis A reports the current Covid-19 testing centres in operation within the Sheffield City Council territory, along with their distance from the electoral wards of the city.

Based on the data provided below, on the population data for the electoral wards, and on the distances between wards and testing centres, provide an assessment about the current network of testing centres, by evaluating the following dimensions:

• covered wards and percentage of covered population, by assuming an appropriate covering radius;
• average travel distances from testing centres to wards;
• opportunities for locating new testing centres in Sheffield, and the impact this could have on the performance of the network according to the measures you have adopted;
• further recommendations for future plans (closing/downsizing some existing centres; expanding some existing centres).

Sheffield Electoral Wards	Population	Testing centres and distances from wards (in km)
		Burngreave	Darnall	Halfway	Jordanthorpe	Meadowhall	Sharrow	Stocksbridge	Upperthorpe
Beauchief & Greenhill	19698	7.5	8.17	9.58	1.96	10.2	4.53	18.52	6.78
Beighton	18013	8.69	6.02	1.89	7.23	8.42	8.44	22.21	10.13
Birley	17029	6.36	4.62	4.47	4.16	7.26	5.3	19.85	7.28
Broomhill & Sharrow Vale	23942	3.26	5.65	11.31	6.04	6.41	1.54	13.64	1.71
Burngreave	30495	1.04	3.75	11.28	8.6	3.01	3.29	12.61	2.22
Crookes & Crosspool	18146	4.49	7.39	13.33	7.6	7.56	3.49	12.14	2.52
Darnall	23149	3.13	1.28	8.86	8.72	1.45	5.39	15.52	5.08
Dore & Totley	18664	10	11.92	14.59	6.84	13.16	7.26	17.14	8.36
East Ecclesfield	17884	6.52	8.09	15.75	14.07	5.57	9.32	9.47	7.14
Ecclesall	20286	6.03	7.82	11.59	4.63	9.08	3.17	15.54	4.61
Firth Park	22266	2.95	4.94	12.78	10.48	3.03	5.76	11.38	3.73
Fulwood	20071	9.08	11.83	16.62	9.51	12.02	7.32	13.08	7.08
Gleadless Valley	21054	4.69	4.87	7.82	2.9	7.01	2.36	17.41	4.78
Graves Park	16742	5.93	6.37	8.41	1.85	8.41	3.12	17.81	5.57
Hillsborough	20058	3.57	6.67	13.97	9.67	5.71	4.84	10.22	2.4
Manor Castle	23544	2.59	2.06	7.92	5.69	4.13	2.77	16.08	3.86
Mosborough	16915	9.75	7.32	0.98	6.71	6.17	8.97	23.33	10.9
Nether Edge & Sharrow	23295	3.97	5.6	10.13	4.52	6.96	1.02	15.25	3.04
Park & Abourthorne	19803	3.7	3.55	7.63	4.08	5.74	2.23	10.38	4.28
Richmond	19120	5	2.81	5.44	5.46	5.45	4.79	18.61	6.3
Sheffield City	31190	1.68	3.88	10.15	6.2	4.78	1.37	13.99	1.5
Shiregreen & Brightside	21628	3.81	4.52	12.23	11.25	1.97	6.82	12.6	5.23
Southey	19924	4.2	6.79	14.45	11.36	5.16	6.41	9.43	3.98
Stannington	18534	10.45	13.51	19.97	13.92	12.88	10.16	8.02	8.68
Stocksbridge & Upper Don	18659	15.29	18.31	25.5	20.14	16.83	15.94	4.48	13.78
Walkley	29620	2.69	5.71	12.41	7.85	5.65	3.03	11.95	0.78
West Ecclesfield	17224	7.56	9.62	17.48	14.86	7.4	9.98	7.22	7.53
Woodhouse	17900	6.53	3.66	4.44	7.29	5.94	6.85	19.85	8.16

Section 4 –Routing Analysis

A Logistical Coordinator at IKEA Sheffield, has to arrange the delivery plan for 7 customer orders in Sheffield area. Each customer has to be delivered some flatpack furniture; deliveries will happen by using vans, whose capacity is 12 parcels, available from 6am at the Depot. The average speed of the van is 40 km/h; its operational cost 0.5 £/km. Employing methods you have studied during the module, work out the optimal routing planning.

Station	Address	Type
1	26 East Glade Road Sheffield England United Kingdom	Customer Location
2	28 Boyce Street Sheffield England United Kingdom	Customer Location
3	138 Industry Street Sheffield England United Kingdom	Customer Location
4	76 Leigh Street Sheffield England United Kingdom	Customer Location
5	Manor Way Sheffield England United Kingdom	Customer Location
6	710 Ecclesall Road Sheffield England United Kingdom	Customer Location
7	18 Revill Lane Sheffield England United Kingdom	Customer Location
Depot	IKEA Sheffield	Depot

Order ID	From Station	To Station	Load Amount	Loading Duration (DD:HH:MM)	Unloading Duration (DD:HH:MM)	Pickup Min Time	Pickup Max Time	Delivery Min Time	Delivery Max Time
ORD-1	Depot Station	1	1	00:00:01	00:00:01	26/11/2019 08:00	26/11/2021 08:30	26/11/2021 09:00	26/11/2021 15:00
ORD-2	Depot Station	2	4	00:00:01	00:00:01	26/11/2021 08:00	26/11/2021 08:30	26/11/2021 09:00	26/11/2021 15:00
ORD-3	Depot Station	3	5	00:00:01	00:00:01	26/11/2021 08:00	26/11/2021 08:30	26/11/2021 09:00	26/11/2021 15:00
ORD-4	Depot Station	4	3	00:00:01	00:00:01	26/11/2021 08:00	26/11/2021 08:30	26/11/2021 09:00	26/11/2021 15:00
ORD-5	Depot Station	5	3	00:00:01	00:00:01	26/11/2021 08:00	26/11/2021 08:30	26/11/2021 09:00	26/12/2021 15:00
ORD-6	Depot Station	6	4	00:00:01	00:00:01	26/11/2021 08:00	26/11/2021 08:30	26/11/2021 09:00	26/11/2021 15:00
ORD-7	Depot Station	7	1	00:00:01	00:00:01	26/11/2021 08:00	26/11/2021 08:30	26/11/2021 09:00	26/11/2021 15:00

Section 5 – Warehousing Planning

A nationwide distributor of consumer electronics is going to build a new warehouse near Barnsley in order to supply customers in the UK. On the basis of a preliminary analysis of the problem, it has been decided that the facility will accommodate 780 90×90 cm² pallets. Ten different kind of products need to be stored in the warehouse in a covered parking yard. Based on the monthly demand of the products (reported in the table below in terms of pallets), the company has to choose between a dynamic and a static product allocation strategy. Based on the data provided, could you calculate the number of storage locations required in each case? What are the advantages and the disadvantages of the different policies and which one would you adopt?

	Months
Product	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
1	66	65	49	99	28	4	16	36	15	16	95	37
2	13	37	6	8	41	17	20	53	34	26	25	11
3	99	20	46	49	58	84	18	95	11	25	94	61
4	12	91	26	1	93	16	32	85	48	23	8	48
5	55	67	33	48	58	45	72	41	25	50	28	63
6	92	93	30	61	76	45	93	89	19	18	51	55
7	95	23	23	37	74	18	16	96	26	29	97	60
8	54	47	23	80	55	64	70	42	55	74	52	42
9	86	57	92	40	29	73	67	25	18	16	90	78
10	37	17	30	95	39	18	62	28	73	61	78	2

The goods will be stored onto racks and transported by means of traditional trolleys. Due to physical constraints, each rack has four shelves, each of which can store a single pallet. Each pallet occupies a 1.05 × 1.05 m² area. Racks are arranged as in the figure below, where side aisles are 3.5 m wide, while the central aisle is 4 m wide. The average speed of a trolley is 5 km/h.

Taking into account the minimum number of required storage locations you have determined above, could you determine the length of each warehouse dimension and the distribution of storage locations which would minimise the operational cost of the warehouse?

Section 6 – Scheduling

Trucks departing from a distribution centre based in Doncaster are loaded with pallets of goods.On the 20^th of January, the logistics planner needs to load goods onto ten trucks.

Three docks are available for the process; ten trucks need to be loaded. Each truck can be processed at both the truck docks. The objective of the planner is to minimise the sum of the flow times, in such a way to provide a better service level to truck drivers.

After having identified and classified the problem according to the studied taxonomy, and defined an appropriate algorithm for solving it, could you determine the optimal loading sequence, explaining the adopted approach and comparing its performance (according to selected objective functions) to the one provided by other ones?

Represent the solution in a Gantt diagram (for instance by employing the LEKIN software). Furthermore:

• How would the solution change if just two docks were available, due to absenteeism problems related to the current Covid-19 pandemic?
• How the solution would change if, thanks to some agreements with the third party logistics providers, trucks A, B, C, D, E were available at the beginning of the time horizon (considering the original three docks)? What if all the trucks were available at the beginning of the time horizon?
• How would the solution change if the company was interested to minimise the makespan (considering the original three docks and release times)?

Truck	A	B	C	D	E	F	G	H	I	J
Required Load Processing Time	80	100	65	65	105	120	80	55	80	95
Release Time	10	60	100	120	160	220	220	320	40	270